- A box has a volume of 1,800 cubic cm
*(#3228)*

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 ...

polynomials

- A box with no top is to be made from a piece of metal
*(#3510)*

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 ...

polynomials, factoring polynomials, factoring

- A catering company is designing a box
*(#3145)*

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 ...

polynomials

- A circular pond will be placed
*(#1259)*

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 ...

polynomials

- 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

polynomial functions, functions, polynomials

- A cuts half a rectangular lawn
*(#1081)*

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??

polynomials

- A diver stands at the very end of a diving board
*(#431)*

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}(3L-s) 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

polynomial functions, functions, polynomials

- A homeowner is installing a swimming pool
*(#1838)*

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 manufacturer of screened porches
*(#2631)*

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 ...

polynomials

- A market research finds that at a price
*(#2269)*

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 ...

polynomials

- A photo is 4 inches longer
*(#942)*

A photo is 4 inches longer than it is wide. A 3-inch border is placed around the photo making the total area of the photo and border 165 square ...

polynomials

- A polynomial in x has degree 3
*(#2689)*

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...

polynomials

- A polynomial models the profit a company makes
*(#899)*

The polynomial

s^{3} - 70s^{2} + 1500s - 10800

models the profit a company makes on selling an item at price ...

polynomials

- A quilt patch cut in the shape
*(#1363)*

A quilt patch cut in the shape of a triangle has a base of 5x inches and a height of 1.732x ...

polynomials

- A rectangle has a width
*(#3580)*

A rectangle has a width of 3x+5, the length is twice ...

polynomials

- A rectangle is 15m longer than it is wide
*(#3155)*

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 ...

polynomials

- A rectangular box is (2x + 7) feet wide
*(#1663)*

A rectangular box is (2x + 7) feet wide, (5x + 2) feet long, and (x - 4) feet ...

polynomial functions, functions, polynomials

- A rectangular garden is 5 feet longer
*(#3477)*

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 ...

systems, solving systems of equations, systems of equations, polynomials, solving equations, equations

- A rectangular parking lot
*(#989)*

A rectangular parking lot is 50 ft longer than it is ...

polynomials

- A rectangular picture frame
*(#2383)*

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

perimeter, shapes, polynomials

- A rectangular shipping container
*(#247)*

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 ...

polynomial functions, functions, polynomials

- A rectangular yard has a length
*(#3175)*

A rectangular yard has a length 7 feet greater than it's width. If both dimensions are increased by 8 ...

polynomials

- A red ball and a green ball are simultaneously tossed
*(#3374)*

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 ...

polynomials

- A ruler orders his chamberlain to collect
*(#1294)*

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 ...

polynomials

- A square has sides of length
*(#1289)*

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

polynomials

- A stage is rectangular in shape
*(#1829)*

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

polynomials

- A television video game company has the following total expenses
*(#1899)*

A television video game company has the following total expenses E and total incomes I for producing x number of ...

polynomials

- A triangle has a perimeter
*(#2453)*

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 ...

perimeter, shapes, polynomials

- A triangle has sides
*(#2329)*

A triangle has sides 2x -5, 3x + 1, and 4x + 2...

polynomials

- A triangle has sides
*(#3337)*

A triangle has sides 2x – 5, 3x + 1, and 4x + 2...

polynomials

- A triangle is 10 cm wider than it is tall
*(#3130)*

A triangle is 10 cm wider than it is tall. The area is 28cm^{2}...

polynomials

- A truck and a car leave an intersection
*(#2852)*

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 ...

polynomials

- A water balloon is released from a window
*(#2274)*

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 ...

polynomials

- ABCD is a rectangle
*(#2648)*

ABCD is a rectangle

AC = 4X +6 BD = 5X-2

Find the length of each diagonal.

parallelograms, shapes, plane figures, polynomials

- Alex, Bill and Danny collect tropical fish
*(#2870)*

Alex, Bill and Danny collect tropical fish. Alex has 8 fewer than Danny and Bill has 2 more than ...

polynomials

- Antonio is preparing to make
*(#1291)*

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 ...

polynomials

- At p dollars per ticket
*(#1101)*

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)

polynomials

- Calculate the perimeter of the rectangle
*(#3036)*

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

polynomials

- Choose the polynomial that represents
*(#2923)*

Choose the polynomial that represents the area of the rectangle with sides (x+8) and (x-1)

polynomials

- Colin has a 500 cm ribbon
*(#3487)*

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 ...

