2) We are filling the storage room with packages of toilet paper. The packages measure 18 inches x 13 inches x 9 inches, the warehouse measures 12 feet by 20 feet by 8 feet. Inside
each box are 9 rolls of toilet paper. How many rolls are in this warehouse?

14,175

Step-by-step explanation:

since measurement of packages are used in inches we will convert warehouse dimension in inches to keep the unit same.

1 foot = 12 inch

dimension of room

12 feet by 20 feet by 8 feet

dimension of room in inches

12 feet = 12*12 inches = 144 inches

20 feet = 12*20 inches = 240 inches

8 feet = 12*8 inches = 96 inches

volume of cube = length *width *height

dimension of room = 144 inches * 240 inches * 96 inches

                        = 3,317,760 cubic inches

volume of 1 package = 18 inches * 13 inches * 9 inches = 2,106 cubic inches.

let there be n packages in the room

volume of n package = n*volume of 1 package = 2,106*n cubic inches.

This volume of n packages should be equal to volume of warehouse

2,106*n= 3,317,760

=> n= 3,317,760/2,106 = 1,575.38

since package cannot be in fraction and value after decimal is less than 5 we will round the value to  1,575.

Thus, no of packages is 1,575

1 package has 9 rolls

1,575 package has 9*1575 rolls

thus, no of rolls in the warehouse = 14,175

(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