Polynomials Word Problems
In mathematics, a polynomial is an expression constructed from one or more variables and constants, using the operations of addition, subtraction, multiplication, and constant positive whole number exponents. Polynomials are one of the most important concepts in algebra and throughout mathematics and science. They are used to form polynomial equations, which encode a wide range of problems, from elementary story problems to complicated problems in the sciences.

Linda has a garden. The width of her garden is 8 feet longer than the length of it. Around the garden she has a 4 foot wide sidewalk. The area of the sidewalk is 320 feet squared. What are the dimensions of the garden?
polynomial word problems

Four boys are playing with their marbles. Two boys have the same number of marbles and they both have 1 more marble than the 3rd boy. The 4th boy has 1 marble less than the 3rd boy. If all the number of marbles of each boy is multiplied, the product would be 18. How many marbles does each boy have?
polynomials word problems

Superman wants to build a sidewalk around a lot. Batman says that the current width of the lot is 5 meters and the length is 7 meters. Spiderman says that the final area must be 63 square meters. And Aquaman says that the width of the walkway is X meters wide. What is the width of the walkway?
polynomial word problem examples

In a retail store, a fake diamond ring cost $10 dollars. Joan buys two rings, and pays the cashier with a $2x bill. Write the expression that represents the change she would receive in polynomial form
polynomial word problem

A rectangular shipping container has a volume of 2500 cm3. The container is 4 times as wide as it is deep, and 5cm taller than it is wide. What are the dimensions of the contaner?
factoring polynomials word problems

Pure acid is to be added to a 5% acid solution to obtain 95L of 23% solution. What amounts of each should be used? How many liters of 100% pure acid should be used to make the solution? How many liters of 5% solution should be in the mixture?
adding polynomials word problems

The hypotenuse of a right triangle is 25m long. The length of one leg is 10 m less than twice the other. Find the length of each leg.
problems involving polynomials

What is the area of a square measuring (5a  2b) cm each side ?
Polynomial Word Problems with Solutions

Find the remainder when the polynomial x3+7x6=0 is divided by x1
word problems polynomials

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs^{2}(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long. a) If the deflection at the end of the board is 1 ft, find c b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6
word problems with polynomials

The length of a rectangle is 2 inches more than 3 times the width. Write a polynomial that represents the area of the rectangle.
multiplying polynomials word problems

Kattya has a square garden. When she increases her garden`s width by 3 meters and decreases its length by 4 meters, her garden becomes 60 m^{2}. What is the dimensions of her garden before the change?
adding subtracting polynomials word problems

The owner of a daycare center plans to have a rectangular sandbox built in the outdoor play area. The width (in feet) of the sandbox is given by the polynomial 2x5. If the length of the sandbox is designed to be 10 feet longer than the width, write a polynomial that represents the area of the sandbox. (1) Part A: Solve the above problem using any methods, concepts, and procedures learned in this module. All work must be shown and completed in an equation editor. (2) Part B: Write a 250 word summary of the above problem. Your written work should include but necessarily be limited to the following; an explanation of the problem, a review of the mathematical concepts involved, a critique of the method used to obtain the solution, and an interpretation of the answer. Your summary should be written in APA format, demonstrate proper use of the English language, and be mathematically precise.
word problems involving polynomials

word problem involving polynomials

A company produces a product for $9.45 per unit, plus a fixed cost of $5200. The company sells the product for $15.80 per unit. a) determine a function, c(x), to represent the cost production x units b) determine a function, r(x) to represent the revenue from selling x units c) determine a fucntion to represent profit d) caculate break even point
polynomial application problems

polynomials word problems examples

polynomial word problems with answer

word problems for polynomials

A diagram shows a rectangular region, one of whose corners lie on the graph of y = x^{2} + 2x + 4. Write a polynomial in standard form for the area A of the rectangular region.
word problems involving factoring polynomials

The polynomial s^{3}  70s^{2} + 1500s  10800 models the profit a company makes on selling an item at price s. A second item sold at the same price brings in a profit of s^{3}  30s^{2} + 450s  5000 Write a polynomial that expresses the total profit from the sale of both items.
word problems using polynomials

The length of a rectangle is 3 inches greater than the width. Write a polynomial that represents the area of the rectangle.
multiplying binomials word problems

If a vendor charges P dollars each for rugby shirts, then he expects to sell 2000100P shirts at a tournament. A) Find a polynomial R(P) that represents the total revenue when the shirts are P dollars. B) Find R(5), R(10), AND R(20).
operations with polynomials word problems

The width in feet of the sandbox is given by the polynomial 2x5. If the length of the sandbox is designed to be 10 feet longer than the width, write a polynomial that represents the area of the sandbox.
addition of polynomials word problems

A photo is 4 inches longer than it is wide. A 3inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions of the photo?
word problems with trinomials

Find the area of the rectangle when the width is 10 centimeters.
adding and subtracting polynomial word problems

A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.
word problems of polynomials

Find 3 consecutive even numbers where the product of the smaller two numbers is 64 less than the square of the largest number.
multiplying polynomial word problems

Word problems for factoring polynomials

word problem adding polynomials

adding and subtracting polynomials word problems

The world`s largest swimming pool is the Orthlieb Pool in Casablanca,Morocco. The length is 30 meters longer than 6 times the width. If the perimeter of the pool is 1,110 meters, what are the dimensions of the pool?
word problems on polynomials

The minute hand of a click is 3 cm longer than the hour hand. If the distance between the tips of the hands at 9 o`clock is 15 cm, how long is the minute hand.
polynomials word problem

The area of a rectangle is given by the following polynomial 44t2t^{2}. If the length of one side is 2t what is the polynomial that expresses the length of the other side?
word problems in polynomials

The edge of one cube is 3 shorter than the edge of a second cube. The volumes of the two cubes differ by 513cm^{3}. Find the edge of the smaller cube.
word problem polynomials

The square of the largest of three consecutive integers is 320 less than the sum of the squares of the two smaller integers. Find the three integers.
Polynomial application word problems

The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 times the square of the smaller one. Find the integers.
polynomial area problems

Consider the function f(x) = x^{3} + 4x^{2} + kx  4 The remainder from f(x) divided by (x+2) twice the remainder from f(x) divided by (x2). Determine the value of k.
factoring trinomials word problems

Together Steve and Heather`s ages add up to be ten. If we let "x" be Steve`s age, setup the polynomial describing Heather`s age.
factoring polynomials word problem

A cuts half a rectangular lawn, 50 m by 20 m by mowing strips of equal width around the perimeter. B cuts the small rectangle left. How wide a strip does A cut so that A and B share the work equally??
addition of polynomial word problems

Find a polynomial for the perimeter and area of a rectangle d +2 and d
word problems on operations of polynomials

Total Revenue At p dollars per ticket, a promoter expects to sell 40,000 1000p tickets to a concert. a) How many tickets will she sell at $10 each? b) At $10 per ticket, what is the total revenue? c) Find a polynomial R(p) that represents the total revenue when tickets are p dollars each. d) Find R(20), R(30), and R(35)
word problems involing polynomial functions with solutions

Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: C(g)=3.03(g) a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did. e) If you were to graph C(g), what would be an appropriate domain? Range? Explain your reasoning.
multiplying polynomials shaded region problems

2x^{3}3x^{2}2x divided by 2x3
how to make a word problem using polynomials

The length of a rectangle is 11 cm more than its width. The area of the rectangle is 2040 cm2. Find the dimensions of the rectangle.
word problems involving addition of polynomials

The volume of a right circular cylinder is 12 in. Express the height as a function of the radius, and the total surface area as another function of the radius?
word problems addition subtraction polynomials


A square has sides of length 3x+1 meters. Find a polynomial A(x) that represents the area of the square. Find A(1)


A circular pond will be placed on a square piece of land. The length of a side of the square is 2x. The radius of the pond is x. The part of the square not covered by the pond will be planted with flowers. What is the area of the region that will be planted with flowers? Write your answer in factored form.

Antonio is preparing to make an ice sculpture. He has a block of ice that he wants to reduce in size by shaving off the same amount from the length (3ft.), width (5ft.), and height (4ft.). He wants to reduce the volume of the ice block to 24 cubic feet. Write a polynomial equation to model this situation.

A ruler orders his chamberlain to collect an army from 30 houses, in such a way that he takes the same number of men from each house as he has already collected. The servant goes to the first house alone; to the second house he goes with one other and so on. How many men did he collect in all?

The length of a rectangle is 8 times its width. If the length was decreased by 10m and the width decreased by 2m, the area would be decreased by 162m^{2}. What are the original dimensions?

A quilt patch cut in the shape of a triangle has a base of 5x inches and a height of 1.732x inches. What polynomial represents its area?

The revenue for selling y units is R = 3y^{2} – 2y + 5 and the cost of producing y units is C = y^{2} + y – 3. Find the polynomial that represents the profit.

When a certain polynomial is divided by x + 2, the quotient is x^{2} 4x + 1 and the remainder is 8. What is the polynomial?

Find the dimensions of a rectangle whose perimeter is 46m and whose area is 104m^{2}.

The length of a rectangle is three inches greater than the width.

Greenshield`s Formula can be used to determine the amount of time a traffic light at an intersection should remain green. G = 2.1n + 3.7 G= green time in seconds n = average number of vehicles traveling in each lane per light cycle. Write a simplified expression to represent the average green light time per vehicle

The smaller of two numbers is 64 less than the square of the largest number.


Find a polynomial A(x) that represents the area of the square. Find A(1) if the square has sides of lenght 3x +1?


A rectangular box is (2x + 7) feet wide, (5x + 2) feet long, and (x  4) feet high. Find the volume of this box.

The length of a rectangle is 8 cm less than 3 times the width. How do you write a polynomial that represents the area of the rectangle?

Two rectangles have same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 5 more square feet than the smaller. What is the width of the rectangles?

(4a^{3}8a^{2}+a^{2})/(4a^{1})

The area of a rectangle is 156 ft. The length is 4ft greater than the width. Find the dimensions of the rectangle.

Suppose the market research company find that at a price of p=$20, they would sell d=42 dresses each month. If the price was lower like p= $10 more people would purchase, and they expect to sell d=52 dresses in a month`s time. Find the equation of the line for the demand equation. In the form of p = md + b.