polynomials

- Consider the function
*(#1093)*

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 (x-2)...

polynomials

- Division Of Monomials
*(#10604)*

find the missing factor

division of monomials, monomials, polynomials

- Division Of Polynomials
*(#7540)*

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 ...

division of polynomials, polynomials

- Evaluating Binomial Coefficients
*(#6100)*

Find the coefficient of y^6 in (2x-3y^2)^6

evaluating binomial coefficients, binomials, coefficients, polynomials, algebraic equations, algebraic expressions, algebraic fractions, expressions, equations

- Factoring Polynomials
*(#8319)*

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 ...

factoring polynomials, factoring, polynomials

- Factoring Polynomials
*(#8544)*

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 ...

factoring polynomials, factoring, polynomials

- Factoring Polynomials
*(#9358)*

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

factoring polynomials, factoring, polynomials

- Factoring Polynomials
*(#9656)*

without ...

factoring polynomials, factoring, polynomials

- Find 3 consecutive even numbers
*(#1010)*

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

polynomials, consecutive integers, integers, number sense, numbers

- Find 3 consecutive even numbers
*(#3023)*

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

polynomials

- Find 4 consecutive odd integers
*(#3425)*

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

polynomials

- Find a polynomial A(x) that represents the area
*(#1606)*

Find a polynomial A(x) that represents the area of the ...

polynomials

- Find a polynomial for the perimeter and area
*(#1086)*

Find a polynomial for the perimeter and area of a rectangle d +2 and d

polynomials

- Find the area of the rectangle
*(#943)*

Find the area of the rectangle when the width is 10 centimeters.

polynomials

- Find the polynomial that repersents
*(#1737)*

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

polynomials

- Find the polynominal for the rectangle
*(#2634)*

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

polynomials

- Find the remainder when the polynomial
*(#424)*

Find the remainder when the polynomial -x3+7x-6=0 is divided by x-1

synthetic division, polynomial division, division of polynomials, polynomials, division, operations, arithmetic operations

- Find the volume of a cylinder
*(#2192)*

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

polynomials

- Find two consecutive odd integers
*(#2265)*

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

polynomials, consecutive integers, integers, number sense, numbers

- From 1992 to 2003, the number of people in the United States
*(#1854)*

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...

polynomials

- Given a trapezoid where the small base
*(#3207)*

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 ...

polynomials, trapezoids, plane figures, shapes

- Graphing Polynomial Functions
*(#6925)*

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 ...

graphing polynomial functions, graphing, polynomial functions, graphs, functions, polynomials

- Greenshield`s Formula can be used
*(#1541)*

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

polynomials, functions, polynomial functions

- If a cylinder with a height of 3 inches
*(#1849)*

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?

polynomials

- If a vendor charges P dollars
*(#918)*

If a vendor charges P dollars each for rugby shirts, then he expects to sell 2000-100P 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)...

polynomials

- If the ticket agency charges
*(#2108)*

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.

...

polynomials

- If two numbers differ
*(#1802)*

If two numbers differ by 7, then what polynomial represents their ...

polynomials

- In a retail store, a fake diamond ring
*(#245)*

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

monomials, polynomials

- James is 5 years older than Jennifer
*(#2421)*

James is 5 years older than Jennifer. Three years ago the product of their ages was 36 less than the product of their ...

polynomials

- Jurassic Park charges $20 for adults
*(#3468)*

Jurassic Park charges $20 for adults and $12 for children. Total bill for 454 people was $3860...

systems, polynomials, solving systems of equations, systems of equations, solving equations, equations

- Kattya has a square garden
*(#509)*

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}...

binomials, foil method, polynomials

- Linda has a garden
*(#35)*

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 ...

polynomials

- Long Polynomial Division
*(#3832)*

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

long polynomial division, polynomials, binomials

- Monomials
*(#8840)*

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

monomials, polynomials

- Multiplication Of Polynomials
*(#4027)*

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

multiplication of polynomials, polynomials

- Multiplication Of Polynomials
*(#10405)*

suppose that the area of a square is six times its ...

