Algebra 2: Solving Linear Equations & Quadratic Heights

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) of renting a car for x miles. How much would it cost to drive 150 miles?

• $100

• $60

• $120

• $80

A rectangle has a length that is 3 meters longer than its width. If the perimeter of the rectangle is 30 meters, write a linear equation to find the width (w) of the rectangle. What is the width?

• 6

• 4

• 8

• 10

The height of a ball thrown into the air can be modeled by the equation h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. What is the maximum height the ball reaches?

• 15 feet

• 25 feet

• 21 feet

• 18 feet

A store sells two types of shirts: regular shirts for $15 each and premium shirts for $25 each. If a customer buys a total of 10 shirts for $200, write a system of linear equations to represent the situation. How many regular shirts did the customer buy?

• 5

• 8

• 3

• 7

The path of a projectile can be modeled by the quadratic function h(t) = -4.9t^2 + 20t, where h is the height in meters and t is the time in seconds. At what time does the projectile hit the ground?

• 4.08

• 5.2

• 6.0

• 3.5

A farmer has a rectangular field with a length that is twice its width. If the area of the field is 200 square meters, write a quadratic equation to find the dimensions of the field. What are the dimensions?

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

• Width: 8 meters, Length: 16 meters

A concert hall has a seating arrangement where the number of seats in each row increases by 5 for every additional row. If there are 8 rows and the total number of seats is 240, write a linear equation to find the number of seats in the first row. How many seats are in the first row?

• 20

• 15

• 5

• 10

The profit (P) from selling x items can be modeled by the equation P(x) = -2x^2 + 40x - 100. What is the maximum profit, and how many items should be sold to achieve this profit?

• Maximum profit is 90 when 8 items are sold.

• Maximum profit is 120 when 15 items are sold.

• Maximum profit is 80 when 5 items are sold.

• Maximum profit is 100 when 10 items are sold.

A swimming pool is being filled with water at a rate of 10 gallons per minute. If the pool can hold 500 gallons, write a linear equation to determine how long it will take to fill the pool. How many minutes will it take?

• 50 minutes

• 100 minutes

• 30 minutes

• 70 minutes

The height of a bridge can be modeled by the quadratic function h(x) = -x^2 + 4x + 1, where x is the distance from the base of the bridge. What is the height of the bridge at its highest point?

• 4

• 6

• 5

• 3