Find the polynomial that repersents the volume of a cube if each side measures x+6

The square of the largest of the three consecutive integers is 320 less than the sum of the squares of the two smaller integers. Find the three integers

A stage is rectangular in shape. The width is 10ft less then the length. If the area of the stage is 600ft, find the length and width of the stage.

If a cylinder with a height of 3 inches and a raduis of 2 inches is compared to a cube with 3 inche edges which expression represents the volume of the cylinder to the volume of the cube?

If two numbers differ by 7, then what polynomial represents their product? Let x represent the smaller number.

Write an expression for the area of a 1 foot border around a circular pool with a radius of r feet.

Suppose that P dollars is invested in a savings account at interest rate i, compounded annually, for 2 years. The amount A in the account after 2 years is given by: A=P(1+i)^{2}

From 1992 to 2003, the number of people in the United States who participated in snowboarding can be modeled by f(t) =0.013t^{4}0.021t^{3}+0.084t^{2}+0.037t+1.2 where f(t) is the number of participants ( in millions) and t is the number of year since 1992. Find f(0) and interpret your results.

A homeowner is installing a swimming pool in his backyard. He wants its length to be 4 feet longer than its width. Then he wants to surround it with a concrete walkway 3 feet wide. If he can only afford 300 square feet of concrete for the walkway, what should the dimensions for the pool be?

The Robertsons put a rectangular pool with a stone walkway around it in their back yard. The total length of the pool and walkway is 3 times the total width. The walkway is 2ft. wide all around. a.) Write an expression for the area of the pool. b.) Find the area of the pool when the total width is 10ft. c.) Find the area of the pool when the total width is 9ft.

The sides of a sandbox are 3x^{2} and x+8 feet wide. a. What is the area of the sandbox? b. If the depth of the sandbox is x feet, what is the volume of sand required to fill the box?

The measure of the area of a rectangle is 4m^{2}3mp+3p4m. If the dimensions of the rectangle are represented by polynomials with integral coefficients, find the dimensions?

The area of a rectangle is 2x^{2} +7x 9 and the width is x1. Find the rectangle`s length.

A television video game company has the following total expenses E and total incomes I for producing x number of videos. E = 200 + 11x I=120 + x^{2} How many videos must be sold to break even?

The length of the pool is 30 meters longer than 6 times the width. The perimeter of the pool is 1110 meters. What are the dimensions of the pool?


The width of a triangle is 3 feet less than the length. The area is10ft^{2}. Find the length and the width.


Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 4 more square feet than the smaller. What is the width of the rectangles?

The length of a rectangle is x+5 and the width is x2. What is the area as a polynomial?

The area of a rectangle is 165 ft squared. The length is 4 ft greater than the width. What is the dimensions of the rectangle?

If the ticket agency charges "p" dollars per ticket for a concert, it can sell maximum of (40000 – p) tickets. Find: a. A polynomial to represent the total revenue with a ticket price as p dollars. b. How many tickets will be sold for a price of $10 each. c. Total revenue if the price of each ticket is $10.

The length of a rectangle is increased by 20% and its width 50%. Which part represents the increase in area?

Find the volume of a cylinder with radius 3b and height bc.

A(x)=x^{3}1 the length is x1 A) Find the polynomial to represent the width of the rectangle. B) Find the width when x is 6cm.

The length of a rectangle is 4 less than 3 times its width. Represent the area for this rectangle

Find a polynomial for the perimeter and for the area using d+4 and d

Write a polynomial for the length of the rectangle: Area is 7x^{4}  14x

A rectangular picture frame is 4 times as wide as its length with a perimeter of 80 inches. Find the dimensions.

The product of two consecutive odd numbers is 195. Find the numbers.

Find two consecutive odd integers such that the square of the larger is 3 less than 12 times the smaller

(3x^{3} – x^{2} + 10x – 4) ÷ (x + 3)

The length of a rectangle is 3 cm greater than the width. If each dimenstion is increased by 2 cm, the area is increased by 26 cm squared. Fin the orginal dimensions of the rectangle.

A market research finds that at a price of p=20, they would sell x=42 tiles each month. If they up the price to p=10, then more people would purchase the tile, and they can expect to sell x=52 tiles a months time. Find the equation.

A water balloon is released from a window 96 feet above the ground. The formula h=16t^{2}+16t+96 describes the height of the water balloon above the ground, h, in feet, t seconds after the release. How long will it take the water balloon to strike the ground?

The volume of a box with height x, length x +1, And width 2x  4 is given by the trinomial 2x^{3}  2 x^{2}  4 x. What is the volume of the box if its height is 3 inches?

The mainsail of a lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24 ft tall mainsail has a leech length of 26ft and if Dacron sailcloth casts $10 per square foot, find the cost of a new mainsail.


The lenght of a rectangle is 30cm less then three times the width. the perimeter of this rectangle is 180cm. What are the dimensison of this rectangle?

Find the height and length of the container using (3t+2)(2t+4)

A triangle has sides 2x 5, 3x + 1, and 4x + 2. Find the polynomial that represents its perimeter.


James is 5 years older than Jennifer. Three years ago the product of their ages was 36 less than the product of their ages. FInd Jennifer`s present age.

Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.

A triangle has a perimeter of 197 centimeters. The sum of the smallest and medium sides is 49 cm more than the longest side. The difference of the longest side and shortest sides is 22 cm. find the lengths of the three sides.

The length of a rectangle is 5 centimeters less than twice its width the perimeter of the rectangle is 26cm what are the dimensions of the retangle?

The quotient of two numbers is 4 and their difference is 39. what is the smaller number?



The perimeter of a rectangle is 140m. The length is 4m more than twice the width. Find the dimensions.


The length of a rectangular swimming pool is 2x1 meters and the width is x + 2 meters. Write a polynomial A(x) that represents the area. Find A(5)

The difference of two positive numbers is 5 and the sum of thier squares is 233. What are the numbers?

A manufacturer of screened porches sells a model that sells for p dollars. The revenue from the sale of this model is given by the following polynomial: R = 0.25p^{2} + 250p If revenue is found by multiplying price by demand, what is the polynomial representing the demand?

The perimeter of a rectangular swimming pool is 42 meters. The length is 5 meters more than the width. What is the length of the swimming pool?

Find the polynominal for the rectangle with the perimeter c+6 and for the area c.

ABCD is a rectangle AC = 4X +6 BD = 5X2 Find the length of each diagonal.

A polynomial in x has degree 3. The coefficient of x^{2} is 3 less than the coefficient of x^{3}. Te coefficient of x is three times the coefficient of x^{2}. The remaining coefficient is more than the coefficient of x^{3}. The sum of the coefficients is 4. Find the polynomial.

If you multiply (x+1)^20 how many terms will there be?

The length is 30 meters longer than 6 times the width. If the perimeter of the pool is 1,110 meters, what are the dimensions of the pool?

Jurassic Park charges $20 for adults and $12 for children. Total bill for 454 people was $3860. How many adults and how many kids went to the park?

A truck and a car leave an intersection. The truck travels south and the car travels east. When the truck had gone 24 miles, the distance between the car and the truck was four miles more than three times the distance traveled by the car heading east. Suppose the truck stops at point c and the car stops at point b. Write a polynomial to express the sum of the distances traveled by the car and the truck.

The volume of a rectangular prism is (15r^{3}17r^{2}42r). If the dimensions of the prism are represented by polynomials with integral coefficients, find the dimensions of the prism.

You are making a srapbook out of a picture that are 7 inches long and 5 inches wide. you want to place a border of equal width on each edge. Write a polynomial that represents the total area of the picture with the border.

Alex, Bill and Danny collect tropical fish. Alex has 8 fewer than Danny and Bill has 2 more than Danny. Write a polynomial to express how many fish Alex and Bill have together.

Choose the polynomial that represents the area of the rectangle with sides (x+8) and (x1)


Vanessa built a rectangular pen for her dogs. She used an outside wall of the garage for one of the sides of the pen. She had to buy 20 m of fencing in order to build the other sides of the pen. Find the dimensions of the pen if its area is 325m^{2}.

The area of a rectangle is 54cm^{2}. The length is 3 cm less than twice the width. Find the length and width.

Find 3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number.

Find the side length of a square whose area is 529 ft^{2}

The volume of one of the buildings in the downtown area is 839,808 cubic meters. The building is 9 times a s tall as the radio tower on top of the building. The square base has a side that is 27 times 4 meters less than the height of the radio tower. How tall is the radio tower?

Calculate the perimeter of the rectangle if the area of the polynomial is 6x^{2}+17x+5

Two rectangles have the same width. The length of one is 2 feet longer than the width. The length of the other is 4 feet longer than the width. The larger rectangle has 8 more square feet than the smaller. What is the width of the rectangles?

A rectangle has a width of 3x+5, the length is twice this. If the perimeter is 156 find the dimensions and area.

You are designing a rectangular flower bed that you will border using bricks pavers. The width of the border around the bed will be the same on every side. a. Write a polynomial that represents the total area of the flower bed and the border. b. Find the total area of the flower bed and border when the width of the border is 1.5 feet.

A triangle is 10 cm wider than it is tall. The area is 28cm^{2}. Find the height and the base.

A catering company is designing a box. The volume box is to be 54 cubic inches and the bottom of the box to be a square. Suppose the bottom of the box has a width that is 3 inches smaller than the height x of the box. write a polynomial equation of the box.

A rectangle is 15m longer than it is wide. If both its length and width are increased by 5 m and its area is increased by 200 m. Find the original dimensions of the rectangle.

A rectangular yard has a length 7 feet greater than it`s width. If both dimensions are increased by 8 feet, whcich expression gives the resulting increase in are?

Solution A is 10% alcohol. Solution B is 60% alcohol. How much of each is needed to make 50 L of a solution that is 30% alcohol?

The length of a rectangular board is 9 meters greater than the width. If the perimeter of the board is 26 meters, then what are the length and the width?

Three students in an outdoor pursuits program collaborated to write an adventure travel guidebook for Alberta and BC. Two local publishers are interested in marketing and publishing it and both anticipate retailing the book for $20. Publisher "A" offers a straight royalty of 10% (on the retail price) on all book sales. Publisher "B" offers an 8% royalty for any books sold up to 5000 copies and will then increase the royalty to 15% for any copies sold in excess of 5000. a) Describe the type of function b) Find the functions A(x) and B(x)  notice that function A(x) is apiecewise defined function. c) Let x be the number of books sold and let A(x) give the income under plan "A" and B(x) give the income under plan "B". Graph functions on the interval 0,10000

Given a trapezoid where the small base is 6 greater than the height and the larger base is 4 greater then three times the height, find all three dimensions (small base, large base, and height) if the area of the trapezoid is 133 square feet.