multiplication of polynomials, polynomials

- Operations With Polynomials
*(#4515)*

jennifer traveled 2x+50 miles in the morning and 3x-10 miles in the afternoon. Write a polynomial T(x) that represents the total distance the she traveled. Find the T(20)"

operations with polynomials, polynomials

- Operations With Polynomials
*(#8698)*

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 ...

operations with polynomials, polynomials

- polynomial functions
*(#115)*

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...

polynomial functions, functions, polynomials

- Polynomial representation of the width of a rectangle
*(#2157)*

A(x)=x^{3}-1 the length is x-1

A) Find the polynomial to represent the width of the ...

polynomials

- polynomials
*(#131)*

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 ...

polynomials

- Polynomials
*(#1527)*

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

polynomials

- Polynomials
*(#2026)*

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

polynomials, division of polynomials

- Polynomials
*(#3600)*

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

polynomials

- Polynomials
*(#4223)*

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)

polynomials

- Polynomials
*(#4217)*

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

polynomials

- Polynomials
*(#4252)*

A triangle has sides 3x+7, 4x-9, and 5x +6. Find the polynomial that represents its perimeter

polynomials

- Polynomials
*(#3322)*

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

polynomials

- Polynomials
*(#3733)*

The perimeter of a notebook is 30 inches the length is twice its width find the dimension o the notebook

polynomials

- Polynomials
*(#3889)*

A rectangle has width (x-5) and length (4x+3). If the area of the

rectangle is 105...

polynomials

- Polynomials
*(#4020)*

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...

polynomials

- Polynomials
*(#4071)*

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 ...

polynomials

- Polynomials
*(#4080)*

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

polynomials

- Polynomials
*(#4115)*

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

polynomials

- Polynomials
*(#4161)*

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...

polynomials

- Polynomials
*(#4172)*

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 ...

polynomials

- Polynomials
*(#4386)*

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 (...

polynomials

- Polynomials
*(#4409)*

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 ...

polynomials

- Polynomials
*(#4546)*

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

polynomials

- Polynomials
*(#4786)*

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...

polynomials

- Polynomials
*(#4790)*

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

polynomials

- Polynomials
*(#4805)*

he length width and height of a rectangular bow are consecutive integers, and the largest dimension is k ...

polynomials

- Polynomials
*(#4958)*

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 ...

polynomials

- Polynomials
*(#4969)*

The length and width of a rectangle are consecutive even integers and the length is l ...

polynomials

- Polynomials
*(#5027)*

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

polynomials

- Polynomials
*(#5055)*

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

polynomials

- Polynomials
*(#5164)*

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

polynomials

- Polynomials
*(#5486)*

if a vendor charges p dollars each for a rugby shirts then he expects to sell 2000-100p shirts at a ...

polynomials

- Polynomials
*(#5739)*

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

polynomials

- Polynomials
*(#5743)*

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

polynomials

- Polynomials
*(#5819)*

A retailor of boom boxes knows that at a price of p dollars each, he can sell 900-3p 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

polynomials

- Polynomials
*(#5860)*

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

polynomials

- Polynomials
*(#5957)*

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

polynomials

- Polynomials
*(#5995)*

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

polynomials

- Polynomials
*(#6039)*

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 ...

polynomials

- Polynomials
*(#6188)*

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...

polynomials

- Polynomials
*(#6311)*

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)

polynomials

- Polynomials
*(#6379)*

the area of a right triangle is 44m^2...

polynomials

- Polynomials
*(#6427)*

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 ...

polynomials

- Polynomials
*(#6488)*

pure acid is to be added to a 5% acid solution to obtain 95L of 26% solution. What amounts of each should be ...

polynomials

- Polynomials
*(#6489)*

The sum of two integers is 131...

polynomials

- Polynomials
*(#6503)*

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

polynomials

- Polynomials
*(#6528)*

the product of two odd consecutive integers is 143...

polynomials

- Polynomials
*(#6546)*

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)...

polynomials

- Polynomials
*(#6588)*

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 ...

polynomials

- Polynomials
*(#6635)*

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...

polynomials

- Polynomials
*(#6702)*

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

polynomials

- Polynomials
*(#6874)*

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 ...

polynomials

- Polynomials
*(#6904)*

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

polynomials

- Polynomials
*(#6945)*

The total profit in dollars for sales of x lawn mowers in a given month is given by : P(x) =-0.2x^2+300x-200

How many lawn mowers need to be sold to produce maximum ...

