A builder cuts a rectangular hole in a ceiling to install an exhaust fan. The width is 3 inches less than the length and the area is 180inches squared. Find the length and width of the hole

length of hole = 15 inches

Width of hole = 12 inches

Step-by-step explanation:

Let L represent the length of the hole.

Let W represent the width of the hole.

The width is 3 inches less than the length. It means that

W = L - 3

The formula for determining the area of a rectangle is expressed as

Area = LW

The area of the rectangular hole is 180inches squared. It means that

LW = 180- - - - - - - - - - 1

Substituting W = L - 3 into equation 1, it becomes

L(L - 3) = 180

L² - 3L = 180

L² - 3L - 180 = 0

L² + 12L - 15L - 180 = 0

L(L + 12) - 15(L + 12) = 0

L - 15 = 0 or L + 12 = 0

L = 15 or L = - 12

Since the length cannot be negative, then L = 15

W = L - 3 = 15 - 3

W = 12

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)