A box has a volume of 1,800 cubic cm. The length is 6 times the height. As well, the length is 18 cm longer than the width. If the length is increased by 2 cm, the width by 3 cm and the height by 4 cm, the volume becomes 4,320 cubic cm. What is the original length of the box in cm?

The area of a rectangle is 165 ft^{2}. The length is 4 ft greater than the width. What are the dimensions of the rectangle?

The length of a triangle is twice the width. A square is cut out at the center. The remaining area is 63 square cm. Determine the lenght of the rectangle if the area of the square is 9 square cm.

The base of a triangle is 3 cm greater than the height. The area is 44cm. Find the height and the length of the base.

The width of a rectangle is 4 feet less than the lengh. The area is 5ft^{2}. Find the lenght and width.

A triangle has sides 2x – 5, 3x + 1, and 4x + 2. Find the polynomial that represents its perimeter.

A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is feet. Find a polynomial that represents the difference in the heights of the two balls.


A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square feet. Find the dimensions of the garden.

The area of a rug is 36 square feet. The length of the rug is 5 feet longer than the width. What is the width of the rug?

Colin has a 500 cm ribbon that is cut into 3 pieces. The second piece is 3 times longer than the first. The third piece is 4 cm less than 4 times the length of the first. What are the lengths of the three peices?

A box with no top is to be made from an 8 inch by 6 inch piece of metal by cutting identical squares from each corner and turning up the sides. The volume of the box is modeled by the polynomial 4x^{3}28x^{2}+48x. Factor the polynomial completely. Then use the dimensions given on the box and and show that its volume is equivalent to the factorization that you obtain.


(36b^{3}+18b^{2}+44b+49) / (6b+5)


How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school?




the length, x of a rectangle sheet of plywood is 2ft longer than its width. Write a polynomial in simplified form that represent the area of the plywood sheet. using the polynomial that you wrote find the area of the plywood given the length is 5ft

At p dollars per ticket, a promoter expects to sell 40,000 _ 1000p tickets to a concert answer ask


rectangular stage. one side of a rectangular stage is 2 meter longer than the other. if the diagonal is 10 meters, then what are the lengths of the sides?

if a rectabgular box the width is 2x5 in polynomial if the length is design to be 10 feet longer than the width what is the solution written in polynomial

suppose you are at the gas station filling your tank with gas. the function c(g) represents the cost c of filling up the gas tank with g gallons. given the equation: c(g)=3.03(g)

one side of a rectangular stage is 2 meters longer than the othe. If the diagonal is 10 meters then what are the lengths of the sides?

how do the various areas of rectangle dimensions illustrate multiplicatiom of polynomials

The jurassic zoo charges $38.00 for each adult and $12.00 for each child. there was 254 people and the total bill was $3864. How many adults and how many children went to the zoo

A construction company is planning to pour concrete for a driveway. The length of the driveway is 16 feet longer than its width w.

3x^512x^4+0x^313x^2+36x/3x^3+x9


sara makes $23 more dollars an hour than stan, stan makes $16 dollars an hour, last week his check was $680

The perimeter of a rectangle is 46m. the length is 2m more than twice the width.

For 1980 through 1990, the population, P, (in thousands), of Hawaiican be modeled by P=17(t+56.6) where t=0 represents1980. What was the population in 1987?

suppose a market research company finds that a price of p=$20, they would sell x=42 tiles each month. If they lower the price ato p=$10 per month, then more people would purchase the tile, and they can expect to sell x=52 tiles in amonth`s time. Find equation of the line for the demand equation. Write answer in the form p=mx+b

1. Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did. e) If you were to graph C(g), what would be an appropriate domain? Range? Explain your reasoning.

A rectangle has width (x5) and length (4x+3). If the area of the rectangle is 105, find the length and the width.

1. (14x + 5) + (10x + 5) 2. (10x + 12) + (6x + 20) 3. (19x2 + 12x + 12) + (7x2 + 10x + 13) 4. (17x2 + 20x + 11) + (15x2 + 11x + 17) 5. (15x2  5x + 9) + (6x2  19x  16) + (15x2  14x  13) + (9x2  14x + 20) 6. (13x2  13x  10) + (19x2  19x  5) 7. (4x2  6x + 7) + (19x2  15x  18) 8. (13x2  5x  14) + (14x2  20x + 8) 9. (20x7  10x6  9x5  14x4 + 18x) + (6x6  12x5  9x4  9x) 10. (20x2 + 13x  4) + (11x2  13x  10) 11. (14x2  15x  17) + (14x2 + 9x  17) 12. (10x6 + 18x3 + 13) + (7x6  7x2 + 17) 13. (11x2 + 5x + 6) + (18x2 + 17x + 17) 14. (4x2  19x + 15) + (18x2 + 15x + 16) 15. (7x2 + 14x + 17) + (19x2  6x  20) + (14x2  18x + 20) + (20x2 + 19x + 17) 16. (14x7 + 19x6  17) + (5x5  10x4 + 18) 17. (9x6  4) + (10x5  15x4 + 14) 18. (17x6  6x3  20x) + (10x4 + 9x3  18) 19. (20x2 + 15x + 13) + (19x2 + 17x + 5) 20. (5x6 + 9x3  6x) + (9x7  20x2  6x)

a rectangle is 10 feet longer than it is wide, and its area is 39 square feet. find its dimensions

Choose the polynominal that represents the area of the rectangle with sides (x + 7) and (x  5):

A polynomial in x has degree of 3. The coefficient of x squared is 3 less than the coefficient of x to the third. The coefficient of x is three times the coefficient of x squared. The remaining coefficient is 2 more than the coefficient of x to the third. The sum of the coefficients is 4. Find the polynomial.

Find the polynomial for x(3)+4(x+4)

Hadley Electronics determines that the cost C of producing x plasma TVs is given by C=5000+0.6xsquared dollars. What is the total cost of producing 500 TVs and 600 TVs?

A red ball and Green bal are simultaneously tossed into the air. The red ball given A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is 16t2 96t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is 16t2 80t feet. find the polynomial D(t) that represnts the difference in heights of two balls.

You are on hte board of the condominium association. A pool 35 foot by 30 foot has just been installed. Your task is to choose a material to border around the pool. The pool border must be uniform in width. a) Write an algebraic expression for the area, in square feet, of the border around the pool. b) You must select one of the following possible materials to border the pool. Concrete: $9 per square foot Outdoor Carpeting: $5.50 per square foote p lus $15 per foot to install edging aroudn the rectangular border Brick: $8.50 per square foot plus a $250 charge for delivering the bricks Write an algebraic expression for the cost of installing the border for each of the options listed c) a decision to make the border 5 feet wide was determined by the board members. Use the algebraic expression from part (b) and find the cost of each option to border the pool. d) after furhter discussions, a dicision was made to not use concrete. the conodominium association has only budgeted $7000 for this project. You must now decide if carpeting or brick border can be installed at the width determined by the board. indicate the options to be selected and why

length of table is 4 m greater than width. area is 60 m squared

The length of a picture frame is 1.2 times the width. If the length is 27 cm, what is the width?

Suppose that a market research company finds that at a price of p= $20, they would sell x= 42 tiles each month. If they lower the price to p= $10, then more people would purchase the tile, and they can expect to sell x= 52 tiles in a month`s time. Find the equation of the line for the demand equation. Write your answer in the form p= mx + b

The volume, in cubic units, of a rectangular prism is x^3 + 2x^2  11x 12. Its length is x3 units and its width is x+1 units. What is its height?

A manufacturer of work gloves can sell (3000  150x) pairs of work gloves per week, where the sell price of a pair of work gloves is $10. (a) Find the polynomial expression that represents the revenue for one week of sales.

Express the hypotenuse h of a right triangle with area 25m square as a function of its perimeter P.

The mass of saturn is about 5.688 x10^23 metric tons. The mass of the sun is about 1.998 x 10^27 metric tons. About how many times the mass of Saturn is the mass of the sun?


A triangle has sides 3x+7, 4x9, and 5x +6. Find the polynomial that represents its perimeter

A triangle has sides 3x+7, 4x9, and 5x +6

Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

The width of a rectangular playground is 2x 5 feet, and the lenght is 3x + 9 feet.write a polynomial that represents the perimeter and then evaluate this perimeter polynomial if x is 4 feet.

One side of a triangle is half the longest side. The third side is 11 meters less than the longest side. The perimeter is 49 meters.

the world largest swimming pool length is 30 meters longer than 6 times its with.its perimeter is 1,110 meter what are the dimesions of the pool

A 36footlong ribbon is cut into 3 pieces. The first piece of ribbon is half as long as the second piece of ribbon. The third piece of ribbon is 1 foot longer then twice the length of the second piece of ribbon. What is the length of the longest piece of ribbon?

a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).

Selling shirts. If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000 100p shirts at a tournament. Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each

If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000100p. Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each.

The width of a pool table is x feet, and the length is 4 feet longer than the width. Find the polynomials A (x) & P (X) that represent the area and perimeter of the pool table. Find A (4) & P (4).

write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge

The manager of a furniture factory finds that is costs $3000 to manufacture 100 chairs in one day and $4800 to produce 3000 chairs in one day. Express the cost C (in dollars) as a function of the number of chairs X produced, assuming that it is linear.


jennifer traveled 2x+50 miles in the morning and 3x10 miles in the afternoon. Write a polynomial T(x) that represents the total distance the she traveled. Find the T(20)"

The length of a rectangle is 3 meters less than 5 times the width. The perimeter is 18 meters. Find the lenght and width.


Suppose that a rectangle has an area of 60 square meters. Express the perimeter as a function of the length of one of the sides.

a rectangle has an area of 60 square meters. Express the perimeter as a function of the length of one of the sides.

A) 3 times 2 b) 10 times 3 equals 30

length of a rectangle is 1 centimeter more than 3 times its width. If the perimeter is 50 centimeters, what is the lengh of the rectangle


darrell has$2 less than fivetimes as much money as Bob. mary has as much money as darrell and Bob together if all three of them have $80, how much money does mary have?