polynomials

- Polynomials
*(#7037)*

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

polynomials

- Polynomials
*(#7183)*

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

polynomials

- Polynomials
*(#7250)*

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 ...

polynomials

- Polynomials
*(#7252)*

if malcolm adds a 10% tip for the ...

polynomials

- Polynomials
*(#7259)*

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 ...

polynomials

- Polynomials
*(#7314)*

Find the maximum volume of a bos that can be made by cutting out ...

polynomials

- Polynomials
*(#7608)*

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 ...

polynomials

- Polynomials
*(#7618)*

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^2-0.0013x^3-372. 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 ...

polynomials

- Polynomials
*(#7673)*

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

polynomials

- Polynomials
*(#7679)*

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 ...

polynomials

- Polynomials
*(#7730)*

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...

polynomials

- Polynomials
*(#7754)*

$25 for each adult. $16 for each child. 254 People went on a cruise and the bill equaled $3000...

polynomials

- Polynomials
*(#7794)*

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

polynomials

- Polynomials
*(#7991)*

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

polynomials

- Polynomials
*(#8059)*

the polynonmial 0.041h-0.018a-2.69 can be used to estimate the lung capacity, in liters, of a female witrh the height h, in centimeters, and age a, in ...

polynomials

- Polynomials
*(#8175)*

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 ...

polynomials

- Polynomials
*(#8271)*

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...

polynomials

- Polynomials
*(#8331)*

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 ...

polynomials

- Polynomials
*(#8391)*

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...

polynomials

- Polynomials
*(#8427)*

the length of a rectangle is 26 centimeters less than 5 times it's width. it's area is 63 square ...

polynomials

- Polynomials
*(#8429)*

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 ...

polynomials

- Polynomials
*(#8538)*

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 ...

polynomials

- Polynomials
*(#8615)*

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

polynomials

- Polynomials
*(#8673)*

the cost of production for an item in a factory is given by the formula c=n^2-9n+14, where n is the number of that item produced. Find the number of units produced if the cost of production is $7800

polynomials

- Polynomials
*(#8732)*

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

polynomials

- Polynomials
*(#8769)*

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)...

polynomials

- Polynomials
*(#8863)*

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

polynomials

- Polynomials
*(#8965)*

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 ...

polynomials

- Polynomials
*(#8967)*

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 ...

polynomials

- Polynomials
*(#8971)*

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

polynomials

- Polynomials
*(#9044)*

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 + ...

polynomials

- Polynomials
*(#9121)*

: 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.

...

polynomials

- Polynomials
*(#9141)*

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 prices as p dollars. b. how many tickets will be sold for a price of $10 each. ...

polynomials

- Polynomials
*(#9146)*

If a garden bed were of length 'n' ...

polynomials

- Polynomials
*(#9215)*

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 ...

polynomials

- Polynomials
*(#9261)*

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

polynomials

- Polynomials
*(#9309)*

Find the length, in ...

polynomials

- Polynomials
*(#9353)*

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

polynomials

- Polynomials
*(#9414)*

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

polynomials

- Polynomials
*(#9418)*

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

polynomials

- Polynomials
*(#9447)*

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 ...

polynomials

- Polynomials
*(#9569)*

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)...

polynomials

- Polynomials
*(#9584)*

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

polynomials

- Polynomials
*(#9604)*

a 26-oz 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

polynomials

- Polynomials
*(#9620)*

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

polynomials

- Polynomials
*(#9637)*

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

polynomials

- Polynomials
*(#9659)*

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 ...

polynomials

- Polynomials
*(#9691)*

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 ...

polynomials

- Polynomials
*(#9721)*

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

polynomials

- Polynomials
*(#9746)*

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 ...

polynomials

- Polynomials
*(#9775)*

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

polynomials

- Polynomials
*(#9785)*

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

polynomials

- Polynomials
*(#9787)*

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 ...

polynomials

- Polynomials
*(#9960)*

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

polynomials

- Polynomials
*(#10028)*

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...

polynomials

- Polynomials
*(#10043)*

the lengths of the sides of a triangle are consecutive even ...

polynomials

- Polynomials
*(#10084)*

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 non-linear 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 x-intercepts.

