Problem: Craig earns extra money as a lifeguard. He earns $37 for 4 hours and $64.75 for 7 hours.

The answer is: y = 9.25x

Step-by-step explanation:

Let the equation for the proportionality relation is y = mx (1), where y represents the money that Craig earns for a duty of x hours.

Here, m is the constant of proportionality and we have to find its value.

Given that Craig earns $37 for 4 hours duty.

So, from equation (1), we have 37 = 4m, ⇒ m = 9.25

Therefore, the equation becomes y = 9.25x. (Answer)

(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