The length, width, and height of a rectangular box are consecutive interges and the largest dimension is K cm. Find the volume V of the box.

The length of a rectangle is four times its width, if the perimeter of the retangle is 50 ft, find its area?

he length width and height of a rectangular bow are consecutive integers, and the largest dimension is k cm. Find the volume V of the box.

two jets leave an airport at noon, one flying north at r mi/h and the other flying south at twice that speed. After 3 h, how far apart are the planes?

a rectangles length is 3 times the width decreased by 4. Write and expression to calculate the perimeter and simplify.

subtract eight more than three times a number from six less than five times a number


What expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?

Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 5 more square feet than the smaller. What is the width of the rectangles?

Consider a rectangular box of volume 200 cubic centimeters. Suppose that the base is a rectangle with sides x centimeters and 5x centimeters. Let h(x) give the height of the box in centimeters and let A(x) be the total area of the six sides of the box.

The length of a rectangle is twice its width. If the area of the rectangle is 162m2 , find its perimeter.

According to Car and Driver, an Alfa Romeo going 70 mph requires 177 feet to stop. Assuming that the stopping distance is proportional to the square of the velocity, find the stopping distance required by an Alfa Romeo going at 35 mph and at 125 mph.

The length and width of a rectangle are consecutive even integers and the length is l cm. Find the area and the perimeter of the rectangle.

Area of a square. Find a polynomial A(x) that represents the area of the shaded region in the accompanying figure

the width of a rectangular rug is four feet more than onethird of its length. the perimeter is 64 feet. that are the length and the width?

the width of a rectangular rug is four feet more than onethird of its length. the perimeter is 64 feet. what are the length and the width?

If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000100p shirts at a tournament. Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each

if a vendor charges p dollars each for rugby shirts, then he expects to sell 2000100p shirts as a tournament. find polnomial R(p) that represents the total revenue when the shirts are p dollars each. find R(s), R(10), and R(20). use bar graph to determine the price that will give the maximum total revenue

what does 3.03 equal when c(g)=3.03(g)

If a vendor charges p dollars each for rugby shirts, then he expects to sell 200100p shirts at a tournament

find the polynomial for the perimeter and the area of a square where the base side is given as a+2 and a

The length of a rectangular swimming pool is 2x  1 meters, and the width is x +2 meters. Write a polynomial A(x) that represents the area. Find A(5).

the width of a rectangle is 4 ft less than the length the area is 5ft find the width and length

The wildfire travels at x mph for 2 hours, it then increases its spread to x+20 mph and traveled 1 more hours. Write a polynomial D(x) that represents the total distance that wildfire traveled. Find D(60)




Suppose that the length of a certain rectangle is 9 meters less than two times its width. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle.


The square of 9 more than a number is equal to 9 more than the square of the number. What is the number?

find a polynominal for the perminiter and for the area c+6 c

3 less than twice x and 2 more than the quantity 3 times x



find two consecutive numbers with a product of 2862

if a vendor charges p dollars each for a rugby shirts then he expects to sell 2000100p shirts at a tournament. find the polynominalR(p) that represents the total revenue when the shirts are p dollars each.

If I multiply a number by 10 and subtract 9, I get the square of a number. What could it be?

Selling shirts. If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000100p shirts at a tournament.



an online music store is having a sale. Any sings cost 75 cents and any ringtones cost 50 cents. Emma can buy 6 songs and 2 audiobooks for the same price as 5 ringtones and 3 audiobooks. What is the cost of an audiobook?





the length of a rectangle storage room is 2 feet longer than its width. If the room`s area is 195 square feet, find its length and width.


jessica wants to enclose a rectangular feed area in her backyard using a barbed wire fence. she only has 64 feet of fencing, and wants to maximize the area of the rectangle. express the area as a function of x.

product of 3 less than twice x and 2 more than quanity 3 times x

the perimeter of a rectangle is 12 meters. if the side lengths are given by integers, find all possible dimensions, and determine the area of each.


One hundred feet of fencing is used to enclose three sides of a rectangular pasture. The side of a barn closes off the fourth side. let x be one of the sides perpendicular to the barn.


Selling shirts. If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000 100p shirts at a tournament.

the perimeter of a standard sized rectangular rug is 44ft. The length is 2ft longer then the width. Find the dimensions.

The width of a rectangular park is 5 m shorter than its length. If the area of the park is 300 m2, find the length and width



You are designing a rectangular flower bed that you will border using brick pavers. The width of the border around the bed will be the same on every side. The flower be is 6ft by 5ft.

A retailor of boom boxes knows that at a price of p dollars each, he can sell 9003p boom boxes per month. Find: a) A polynomial that represents the monthly revenue for the boom boxes How many boom boxes will he sell of the price is $200 each How many boom boxes will he sell if the price is $300 each

a rectangular shipping container has a volume of 2500cm3. the container is 4 times as wide as nit is deep, and 5cm taller than it is?


the perimeter of a rectangle is 152m. The lenght is 4m more than twice the width. find the dimensions


In a rectagular piece of cardboard with perimeter 30 in, two parallel and equally spaced creases are made. The cardboard is then folded to make prism with open ends that are equilateral triangles. what is the volume of prism? What is domain of V? Find approximate value of x that maximizes volume. Then give approximate maximum volume.


i have a box with 2 equals sides measuring 5 in, the other 2 sides measure 2 in with the perimeter being 20

If two numbers have a sum of 9, then what polynomial represents their product?

If a vendor changes P dollars each for rugby shirts then he expects to sell 2000100p shirts at a tournament. Find the polynomial R(p) that represents the total revenue when the shirts are p dollars each. Find R(5), R(10), and R(20). Determine the price that gives the maximum total revenue.

The sum of two positive numbers, x and y, is 60. Find a function of x that models the sum S of the square of the number y and three times the square of the number x.

The sum of two numbers is 28. The sum of the square of the two numbers is 490. Find the numbers

A hallway has an area of 63 square feet. The length of the hallway is 7 times longer than the width. What is the length of the hallway?

twelve is three less than the product of a number and five

The length of a rectangular rug is 12 inches shorther than the width. If the length is 30 inches, write and solve an equation to find the width

A rectangular pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?


A rectangle is three times as long as it is wide. If its legnth and width are both decreased by 2cm, its area is decreased by 36cm squared. Find its original demensions.

The height "y" (in feet) of a punted foot ball is given by y=(16/2026)x^2+(9/5)x+3/2 where x is the horizontal distance (in feet) from the point at which the ball is punted. Find the maximum height. How far did the punt go?

a cubic packing box has dimensions of 1.2 feet on each side. What is the volume of the box

the length of a rectangular garden is 3 yards more than twice its width the perimeter of the garden is 36 yards

Find the coefficient of y^6 in (2x3y^2)^6




5. Which has the greater area, a square with sides each (x+2) units long or a rectangle with length (x+4) units and width X units?


Write an expression for: the perimeter increased by 26 meters

a rectangular bos has a volume equal to 12x + 19x 12x  4. The width of the box is x + 2 and the height is 3x  2. Find the length.


find the value of the coefficient of 1/x in the expansion (2x  1/x)^5


the length of the table is 5 times greater than the width the are is 140m^2 what is the length


Find two consecutive odd integers such that their sum is 60 and their product is 899.

if 1,110 is the peremeter of a retangle and the lenght is 30 more than 6 times the width then what is the lenght and width

Area of a square. A square has sides of length 3x1 meters. Find a polynomial A(x) that represents the area of the square. Find A(1).

A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car`s new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

if the ticket agency charges `p` dollars per ticket for a concert, it can sell maximumof (40000p) tickets. find:

The area of a rectangular lawn is x + x – 30 square meters. If the length is x + 6 meters, find a binomial that represents the width.

Total Revenue At p dollars per ticket, a promoter expects to sell 40,000 1000p tickets to a concert. a) How many tickets will she sell at $10 each? b) At $10 per ticket, what is the total revenue? c) Find a polynomial R(p) that represents the total revenue when tickets are p dollars each. d) Find R(20), R(30), and R(35)

A rectangular lawn measures 7m by 5m. A uniform border of flowers is to be planted along two adjacent sides of the lawn. If the flowers that have been purchased will cover an area of 6.2m2, how wide is the border?

write the following in polynomial form: g(x)= 2(x5)(x2)

the area of a right triangle is 44m^2. Find the lengths of its legs if one of the legs is 3 m longer than the other.


The perimeter of a rectangle is 156 meters. The length of the rectangle is six more than five times the width. What is the length of the rectangle?

A swimming pool 20 m long and 10 m wide is surrounded by a ddeck of uniform width. The total area of the swimming pool and the deck is 704 m squared. Find the width of the deck.




the prism has a volume of V= 2x3 + 6x2 + 4x what could be the dimensions of this prism be

what is the product of 3 less than twice x and 2 more than the quantity 3 times x?

find area of pool with a length of 30ft and a width of 18ft but a 4ft width all around

pure acid is to be added to a 5% acid solution to obtain 95L of 26% solution. What amounts of each should be used? How many liters of 100% pure acid should be used to make the solution?

The sum of two integers is 131. Find the two integers if the larger one is 8 more than twice the smaller.

area of a square. find a polynomial a x that represents

the perimeter of a rectangle rug is 44 ft. the length is 2ft longer then the width find the dimesion

the product of two odd consecutive integers is 143.Find the numbers?

a running track 4m wide goes around a soccer field that is twice as long as it is wide. at each end of the soccer field the track is a semicircle with inner radius r. find a formula for the area of the track in terms of pie and r.

An open carton is formed from a rectangular piece of cardboard that is 4 ft longer than it is wide, by removing 1ft squares from each corner and folding up the sides. If the volume of the carton is then 32ft^3, what were the original piece of material

Total revenue. At p dollars per ticket, a promoter expects to sell 40,000 1000p tickets to a concert. a) How many tickets will she sell at $10 each? b) At $10 per ticket, what is the total revenue? c) Find a polynomial R(p) that represents the total revenue when tickets are p dollars each. d) Find R(20), R(30), and R(35).

The length of a rectangular swimming pool is 2x  1 meters, and the width is x + 2 meters. Write a polynomial A(x) that represents the area. Find A(5).

A package may be sent by mail only if the sum of its height and the perimeter of the base is not more than 72 inches. Find the dimensions of the box of maximum volume that can be sent if the base of the box is a square.

darrell has $2 less than five times as much as bob. Mary has as much money as darrell and bob together. if all three of them together have $80, how much money does Mary have?

