A rectangle has a perimeter of 23 cm. Its area is 33 cm2. Determine the dimensions of the rectangle. You must show all work to earn full marks. No work
shown & a correct answer will earn a mark of zero.

length = 6 cm; width = 5.5 cm

Step-by-step explanation:

Let the length = x. Let the width = y.

We use the formulas for area and perimeter using x and y, and the given values.

area = length * width

perimeter = 2(length + width)

xy = 33

2(x + y) = 23

Solve the first equation for x:

x = 33/y

Substitute 33/y for x in the second equation.

2(33/y + y) = 23

66/y + 2y = 23

Mulrtiply both sides by y.

66 + 2y^2 = 23y

2y^2 - 23y + 66 = 0

(2y - 11)(y - 6) = 0

2y - 11 = 0   or   y - 6 = 0

y = 11/2 = 5.5   or   y = 6

xy = 33

x * 11/2 = 33

x = 33 * 2/11

x = 6

length = 6 cm; width = 5.5 cm

(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