Sawyer wants to fence in a rectangular spot for his garden. If he has 92 feet of fencing and works the length of the garden to be five feet less than twice it's width, what will be the area of the garden?

the area of the garden is 493 ft²

Step-by-step explanation:

Let L represent the length of the rectangular garden.

Let W represent the width of the rectangular garden.

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

Perimeter = 2(L + W)

If he has 92 feet of fencing, it means that

2(L + W) = 92

Dividing through by 2, it becomes

L + W = 46 - - - - - - - - - - - -1

He wants the length of the garden to be five feet less than twice its width. This means that

L = 2W - 5

Substituting L = 2W - 5 into equation 1, it becomes

2W - 5 + W = 46

2W + W = 46 + 5

3W = 51

W = 51/3

W = 17 feet

L = 2W - 5 = 2 × 17 - 5

L = 29 feet

The area of the garden is

LW = 29 × 17 = 493 ft²

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.