3. If n – m = 3 and n2 – m2 = 24, what is the sum of n and m?


A polynomial f of degree 10 has only linear factors, a single xintercept 10, and a leading coefficient of 3. Find f(x).

find the largest of two consecutive even integers such that three times the larger added to the small is 54

Jim and John`s ages add up to 10. If Jim`s age is x, what is Heather`s age?

math functions total construction cost as function of length of brick wall

divide x^6 + 5x^5 + 11x^4 + 13x^3  3x^2  8x + 5 by x^2 + 2x + 5



A decorator plans to place a rug in a room 9 m x 12 m in such a way that a uniforom strip of flooring around the rug will remain uncovered. If the rug is to cover half the floor space, what should the dimensions of the rug be?

find 3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number

a circular pool had radius of 3.7 meters. you want to build a walkway all the way around it, with a width of 1.0 meters. Estimate the area of the walkway ( to the nearest tench of a square meter).



An investor must invest a total of $5,000 in two accounts, on paying 4% annual simple interest, and to other 3%. If he wants to earn $550 annual interest, how much should he invest at each rate?

The length of the base of a triangle is four times the height. The area of the triangle is 50 sq ft. Find the base and height of the triangle.

When there are 22 apple trees pre acre, the average yield has been found to be 500 apples per tree. For each additional tree planted per acre, the yield per tree decreases by 15 apples per tree. How many additional trees per acre should be planted to maximize the yield?

solve word problem in polynomials

give three example of word problem in polynomials

John brought 2 redskins tickets. both tickets cost 5x3 +4x. one ticket cost 2x3+3x dollars. what is the cost of the other ticket? write your answer in simplest form.

give three example of word problem in polynomials with solution

algebra word problems with solutions on polynomials

The length of a picture frame is twice the its width. The perimeter is 18 inches. What is the width f the picture frame in inches?

A rectangular flower bed measures 10ft. by 15ft. I want to add a walkway all around that measures 186 sq. ft. How wide should the walkway be?

The total profit in dollars for sales of x lawn mowers in a given month is given by : P(x) =0.2x^2+300x200 How many lawn mowers need to be sold to produce maximum profit? What is the maximum profit?

A slice of thickness Icm is cut off from one side of a cube. If the volume of the remaining figure is 180 cm3, how long is the edge of the original cube?


Write a polynomial for the lenght of a rectangle when the area is 7x^4  14x square units

find a polynomial for the perimeter and for area


treating 863 subjects with lipitor and asking each subject "how does your head feel?"

The sum of two numbers is . If the larger is divided by the smaller the quotient is and the remainder is . Find the difference of the two numbers.


Using long division, solve: x^39 divided by x^2+1

with a perimeter of 1110 meters, this rectangular shaped pool is 30 meters longer than 6 times its width. Find its dimensions

three times the smaller number of three consecutive even numbers is four more then twice the larger

the product of 3 less than twice x + 2 more than the quantity 3 times x

Find a trinomial that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters.

length of a rectangle is twice the width. the perimeter is 84cm more then the width. find the rectangles dimensions

find a trinomial a(x) that represents the area of a rectangular rug whose sides are x+3 feet and 2x1 feet.find a (4)


Choose the polynominal that represents the area of the rectangle with sides (x + 6) and (x  3)

find a monomial with GCF,LCM, and monomial given

The lenght of a FedEx 25 kg box is 7 inches more t han its height. The width of the box is 4 inches more than its height. If the volume of the box is 4,420 cubic inches, find the height of the box.

if malcolm adds a 10% tip for the driver, how much money will he pay in total?



Suppose that a market research company finds that at a price of p=$20, they would sell x=42 tiles each month. If they lower the price to p=$10, then more people would purchase the tile, and they can expect to sell x=52 tiles in a month`s time. Find the equation of the line for the demand equation. Write your answer in the form p=mx+b.

The length of the smaller rectangle at the right is 1 inch les than twice its width. Both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. The area of the sheaded region is 86 square inches. What are the dimensions of the smaller rectangle?

Given the length is represented by x+1, the width is three less than the length, and the volume is represented by x sqaured+3xsquared6x8. Determind the height as a polynomial.

Terry invests $1500 in two mutual funds. The first year, one fund grows 3.8% and the other grows 6%. Write a polynomial to represent the amount Terry`s $1500 grow to in that year if x represents the amount he invested in the fund with the lesser growth rate.



Find the maximum volume of a bos that can be made by cutting out squares, from the corners of an 8 inch by 15 inch rectangular sheet of cardboard and folding up the sides.



the question is..... the area of a walk around a rectangular swimming pool if the walk is 6 feet wide and the length of the pool is 7 feet more than its width x

Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is 16t2 + 96t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is 16t2 + 80t feet.


Which has a greater area a rectangular pen with dimensions 25m x 5 m. or a circular pen with a radius of 7 m.


Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x?

A market research company finds that a price of p=$20, they would sell x=42 tiles each month. If they lower the price to p=$10, then more people would purchase the tile, and they can expect to sell x=52 tiles in a month`s time. Find the equation of the line for the demand equation. Write your answer in the form of p=mx+b.

suppose you are desinging a rectangular garden. the lenght is twice the width. you wanted awalk

Write a 250word summary of the above problem. Your written work should include, but not necessarily be limited to, the following: an explanation of the problem, a review of the mathematical concepts involved, a critique of the method used to obtain the solution, and an interpretation of the answer. Your summary should be written in APA format, demonstrate proper use of the English language, and be mathematically precise.

a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b.

a juice box measures 6.4 cm by 4.0 cm by 10.5 cm. It contains 25o mL of juice. The manufacturer wants to design a larger box by increasing each dimension by the same amount. Suppose the larger box holds twice as much juice. What are its dimensions?

A market analyst working for a small appliance manufacturer finds that if the firm produces and sell x blenders annually, the total profit (in dollars) is p(x)=8x+0.3x^20.0013x^3372. Graph the function P in appropriate window and use the graph to answer the following questions. a, when just a few blenders are manufactured the firm loses money (profit is negetive). how many blenders must the firm produce to break even? b, does profit increase indefinitely as more blenders are produced and sold? if not, what is the largest possible profit the firm could have?

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find 3 consecutive even numbers where the product of the smaller two numbers is 64 less than the square of the largest number

Find the polynomial that represents the volume of a cube if each side measures x+3

The manufacturer of an ice cream container wants to increase the volume of the container by 25% by increasing the height. The current container is a rectangular solid with a width of 8 cm, a length of 12 cm, and a height of 4 cm. Find the (a) volume of the original container, (b) the new volume, and (c) the height of the new container.

2. Brown’s gas station estimates that they can sell 3,600 gallons of gas per week at $1.30 per gallon, but only 3,300 gallons at $1.50 per gallon. Assuming that the demand is linear, at what price should Brown sell gas to get the largest revenue?

if 2 numbers differ by 5, what polynomial represents their product?

The Jurassic Zoo charges $28.00 for each adult admission and $12.00 for each child. The total bill for 254 people from a school trip was $3864.00. How many adults and how many chldren went to the zoo?

Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ? A. –6x2 + 25x + 6 B. 6x2 + 5x + 6 C. 6x2 – 5x + 6 D. 6x2 – 5x – 6 E. 6x2 – 13x – 6

lydia is twice older than his daughter what is the age of lydia after three years?

$25 for each adult. $16 for each child. 254 People went on a cruise and the bill equaled $3000. How many children went and how amny adults went?

The perimeter of a rectangle is 140m. The length is 4m more than twice the width. Find the dimensions


The length of a rectangle is four more than its width. Using a single variable, express the perimeter.

List all possible rational zeros of f(x)=3x^33x^2+x+2 given by the rational zeros theorem. Be sure that no value in your list appears more than once.


Worldwide Shipping Company charges (4x + 280) dollars for shipping a package that weighs x pounds from Miami to Denver. Friendly Shipping Company charges (3x + 125) dollars to ship the same package. What is the degree of these polynomials?



The length of a rectangle is 5 cm less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle? (1 point)

suppose you want to buy concrete for a 36 ft by 24 ft by 9 in patio. if concrete costs $55/yd cubed, how much will the concrete for the patio cost

Vendor charges p dollars each for rugby shirs, then he expects to sell 2000100p shirts at tournament. a) find a polynomial R(p) that represents the total revenue when the shirts are p dollars each

The width of a rectangular painting is 3 in. more than twice the height. a frame that is 2.5 in. wide goes around the painting. a) write an expression for the combined area of the painting and frame. b) use the expression to find the combined area when the height of the painting is 12 in. c) use the expression to find the combined area when the height of the painting is 15 iin.

a photo is 3 cm longer than it is wide. Find the length and width if the area is 108 cm^2

a rectangular column of cement is to have a volume of 20.25 cubic feet. The base is square, with 3 feet less than onehalf the height of the column. What should the dimensions of the column be?


I am building a shed and the dimensions are (2x+5) feet wide, (3x+6) feet long, and (6x4) feet high what is the total square feet of the shed?



the polynonmial 0.041h0.018a2.69 can be used to estimate the lung capacity, in liters, of a female witrh the height h, in centimeters, and age a, in years. Find the lung capicity of a 60 year old woman who is 150 centimeters tall.

the lenth of a rectangular board is 10 cenimeters longer than its width the width of the board is 26 cenimeters the boardis cut into 9 equal

vendor charges p dollars each for shirts, he expects to sell 2000  100p shirts find r(p)

A company produces a product (#687) A company produces a product for $9.45 per unit, plus a fixed cost of $5200. The company sells the product for $15.80 per unit. a) determine a function, c(x), to represent the cost production x units b) determine a function, r(x) to represent the revenue from selling x units c) determine a fucntion to represent profit d) caculate break even point

The area of a rug is 36 square feet. The length of the rug is 5 feet longer than the width. What is the width of the rug?

The world`s largest swimming pool is the Orthlieb Pool in Casablanca, Morocco. The length is 30 meters longer than 6 times the width. If the perimeter of the pool is 1,110 meters, what are the dimensions of the pool?

the profits of a company are found by subtracting the company`s costs from its revenue. if a company`s cost can be modeled by 14x+120,000 and its revenue can be modeled by 40x0.0002x to the second power, what is an expressionfor the profit?

dimensions of a rectangle whose length is three footfeet longer than twice its width and whose perimeter is 42 feet


A rectangular garden is 10 ft longer than it is wide. Its area is 600 ft2. What are its dimensions?