4. The graph of a quadratic function is a parabola and the x-intercepts 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 ...

polynomials

- Polynomials
*(#10235)*

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

polynomials

- Polynomials
*(#10270)*

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

polynomials

- Polynomials
*(#10271)*

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

polynomials

- Polynomials
*(#10461)*

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

polynomials

- Polynomials
*(#10478)*

If a vendor changes P dollars each for rugby shirts then he expects to sell 2000-100p 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)...

polynomials

- Polynomials
*(#10526)*

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

polynomials

- Polynomials
*(#10536)*

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 ...

polynomials

- Polynomials
*(#10552)*

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

polynomials

- Polynomials
*(#10620)*

A swimming pool measures 30 meters wide by 165 meters long by 2 meters ...

polynomials

- Polynomials
*(#10634)*

find the polynomial for the area a+8 and a

polynomials

- Polynomials
*(#10637)*

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

polynomials

- Polynomials
*(#10669)*

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...

polynomials

- Polynomials
*(#10672)*

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 ...

polynomials

- Polynomials
*(#10693)*

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

polynomials

- Polynomials
*(#10712)*

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

polynomials

- Polynomials
*(#10714)*

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

polynomials

- Polynomials
*(#10740)*

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

polynomials

- Polynomials
*(#10863)*

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

polynomials

- Polynomials
*(#10939)*

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

polynomials

- Polynomials
*(#10947)*

Tim bought some 25 cents and some 29 cents stamps. He paid $7.60 for 28 ...

polynomials

- Polynomials
*(#10955)*

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

polynomials

- Polynomials
*(#10969)*

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

polynomials

- Polynomials
*(#10999)*

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

polynomials

- Pure acid is to be added
*(#255)*

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 ...

polynomials

- Quotient
*(#2509)*

The quotient of two numbers is 4 and their difference is 39...

quotient, polynomials, division, operations, arithmetic operations

- Rational Zeros
*(#9921)*

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 ...

rational zeros, polynomials, rational equations, equations

- Solution A is 10% alcohol
*(#3185)*

Solution A is 10% alcohol. Solution B is 60% ...

factoring trinomials, factoring, trinomials, polynomials

- Suppose that P dollars is invested in a savings account
*(#1819)*

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}

polynomials

- Suppose the market research company find
*(#1718)*

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 ...

polynomials

- Suppose you are at the gas station
*(#1115)*

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? ...

graphing polynomial functions, graphing, graphs, polynomial functions, functions, polynomials, domain of a function, range of a function

- The area of a rectangle
*(#1698)*

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

polynomials

- The area of a rectangle
*(#1993)*

The area of a rectangle is 2x^{2} +7x -9 and the width is x-1...

polynomials

- The area of a rectangle
*(#2076)*

The area of a rectangle is 165 ft squared. The length is 4 ft greater than the ...

polynomials

- The area of a rectangle
*(#2997)*

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

area, shapes, plane figures, polynomials

- The area of a rectangle
*(#3247)*

The area of a rectangle is 165 ft^{2}. The length is 4 ft greater than the ...

polynomials

- The area of a rectangle is given
*(#1044)*

The area of a rectangle is given by the following polynomial 44t-2t^{2}...

multiplication of polynomials, polynomials, multiplication, operations, arithmetic operations

- The area of a rug is 36 square feet
*(#3479)*

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

polynomials

- The base of a triangle is 3 cm greater
*(#3301)*

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

polynomials

- The difference of two positive numbers
*(#2629)*

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

polynomials

- The edge of one cube is 3 shorter
*(#1050)*

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}...

polynomials

- The hypotenuse of a right triangle
*(#347)*

The hypotenuse of a right triangle is 25m long. The length of one leg is 10 m less than twice the ...

polynomials

- The lenght of a rectangle
*(#2372)*

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

shapes, perimeter, polynomials

- The length is 30 meters longer
*(#2766)*

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

polynomials

- The length of a rectangle
*(#474)*

The length of a rectangle is 2 inches more than 3 times the ...

polynomials

- The length of a rectangle
*(#1516)*

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

polynomials

- The length of a rectangle
*(#903)*

The length of a rectangle is 3 inches greater than the ...

polynomials

- The length of a rectangle
*(#1215)*

The length of a rectangle is 11 cm more than its width. The area of the rectangle is 2040 cm2...

polynomials

- The length of a rectangle
*(#1313)*

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}...

polynomials

- The length of a rectangle
*(#2204)*

The length of a rectangle is x+5 and the width is x-2...

