Real-Life Quadratics: Analyzing Dimensions and Profits

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -4.9t^2 + 10t + 1.5. When will the ball hit the ground?

• 1.75 seconds

• 3.10 seconds

• 2.24 seconds

• 4.50 seconds

The product of two consecutive integers is 72. What are the integers?

• 9 and 10

• 8 and 9

• 7 and 8

• 6 and 7

A company finds that the profit P (in dollars) from selling x items can be modeled by the equation P(x) = -2x^2 + 40x - 100. How many items should the company sell to maximize its profit?

• 20

• 5

• 10

• 15

A rectangular swimming pool has a width that is 4 feet less than its length. If the area of the pool is 96 square feet, what are the dimensions of the pool?

• Length: 8 feet, Width: 4 feet

• Length: 12 feet, Width: 8 feet

• Length: 14 feet, Width: 10 feet

• Length: 10 feet, Width: 6 feet

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. How long will it take for the projectile to reach its maximum height?

• 2 seconds

• 0.5 seconds

• 1 second

• 3 seconds

A farmer wants to create a rectangular pen for his sheep. He has 60 meters of fencing. If the length of the pen is 5 meters more than its width, what are the dimensions of the pen?

• Width: 10 meters, Length: 15 meters

• Width: 20 meters, Length: 25 meters

• Width: 15 meters, Length: 20 meters

• Width: 12.5 meters, Length: 17.5 meters

The area of a triangular park is 120 square meters. If the base of the triangle is 10 meters longer than its height, what are the dimensions of the triangle?

• Height: 5 meters, Base: 15 meters

• Height: 10 meters, Base: 20 meters

• Height: 12 meters, Base: 22 meters

• Height: 8 meters, Base: 18 meters

A rectangular box has a volume of 120 cubic centimeters. If the length is twice the width and the height is 3 centimeters less than the width, what are the dimensions of the box?

• Width: 6 cm, Length: 12 cm, Height: 3 cm

• Width: 5 cm, Length: 10 cm, Height: 2 cm

• Width: 4 cm, Length: 8 cm, Height: 1 cm

• Width: 7 cm, Length: 14 cm, Height: 4 cm

A car's value decreases according to the equation V(t) = -500t^2 + 20000, where V is the value in dollars and t is the time in years. After how many years will the car's value be zero?

• 8.10 years

• 5.00 years

• 7.50 years

• 6.32 years