A rectangular garden has a perimeter of 44 ft. The garden is 10 ft. longer than it is wide. What is the width of the garden?

The length of a rectangular box is 4 times its height, and its width is 6 more than its height. The volume of the box is 102 ft^3. Find the height of the box. Round your answer to two decimal places.

the width and a rectangle are given by two consecutive odd integers. write an expression for the area of the rectangle. (use x for the width of rectangle)

22. The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?

find three consecutive even integers such that the sum of the squares of the smaller two is equal to the square of the largest.!

In September the students at Bell Elementary school were given a 100 book reading challenge, to be completed by the end of the school year (or with in 9 months). StudentA reads an average of 5 books per month, while studentB reads twice the amount. By the end of the school year, what will be the total amount of combine books be?

A polynomial in x has degree 3. The coefficient of x2 is 3 less than the coefficient of x3. Te coefficient of x is three times the coefficient of x2. The remaining coefficient is more than the coefficient of x3. The sum of the coefficients is 4. Find the polynomial.

A manufacturer of screened porches sells a model that sells for p dollars. The revenue from the sale of this model is given by the following polynomial: R=0.25p^2+250p If revenue is found by multiplying price by demand, what is the polynomial representing the demand?

circular swimming pool has a depth and a radius that equals five times its depth. A rectangular pool has the same depth as the circular pool. Its width is four feet more than three times its depth and its length is two feet less than six times its depth.

a polynomial in x has degree 3. The coefficient X2 is 3 less than the coefficient of x3. The coefficient of x is three times the coefficient of x2. The remaining coefficient is 2 more than the coefficient of x3. The sum of the coefficients is 4. Find the polynomial.

If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000 p shirts at a tournament. What s the total revenue when shirts are p dollars each.

If an object is propelled upward from a height of 96 feet at an initial velocity of 80 feet per second, then its height after t seconds is given by the equation h = 16t2 + 80t + 96 where h is in feet. After how many seconds will the object reach a height of 196 feet?

Write a polynomial for a rectangle the perimeter


A rectangular yard has a length 8 feet greater than its width. If both dimensions are increased by 5 feet, which expression gives the resulting increase in area?

22. The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle? (2 points)

"The length of a simming pool is 12 feet longer than twothirds its width. If the perimeter of the pool is 44 feet, what is the length of the pool?"

A manufacturer of screened porches sells a model that sells for p dollars. The revenue from the sale of this model is given by the following polynomial: R = 0.25p2 + 250p If revenue is found by multiplying price by demand, what is the polynomial representing the demand?

At p dollars per ticket, a promoter expects to sell 40, 0001000p to a concert. A. howmany tickets at $10 each? B. at $10 per ticket what is the total revenue? C. find a polynomial R(p) that represents the total revenue when tickets are p dollars each? D. find R(20) R(30) AND R(35)?

a picture with a frame has the diminsions shown. 5 inch by 7 inch. The frame is the same width on all sides. What polynomial could be used to represent the area of the picture and its frame?

What is the maximum value for x when the volume of a rectangular prism is 3a (x5) (x8)?

write the algebraic expression that represents the phrase three less than double a number

Darrell has $2 less than five times as much money as Bob. Mary has as much money as Darrell and Bob together. If all three of them together have $80, how much money does Mary have?

a sporting goods store sells about 200 pairs of running shoes each month when it charges $6 per pair. For each $1 increase in price, 2 fewer pairs are sold each month.

the length of a rectangle is 26 centimeters less than 5 times it`s width. it`s area is 63 square centimetes. Find the demensions of the rectangle.

The voltage generated by an electrical circuit changes over time according to the polynomial V(t) = t^3  4t^2  25t + 100, where V is in volts and t is in seconds. Factor the polynomial to find the times when the voltage is equal to zero.

If a rectangle has a length that is 3 cm less than four times

find 4 consecutive even integers where the product of the two smaller numbers is 72 less than the product of the two larger numbers

find three consecutive even numbers where the product of the two smaller numbers is 52 less than the square of the largest number

A culture of bacteria currently has a population of 100 bacteria, and the population doubles each day. a) Find the equation for ( ) population P t = after t days . b) Give a graph for the first 5 days. c) How long will it take for the population to reach 1 million?

the length of a rectangle is 8 inches more than its width. after both its length and width have been increased, the area of the larger rectangle is given as w2 + 14w + 24 square inches where w is the original width. a) factor the polynomial to find the dimensions of the new rectangle. b) by how much was the width increased? c) by how much was the length increased?

two rectangles have the same width. the length of one is 1 foot longer than the width. the length of the other is 2 feet longer than the width. the larger rectangle has 4 more square feet than the smaller one. what is the width of the rectangles.

What represents the product of 3 less than and 2 more than the quanity of 3 times x?

A rectangular prism has a height othat is 4 feet shorter than the width, a length that is 9 feet more than the width, and a volume of 189 cubic feet. Find its dimensions.

Find the two consecutive odd intergers the sum of whose squares equal 130.

find a polynomial for the perimeter and for the area of b+3

the cost of production for an item in a factory is given by the formula c=n^29n+14, where n is the number of that item produced. Find the number of units produced if the cost of production is $7800

A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed 16t296t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is 16t280t feet. Find a polynomial D9t) that represents the difference in the heights of the two balls.

fine the polynomial for the perimiter and the area c+2 and c

If two numbers differ by 7, then what polynomial represents their product? Let x represent the smaller number

Stephanie, the Team Manager of a soccer team, purchases many soccer balls from a retailer and sells them to all the players at her soccer club at a price of x dollars each. She can sell 600 – 15x balls per week. Find a polynomial that represents the weekly revenue for the balls. Find the revenue for a week in which the price is $12 per ball. Use the parabolic graph to illustrate the law of diminishing return, if it occurs in this case. In order for Stephanie to receive the maximum weekly revenue, how would you, as Business Manager, recommend for the price per ball?


chose the polynomial that represents the area of the rectangle with sides (x+5) and (x3)

Find the polynomial that represents the volume of a cube if each side measure x+6


Total revenue. At p dollars per ticket, a promoter expects to sell 40,000 1000p tickets to a concert. a) How many tickets will she sell at $10 each? b) At $10 per ticket, what is the total revenue? c) Find a polynomial R(p) that represents the total revenue when tickets are p dollars each. d) Find R(20), R(30), and R(35).

Find a polynomial for y+7 and y

what are some examples from real life in which one might use polynomial division

the area of the rectangle with sides (x + 3) and (x  1):

the height of a triangle is represented by the expression 15p^6qr^3.the base is represented by 8p^2q^3r^5.find the expression that can be used to represent the area of a triangle

Find the polynomial that represents the volume of a cube if each side measures x+5

find 3 consecutive numbers were the product of the smaller two numbers is 52 less than the square of the largest number.

the length of a conservatory garden is 20 yards greater than its width . the area is 300 square yards . what are the dimensions

a circlular pond will be placed on square piece of land. the lentgh of the side of the square is 2x


The radius of a circle is x + 2 cm. Express the circumference and area of the circle in terms of the variable x . Write the answer as a polynomial in descending powers of x.

The city has an easement adjacent to Mr. Kane`s property that has utility lines running beneath it. Although he likes to keep up the flowerbed, the city can take over any part of that when they want. Since he has to buy lime and fertilizer, but doesn`t know how much the city will be using, he has to be able to calculate what he needs instantly. How much area will Mr. Kane have to cover, depending on h ow much land the city decides to take? His back lot is 25 yards by 10 yards before he figures in the city property.

The city has an easement adjacent to Mr. K`s property that has utility lines running beneath it. Although he likes to keep up the flowerbed, the city can take over any part of that when they want. Since he has to buy lime, but doesn`t know how much the city will be using, he has to be able to calculate what he needs instantly. How much area will Mr. K have to cover, depending on how much land the city decides to take? His back lot is 25 yards by 10 yards BEFORE he figures in the city property. First, what is the area of the back lot ONLY? Second, how do you calculate the area of the flowerbed ONLY? Third, calculate the area of the entire property. Find at least two different ways to represent this.

find the polynomial that represents the volume of a cube if each side measures x+6

the length of a rectangular board is 10 centimers longer than its width. The width of the board is 26 centimeters. the board is cut into 9 equal pieces. what is the area of each piece?

Supose it takes 3 days for a space vehicle to travel from Earth to the moon. About how long would it take the same vehicle traveling at the same speed to reach Neptune? The moon is 240,000 miles from miles. Neptune is 2,700,000,000 miles.

The length of a rectangle is twice its width. If the area of the rectangle is 162m2, finds its perimeter.

During the first part of a trip, a conoeist travals 65 miles at a certain speed. The canoeist travals 7 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 4 hrs. what was the speed on each part of the trip?

a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (.

how to solve when you have the break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values.

The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values.

Which of the following expressions represents the product of 3 or less than twice x and 2 more the the quantity 3 x?

which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?


A rectangle has a perimeter of 60 cm. Its length is 5 times greater than it`s width. what is it`s length

If the ticket agency charges ‘p’ dollars per ticket for a concert, it can sell maximum of (40000 – p) tickets. Find: a. A polynomial to represent the total revenue with a ticket price as p dollars.

: If the ticket agency charges ‘p’ dollars per ticket for a concert, it can sell maximum of (40000 – p) tickets. Find: a. A polynomial to represent the total revenue with a ticket price as p dollars. b. How many tickets will be sold for a price of $10 each. c. Total revenue if the price of each ticket is $10.


If the ticket agency charges `p` dollars per ticket for a concert, it can sell maximum of (40000p) tickets. Find: a. A polynomial to represent the total revenue with a ticket prices as p dollars. b. how many tickets will be sold for a price of $10 each. c. Total revenue if the price of each ticket is $10.

If a garden bed were of length `n` metres, how many pavers would be needed?


the area of a rectangle is the product of its length and width.if a rectangular board has an area of 30 square feet,what are possible measurements of its length?


what is the width of a rectangle if the area is 347 and the length is 2 more than the width

the length the width and the height of a box are x, 2x, and 3x5 inches

find a polynomial for the perimeter and the area when the length is a+8 and the width is a

A Market analyst working for a small electronic manufacturer finds that if the firm produces and sells x cell phones anually, the total profit (in dollars) is P (x) = 6x + 0.25x^2  0.002x^3  350 a) When just a few cellphones are manufactured, the firm loses money. (For example, p(10) = 267, so the firm loses $267, if it produces and sells only 10 cell phones). How many cell phones must the firm produce to break even? b) Does profit increase indefinitely as more cell phones are produced and sold? If not, what is the largest possible profit the firm could have? How many cell phones would be produced and sold at the largest profit.