polynomials

- The length of a rectangle
*(#2225)*

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

area, shapes, plane figures, polynomials

- The length of a rectangle
*(#2267)*

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 ...

polynomials

- The length of a rectangle
*(#2477)*

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?

polynomials

- The length of a rectangle is 8 cm less than 3 times the width
*(#1645)*

The length of a rectangle is 8 cm less than 3 times the ...

polynomials

- The length of a rectangle is increased
*(#2117)*

The length of a rectangle is increased by 20% and its width 50%...

polynomials

- The length of a rectangular board
*(#3192)*

The length of a rectangular board is 9 meters greater than the width. If the perimeter of the board is 26 ...

polynomials

- The length of a rectangular swimming pool
*(#2541)*

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)

polynomials

- The length of a triangle is twice the width
*(#3261)*

The length of a triangle is twice the width. A square is cut out at the center. The remaining area is 63 square ...

polynomials

- The length of the pool is 30 meters longer
*(#1909)*

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

polynomials

- The mainsail of a lightning sailboat
*(#2883)*

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 ...

polynomials, pythagorean theorem, area, right triangles, shapes, triangles, plane figures, curves, polygons

- The measure of the area of a rectangle
*(#1994)*

The measure of the area of a rectangle is 4m^{2}-3mp+3p-4m. If the dimensions of the rectangle are represented by polynomials with integral ...

polynomials

- The minute hand of a click is 3 cm longer
*(#1063)*

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 ...

polynomials

- The owner of a daycare center plans to have a rectangular sandbox
*(#529)*

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 2x-5. 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 ...

polynomials

- The perimeter of a rectangle
*(#2529)*

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

polynomials

- The perimeter of a rectangular swimming pool
*(#2632)*

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

polynomials

- The product of two consecutive odd numbers
*(#2256)*

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

integers, polynomials, consecutive integers, number sense, numbers

- The revenue for selling y units
*(#1511)*

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...

polynomials

- The Robertsons put a rectangular pool
*(#1842)*

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.

...

multiplication of polynomials, polynomials

- The sides of a sandbox
*(#1859)*

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 ...

polynomials

- The smaller of two numbers
*(#1592)*

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

polynomials

- The square of the largest of the three consecutive integers
*(#1741)*

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

polynomials

- The square of the largest of three consecutive integers
*(#1051)*

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

polynomials, consecutive integers, integers, number sense, numbers

- The sum of the squares of the two
*(#1053)*

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 ...

polynomials, consecutive integers, solving systems of equations, systems of equations, solving equations, systems, equations, integers, number sense, numbers

- The volume of a box
*(#2287)*

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 ...

polynomials

- The volume of a rectangular prism
*(#2862)*

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

polynomials

- The volume of a right circular cylinder
*(#1222)*

The volume of a right circular cylinder is 12 in. Express the height as a function of the ...

polynomials

- The volume of one of the buildings
*(#3034)*

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 ...

polynomials

- The width in feet of the sandbox
*(#1378)*

The width in feet of the sandbox is given by the polynomial 2x-5. If the length of the sandbox is designed to be 10 feet longer than the ...

polynomials

- The width of a triangle is 3 feet less
*(#2023)*

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

polynomials

- The world`s largest swimming pool
*(#1031)*

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 ...

polynomials

- Three students in an outdoor pursuits program
*(#3196)*

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

polynomial functions, functions, polynomials

- Together Steve and Heather`s ages
*(#1072)*

Together Steve and Heather's ages add up to be ten. If we let "x" be Steve's ...

polynomial functions, functions, polynomials

- Two rectangles have same width
*(#1649)*

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 ...

polynomials

- Two rectangles have the same width
*(#2068)*

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 ...

polynomials

- Two rectangles have the same width
*(#3048)*

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 ...

polynomials

- Vanessa built a rectangular pen for her dogs
*(#2993)*

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 ...

polynomials

- What is the area of a square
*(#414)*

What is the area of a square measuring (5a - 2b) cm each side ?

polynomials

- When a certain polynomial is divided
*(#1497)*

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

arithmetic operations, operations, polynomial division, division of polynomials, polynomials, division

- Write an expression for the area
*(#1976)*

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

polynomials

- You are designing a rectangular flower bed
*(#3065)*

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...

polynomials

- You are making a srapbook
*(#2868)*

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 ...

polynomials