An open top box is made from a rectangular piece of cardboard, whose length is twice the width, by cutting a 3 in square from each corner and folding up the remaining sides. The area of the bottom of the box is 140 inches squared. What is the width?

Width = 13 inch

Step-by-step explanation:

Assume;

Width = x

Length = 2(width) = 2x

Cut 3 inch from each corner:

Width = x-3-3 = x - 6

Length = = 2x-3-3 = 2x - 6

Area of rectangle = lb

Area of rectangle = [length][width]

Area of rectangle = (2x - 6)(x - 6)

Area of rectangle = (2x - 6)(x - 6)

140 = 2x² - 12x - 6x + 36

2x² - 18x - 104

x² - 9x - 52

x² - (13-4)x - 52

x² - 13x + 4x -52

x(x-13)+4(x-13)

(x-13)(x+4)

So,

x = 13 or x = 4

Width = 13 inch

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3