Can you suggest me another problem and then send the answer after I`ve solved it?

write an expression for the surface area of a circular pool with a radius of r feet

On a walking tour, Nora walks uphill 5 miles to an inn where she has lunch. after lunch, she increases her speed by 2 miles per hour and walks for 8 more miles. is he walked for 1 hour longer before lunch than after, what was her speed before lunch?

the lenght and width of a rectangle are 7m and 5m, respectively. If each dimension is increased by the same amount, the area is tripled. Find the dimensions of the new rectangle.

A sign has the shape of a triangle. The length of the base is 3 m less than the height. What are the measures of the base and height if the area is 44 m squared?


A parabolic satellite television antenna has a diameter of 6 feet and is 1.6 feet deep. How far is the focus from the vertex?

Find the length, in inches, of the smaller side of a right triangle with an area of 294 square inches if its hypotenuse is 35 inches long.


the alligator at one time an endangered species is the subject of a protection program. the formula p=10x^2+475x+3500 models the alligator population P after X years of the protection program , where 0

the length of a rectangular parking lot is 9 meters less than twice it`s width, and the perimeter is 474 meters, find the length of the parking lot

Tne sum of two numbers is 5. The sum of their squares is 53. Find the nunbers.

the following polynomial approximates the rabbit population in a particular area. R(x) = 0.121x^5 + 2.952x^4 +3500, where x is the number of years from 1965. Describe the rabbit population from years 1965 to 1990

how to long divide with hundreds

A ball is thrown straight up from the top of a building 300 tall with an initial velocity of 4ft/sec. Find a algebraic representating of the height above ground of the ball as a function of time.

A triangle is 3 cm wider than it is tall. The area is 27 cm^2. Find the width (length of the base)

the altitude of a triangle is 5m less than half its base. if the area of a triangle is 300m, find the measure of the base


The world\`s largest swimming pool is the Orthlieb Pool in Casablanca, Morocco. The length is 30 meters longer than 6 times the width. If the perimeter of the pool is 1,110 meters, what are the dimensions of the pool?


Revenue is equal to the number of x units sold times the selling price p of each unit. what is the equation for revenue?

the lenght of the box is twice its height and three times its width. if the box has a volume of 36 cubic inches, what is its lenght in inches?

The height of a rectangular box is times its length, and its width is more than its length. The volume of the box is 96 in^3

The area of a rectangle is numerically 44 more than its perimeter. If the length of the rectangle is 8 inches more than its width, what are the dimensions of the rectangle?

At p dollars per ticket, a promoter expects to sell 40,000 _ 1000p tickets to a concert

At p dollars per ticket, a promoter expects to sell 40,000 _ 1000p tickets to a concert. a) How many tickets will she sell at $10 each? b) At $10 per ticket, what is the total revenue? c) Find a polynomial R(p) that represents the total revenue when tickets are p dollars each. d) Find R(20), R(30), and R(35).

the area of a window is 52ft. squared.what is the approximate witdh of the window to be replaced?find your answwer to the nearest foot.

the perimeter of a rectangle is 24 meters and its area is 27 square meters. Find the dimensions of the rectangle

a 26oz coffee can hasa height of 6.5 in. and a radius of 2.5 in. evaluate the polynomial when h=6.5 and r=2.5 to find the area of the can. use 3.14fr pi

On my last birthday I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?

R9p)= 4p^2+1020p find the maximum revenue when price is p

find the dimensions of a rectangle with perimeter of 54 meters, of its length and its width is represented by two consecutive even integers

A rectangle is twice as long as it is wide. If both its dimensions are increased by 4, its area is increased by 88. Find its orginal dimensions.

without graphing, find the xintercept and the yintercept for the of each equation.

suppose that market research company finds that the price of p=20, they would sell x=42 tiles per month. if they lower the price to p=20, then more people would purchase the tile, and they expect to sell x=52 tiles in a months time. Find the equation of the line for the demand equation. Write your answer in the form p=mx+b.

find a polynomial for the perimeter and for the area m=m+3

The length of the smaller rectangle at the right is 1 inch less than twice its width. Both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. The area of the shaded region is 86 square inches. What is the area of the larger rectangle?

A veterinarian has 100ft of fencing and wishes to construct four dog kennels by first building a fence around a rectangular region and then subdividing that region into four smaller regions by placing three fences parallel to one of the sides. What dimensions of the region will maximize the total area?

A rectangular garden plot is 10m longer than it is wide. If the length is increased by 1 meter and the width decreased by 2 meters, the area is decreased by 42 m2. What are the original dimensions?

The length of a rectangular floor is 2 meters less than twice its width. If a diagonal of the floor is 5 meters., find the length and the width.

write a polynomial expression to represent the area of this rectangle..one side being 3x+4 the other x4

A 12 ft board is cut into 2 pieces so that one peice is 4 feet longer then 3 times the shorter peice. if the shorter peice is x feet long, find the lengths of both peices.

The length of a rectangular rug is 3 feet more than the width. If the area of the rug is 180 ft squared. Find the dimentions

Rectangle has a perimeter of 18 cm. its length is 5 cm more than its width. find the dimensions

A monument consists of two cubical blocks of granite, the smaller resting on the larger. The total height of the monument is 5 ft, and the area of the exposed surface is 61 squared ft. Find the dimensions of the blocks.

A 3 ft. by 5 picnic table is placed on an outdoor patio measuring x ft. by (x+1). Find a polynomial for the remaining open space on the patio in square feet.

Lisa bought an argyle sweater for her husband for his birthday. She needed a box that was 16 feet by 12 inches to wrap the sweater in, and 2 yards of wrapping paper to insure that she would have enough. What is the area of the gift box?


In a certain city a birth occurs on the average every 24 min and a death every 1/2 hour. Aresident moves out of the city every 1.5hr, and a new person moves into the city every 4.5hr. how long does it take on the average for the population to increase by 1 person.

A rancher in Centreville decides to build a silo inside his corral. The rectangular corral measures 23 m by 18 m and the silo`s base is circular with a diameter of 2x meters. Find a polynomial for the remaining area of the corral (in square meters) after the silo is built.


The length of a rectangle is 2x^33x^2+x1 feet, and the width is x^2+2x3 feet. What is the polynomial that expresses the area?

Jim has calculated the area of a rectangle to be x3 + x2 + x + 1. If the width of the rectangle is x + 1, then its length is

the revenue of a charter bus company depends on the number of unsold seats. If 100 seats are sold, the price is $50. Each unsold seat increases the cost per passenger by $1. Let x represent the number of unsold seats. Write and expression for the number of seats that are sold. Write and expression for the price per seat. Write and expression for the revenue. Find the number of unsold seats that will produce the maximum revenue. Find the maximum revenue.




a rectangle 180 feet what is the maximum

The product of two consective odd intergers is one less than three times their sums

The product of the page numbers on two facing pages of a book is 420. Find the page numbers.

for 1980 through 1996, the total exports E (in billions of dollars) of the United States can be modeled by E(t)=

haha alright... i might text you up on it...but you would have to find some hot baseball players for my friends... lol that a problem?

a party of students rented a motor boat, B, and shared the cost equally. if the number of the students had been 5 less, they could have used a smaller boat costing only half as much as B and the expense to each would have been 50 cents less. if there had ben ten more students in the party they would have required a larger boat costing 20% more than B, but the expense to each would have been 30 cents less. how many students were in the part?

a cement walkway around a garden is 3 inches thick and 4 feet wide. THe garden is x+5 feet wide and 2x feet long. Express the volume of the cement needed for the walkway in cubic feet as a polynomial in x

Find the radius if the width of the border is 2ft and its area is 176cm sq

Find a polynomial for the perimeter and for the area d+9x9

The polynomial in x has a degree 3. The coefficient of x2 is 3 less than the coefficient of x3. The coefficient of x is 3 times the coefficient of x2. The remaining coefficient is 2 more than the coefficient of x3. The constant term is 3. The sum of the coefficients and constant term is 4. Find the polynomial.

the lengths of the sides of a triangle are consecutive even integers. find the length of the longest side if it is 22 units shorter than the perimeter.

A boardwalk that is x feet wide is built around a retangular pond. The combined area of the pond and the boardwalk is 4x2 + 140 x + 1200 square feet. What are the domensions of the pond?

the area of a rectangular garden is 39 square feet. The width of the garden is 10 feet less than the length. What is the width of the garden

STAGE 1: IDENTIFY DESIRED RESULTS Content Standard(s) Generalizations about what students should know and be able to do Established Goals: CT Frameworks: e) Tables, graphs, and equations can be used to analyze nonlinear functions for which the rate of change is not constant. f) Functions are used in a variety of situations including to model data and to make predictions. g) A wide variety of functions can be used to model real world situations. h) Functions can be viewed as objects on which operations can be performed. NCTM Standards: a) Understands patterns, relations and functions. b) Represents and analyze mathematical situations and structures using algebraic symbols. c) Use mathematical models to represent and understand quantitative relationships. d) Analyze change in various contexts. e) Apply and adapt a variety of appropriate strategies to solve problems. f) Use the language of mathematics to express mathematical ideas precisely. g) Recognize and use connections among mathematical ideas. h) Select, apply and translate among mathematical representations to solve problems. Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…) Essential Questions Inquiry used to explore generalizations The student will understand that: 1. Polynomials can be added, subtracted, and multiplied. 2. Polynomial equations can be factored and solved. 3. Factoring is used to solve quadratic equations and find xintercepts. 4. The graph of a quadratic function is a parabola and the xintercepts are solutions to the quadratic equation. 5. Quadratic equations can model real world problems. 1. How do you add, subtract and multiply polynomials? 2. What techniques can you use to factor and solve polynomial equations? 3. How do you solve a quadratic equation? 4. How are quadratic functions and their graphs related? 5. When will you ever use quadratic equations in real life? Knowledge and Skills What students are expected to know and be able to do Students will know… 1. How to perform operations on polynomials. 2. How to factor and solve polynomials. 3. How to use square roots or factoring to solve quadratic equations. 4. How to relate the factors and x intercepts of a quadratic equation. 5. That a parabola is the graph of a quadratic equation. 6. How to write quadratic models for real life situations and find the solution. Students will be able to… 1. Add, subtract, and multiply polynomials. Multiply polynomials using the distributive property, FOIL pattern and special product patterns (Sum and Difference Pattern, Square of a Binomial Pattern). 2. Factor a polynomial using the following techniques. a) GCF and the distributive property. (common monomial factor) b) Special product patterns (Difference of Two Squares, Perfect Square Trinomial). c) Quadratic trinomial where leading coefficient equals 1 or does not equal 1. 3. Solve a quadratic equation by factoring and the zero product property or by finding square roots. 4. Find x intercepts by factoring. 5. Recognize that quadratic equations are U shaped and can be solved by graphing. 6. Apply factoring skills to solve real life problems. STAGE 2: DETERMINE ACCEPTABLE EVIDENCE Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards) Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results As director of the marching high school band, it is your duty to determine if the space allotted your group for the parade is adequate. The band is allowed 3200 square feet in the parade and must stay at least 5 feet from the curb. The width of the street is x feet and the length of the space allotted is x+30 feet. Rows should be 4 feet apart and each row will contain 8 band members. Write a polynomial expression representing the area the band is allotted. Find the dimensions for the area of the space allowed for the band by solving the quadratic equation. Find the number of rows your band will take up. Can all 200 members be in the band? If not, how many square feet are needed.


