Non-linear equations (one variable)

A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 56 square meters, what are the dimensions of the garden?

• The dimensions of the garden are 4 meters by 7 meters.

• The dimensions of the garden are 7 meters by 10 meters.

• The dimensions of the garden are 6 meters by 9 meters.

• The dimensions of the garden are 5 meters by 8 meters.

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x³ + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x³ – 3x – 520. The variable x represents the number of skateboards sold.

What expression represents the profit?

• 27x – 650

• 27x + 390

• 33x – 650

• 33x + 390

Find the area if x = 3.

• 27 units²

• 45 units²

• 33 units²

• 15 units²

The width of a rectangle is 4 inches less than the length. The perimeter is 100 inches. What is the length of the rectangle?

• 23

• 31

• 46

• 27

Darnell and Stephanie work for competing refreshment stand companies. Darian's profit can be modeled using the polynomial 2c² - 7c - 200, where c is the number of items sold. Stephanie's profit can be modeled with the polynomial c² + 8c - 100. Write a polynomial to represent the difference between their profits.

• c² -15c - 100
• 3c² -c - 300
• c² +15c + 300
• 3c² -15c - 100

Sally is creating a rectangular quilt and the length is equal to five inches less than the width. The perimeter is 30 inches. What are the dimensions of the quilt

• width = 10 and length = 5

• Width = 5 and length = 10

• Width = 5 and length = 30

• Width = 30 and length = 5

A rectangular pond has a length that is 10 feet longer than its width. A 2-foot-wide sidewalk surrounds the pond. Which expression best represents the area of both the sidewalk and the pond?

• (w + 2)(w + 12)

• w(w + 10)

• (w + 4)(w + 14)

• (w + 10)(w + 10)

Find three positive consecutive odd integers such that the sum of the squares of the smallest integer and the largest integer is 129 more than the square of the median integer.

• 7, 9, 11

• 9, 11, 13

• 15, 17, 19

• 3, 5, 7

The perimeter of a rectangle is 60 cm. The length of the rectangle is equal to six more than the width. Find the length of the rectangle.

• 12 in

• 18 in

• 24 in

• 36 in

The perimeter of a rectangle is 48cm. If the length is 6cm more than the width, determine the sides.

• length=9cm & width=3cm

• length=9cm & width=15cm

• length=15cm & width=9cm

• length=3cm & width=9cm