Select all that are true.

Question

eugenes computer repairs charges a one time fee to run a manadatory diagnostic test on a laptop in order to determine what is wrong, plus an hourly rate to repair it. the function c = 20t + 59 can be used to determine the cost, c. to repair a laptop after t hours. select all that are true

a the slope of the function is 20
b the x-intercept for the function is 59.
c it costs $ 20 per hour to repair a laptop
d a laptop that requires 3 hours of repair will cost $60

Answer 1

Let's analyze the function \( c = 20t + 59 \) to determine which statements are true.

1. a. The slope of the function is 20.
   True. In the equation \( c = 20t + 59 \), the coefficient of \( t \) (which represents the hourly rate) is 20, hence the slope is indeed 20.

2. b. The x-intercept for the function is 59.
   False. To find the x-intercept, we set \( c = 0 \): \[ 0 = 20t + 59 \implies 20t = -59 \implies t = -\frac{59}{20} \] Therefore, the x-intercept (the value of \( t \) when \( c = 0 \)) is actually \(-\frac{59}{20}\), not 59.

3. c. It costs $20 per hour to repair a laptop.
   True. The equation indicates that the repair cost increases by $20 for each additional hour of repair time, which means it costs $20 per hour.

4. d. A laptop that requires 3 hours of repair will cost $60.
   False. To calculate the cost for 3 hours of repair, we substitute \( t = 3 \) into the equation: \[ c = 20(3) + 59 = 60 + 59 = 119 \] So the cost will be $119, not $60.

Based on the analysis, the true statements are:

• a. The slope of the function is 20.
• c. It costs $20 per hour to repair a laptop.