Five sisters are going to clean their playroom. Alice is the oldest, so she works the fastest. Beth would take twice as long as Alice to clean the room herself. Cathy would take twice as long as Beth. Daria would take two days longer than Cathy, and Elaine would take 4 times as long as Daria. Together, the five girls can clean the room in one day. How long would it take each girl by herself?

the sum of two numbers is 5 and the sum of their squares is 233. what are the numbers?

The perimeter of a rectangle is 532 ft. The length is 10 ft longer than the width. Find the area of the rectangle.

Sandbox with 5 boards, each 8 ft long. how big should the sandbox be?

a circular pond will be placed on a square piece of land. the length of a side of the square is 2x. the radius of the pond is x. the part of the square not covered by the pond will be planted with flowers. what is the area of the region that will be planted with flowers? write your answer in factored form

A company that produces radios has costs given by the function , where x is the number of radios manufactured and C(x) is measured in dollars. The average cost to manufacture each radio is given by 15x+25,000/x

The length of a rectangular walkway is 3 meters longer than twice it`s width. The area of the walkway is 44 square meters. Find the length and width of the walkway.

The length of a rectangular walkway is 3 meters longer than twice it\`s width. The area of the walkway is 44 square meters. Find the length and width of the walkway.


The rectangle rug has a length that is three feet longer than its width. Its area is 130 square feet. What are its dimensions?

A box has a volume of 1,800 cubic cm. The length is 6 times the height. As well, the length is 18 cm longer than the width. If the length is increased by 2 cm, the width by 3 cm and the height by 4 cm, the volume becomes 4,320 cubic ...

a rectanglular box has a square base. the combined length of a side of the square base, and the height is 20 inches. let x be the lenght of a side of the base of the box. write a polynomial function in factored form modeling the volume (V) of the box. what is the maximum possible volume of the box?


suppose that the area of a square is six times its perimeter. Find the length of a side of the square.


The length of the sides of a triangular flower bed can be expressed as integral numbers of feet, and the three integers are consecutive. the product of the shortest and longest length is 27 feet more than 12 times the remaining length. Find the length of each side of the flower bed

2. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?

A diagram shows a rectangular region, one of whose corners lie on the graph of y = x2 + 2x + 4. Write a polynomial in standard form for the area A of the rectangular region.

write a polynomial in standard form for the area A of the rectangular region

the width of a box is 2 m less than the length. the height is 1 m less than the length. the volume is 60 m cubed. find the lenght of the box

A garden plot 4 m by 12 m has one side along a fence as shown at the right. The area of the garden is to be doubled by digging a border of uniform width on the other three sides. What should the width of the border be?

a square field has 4 meters added to its length and two meters added to its width making the total area 195 square meters. write an equation for this situation

A swimming pool measures 30 meters wide by 165 meters long by 2 meters deep. How many gallons of water are required to fill the pool?

A homeowner is installing a swimming pool in his backyard. He wants its length to be 4 feet longer than its width. Then he wants to surround it with a concrete walkway 3 feet wide. If he can only afford 300 square feet of concrete for the ... multiplication of polynomials, polynomials

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long.

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long. wih answer

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long. a) If the deflection at the end of the board is 1 ft, find c b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6


Find a polynomial for the perimeter and for the area. Long side of the rectangle is x+7. What is the perimeter? What is the area?

find the polynomial for the area a+8 and a

solve the perimeter of a rectangle is 104m. The length is 1 m more then twice the width. find the dimensions

Area of a square. Find a polynomial A(x) that represents the area of the shaded region in the accompanying figure.

which of the following expressions represent the product of 3 less than twice x and 2 more than the quantity 3 times x


polynomial functions related to economics

If it takes 3 days to go from the earth to the moon with a distance of 240,000, then how many days would it take to get to Mercury with a distance of 57,000,000?

The portion of the company`s fixed costs allotted to this product is $300, and the supplier`s cost for a set of tile is $6 each. Let x represent the number of tile sets. Find the cost equation for the title. Write the answer in the form C=mx+b.


If a number is added to its square, the result is 56.

Find the polynomial for the perimeter and for the area d 8, d

A pool has a length of 50ft and a width of 30ft. It has a border x by x. Write a polynomial for just the border

the lenght of a rectangle is 8 cm less than 3 times the width. Write a plynomial that represents the area of the rectangle.

find a polynomial for the perimeter and for the area. d+8 by d

A jewelry boc is designed such that its length is twice its width and its depth is 2 inches less than its width. The Volume of the box is 64 cubic inches. Use synthetic division to find the roots of the polynomial

ABCD is rectangular garden plot. P is a garden water tap. Find the distance from the tap to corner C. DB=8m, AP=7m, BP=5m, DP=8m

the length of a rectangle is 4 meters longer than twice its width. If the perimeter of the rectangle is 26 meters. Find its dimensions.

a rectangular garden 30 m by 40 m has two paths of equal width crossing through it as shown. Find the width of each path if the total area covered by the paths is 325 m^2

The difference of the two numbers is a cube, and the difference of their cubes is a square.

anna buy 6 bannanas and anne buy 9 bannanas

Find a polynomial for the perimeter and for the area

. 2x2 +2x + 8x + 8 8. Which is the sum of the areas of the rectangles shown above as a polynomial in simplest form? A. 8x + 4 B. x2 + 8x C. 2x2 + 2x + 4 D. 4x2 + 12x + 4

Find 3 consecutive even numbers where the product of the smaller two numbers is 40 less than the square of the largest number.

The length of a rectangle is 4 cm longer than the width. If the perimeter of the rectangle is 20 centimeters, what is the area of the rectangle?

the length of the smaller rectangle at the right is 1 inch less than twice its width. Both the dimensions of the larger rectangle are 2 inches larger than the smaller rectangle. the area of the shaded region is 86 square rectangle. what is the area of the smaller rectangle

There is a rectangle, perimeter 165, the length is 6.5 more than the width, what is the length and width

A square has sides of length 3x 1 meters. Find a polynomial A(x) that represents the area of the square. Find A(1).

a rectangle is 9 ft longer than it is wide. if it`s area is 52 ft squared, find its dimensions.

. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

Dixie Packaging Company has been contracted to manufacture a box without a top that is to be made by removing squares of width x from the corners of a 15 by 60 inch piece of cardboard. Derive the polynomial that models the volume of the box. What value of x would maximize the volume of the box?

if the area of a bowling lane is 30 feet what are the leanth width

the length of a pool is 30 meters longer than 6 times the width. If the perimeter of the pool is 1,110 meters, what are the dimensions of the pool?

a shipping box is shaped like a rectangular prism. it has a total volumer of 96 cubic inches. the hight is two inches less than the width and length is eight inches longer than the width. what are the dimensions of the box?

Suppose that the length of a rectangle is three cm longer than twice the width&that the perimeter of the rec? a) Set up an equation for the perimeter involving only W, the width of the rectangle. b) Solve this equation algebraically to find the length of the rectangle. Find the width as well

Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 6 more square feet than the smaller. What is the width of the rectangles?

the length of a rectangular garden is one more than it`s width. if the diagonal of this garden is 5 meters long, what are the dimensions of the garden?

factor the polynomial completely, given that x + 10 is a facor. f(x)=x^3+21x^2+140x+300

A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 12 feet across and 8 feet tall. How long should the pieces of PVC plumbing pipe be?

A four foot wide walkway surrounds a 10 foot square pool. what is the perimeter of the walkway? What is the area of the walkway? include units

In the silver streak race, jack ran 2km/h slower than Carole did. If 5 is subtracted from Carole`s rate and then that number is multiplied by Jack`s rate, the result is 62km/h less than Carole`s rate multiplied by4 more than Jack`s rate. How fast did Jack run the race?

In the silver streak race, jack ran 2km/h slower than Carole did. If 5 is subtracted from Carole\`s rate and then that number is multiplied by Jack\`s rate, the result is 62km/h less than Carole\`s rate multiplied by4 more than Jack\`s rate. How fast did Jack run the race?

A rug is shaped like a rectagle whose perimeter is 156ft. The length is 5 tims as long as the width. Find the length and the width


Tim bought some 25 cents and some 29 cents stamps. He paid $7.60 for 28 stamps. How many of each type of stamps did he buy?

Rectangular lot. The length of a rectangular lot is 50 feet more than the width. If the perimeter is 500 feet, then what are the length and width?

A rocket is moving vertically upward with a speed 345m/s when ifs fuel runs out. How much further will it travel upward before starting to fall back to the ground

The length of a rectangle is 8 feet more than the width. The perimeter of the rectangle is 52 feet. Find the length.

Suppose that you have a rectangular garden that is 20 feet wide and 30 feet long. You have two cubic yards of concrete and want to create a sidewalk path around the garden. If you make this path three inches deep, how wide will it be? (Answer in feet, rounded to two decimal places.)
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