A3-pound bag of apples costs $5.25. what is the unit price of a pound of apples?
a) $1.25 b) $1.75 c) $2.25 d) $2.75 per pound
at this rate, how many pounds of apples can be purchased for $17.50?
a) 8 b) 9 c) 10 d) 11 pounds of apples
let x represent the number of pounds of apples and y the total cost of the apples. what is the equation that represents the direct variation between the total cost of the apples and the number of pounds of apples?
a) y = 1.25x
b) y = 1.75x
c) y = 2.25x
d) y = 2.75x

Part a) A 3-pound bag of apples costs $5.25. What is the unit price of a pound of apples?

we know that

To find the unit price divide the total cost by the total pounds

so

therefore

the answer Part a) is the option b

Part b) At this rate, how many pounds of apples can be purchased for $17.50?

by proportion

therefore

the answer Part b) is the option c

Part c) Let x represent the number of pounds of apples and y the total cost of the apples. What is the equation that represents the direct variation between the total cost of the apples and the number of pounds of apples?

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form or

In this problem the constant of proportionality k is equal to the unit price of a pound of apples

so

The linear equation is equal to

therefore

the answer Part c) is the option b

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0