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Algebra 1

8.2.5 Practice

Algebra 18.2.5 Practice
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Complete the following questions to practice the skills you have learned in this lesson.

  1. The expression 9 t + 7.25 represents the cost to purchase tickets for a concert, where t is the number of tickets. A group of friends paid $79.25 for tickets. How many tickets were bought?
  1. 12 tickets
  2. 10 tickets
  3. 8 tickets
  4. 6 tickets

Use the following scenario to answer questions 2 – 4.

A model rocket is launched from a launchpad. The function modeling the height of the rocket, in feet, t seconds after being launched is shown.

f ( t ) = − 15 t 2 + 58 t + 8

  1. Which equation would you solve to find the time at which the rocket hits the ground?
  1. 15 t 2 + 58 t + 8 = 0
  2. − 15 t 2 + 58 t = 0
  3. − 15 t 2 + 58 t = 8
  4. − 15 t 2 + 58 t + 8 = 0
  1. Use a non-graphing method to find the solution to the previous equation to determine the time that has passed when the rocket hits the ground.
  1. 5 seconds
  2. 4 seconds
  3. 3 seconds
  4. 2 seconds
  1. How high off the ground is the launchpad from which the rocket lifts off?
  1. 15 feet
  2. 8 feet
  3. 2 feet
  4. 0 feet

Use the following scenario to answer questions 5 – 8.

The expressions t ( 90 − 3 t ) and − 3 t 2 + 90 t define the same function. The function models the number of lumens emitted by a spotlight in an art exhibit over the course of t seconds.
  1. Which equation represents the time when the spotlight is not emitting any light?
  1. − 3 t 2 + 90 t = 30
  2. − 3 t 2 + 90 t = 0
  3. − 3 t 2 + 90 t = 675
  4. t ( 90 − 3 t ) = − 3 t 2 + 90 t
  1. At what time(s) does the spotlight not emit any light?
  1. 15 seconds
  2. Only 0 seconds
  3. 10 and 25 seconds
  4. 0 and 30 seconds
  1. The artist planned for the spotlight to emit 600 lumens at 10 seconds from the start. At what other time will the spotlight emit 600 lumens of light?
  1. 30 seconds
  2. 25 seconds
  3. 20 seconds
  4. 0 seconds
  1. At 5 seconds, the spotlight will emit 375 lumens. Find another time that the spotlight emits 375 lumens.
  1. 25 seconds
  2. 15 seconds
  3. 10 seconds
  4. 0 seconds

9-10.

A bowling alley models the revenue from sales in one day as a function of the cost to rent a lane per hour, c . Here are two expressions defining the same revenue function.

c ( 160 − 10 c )

160 c − 10 c 2

  1. According to this model, how high would the cost to rent a lane have to be for the bowling alley to make $0 in revenue?
  1. 16.0
  2. 14.0
  3. 10.0
  4. 8.0
  1. What equation can you write to determine the lane cost that would allow the bowling alley to make $640 in revenue?
  1. 160 c − 10 c 2 = 0
  2. 160 c − 10 c 2 + 640 = 0
  3. c ( 160 − 10 c ) = 640
  4. c ( 160 − 10 c ) = 0
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