Question

Eugene's Computer Repair charges a one time fee to run mandatory diagnostic tests 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 for the situation.
Select all that are true.


Select one or more answers!

Submit

the slope of the function is 20.

The
x
x
-intercept for the function is 59.

it costs $20 per hour to repair a laptop.

a laptop that requires 3 hours of repair will cost $60.

Answer 1

Let's analyze the given function \( c = 20t + 59 \) based on the statements:

1. **The slope of the function is 20.**
- True. The coefficient of \( t \) in the equation represents the slope, which is 20.

2. **The x-intercept for the function is 59.**
- False. The x-intercept occurs when \( c = 0 \). To find the x-intercept, set \( c = 0 \):
\[
0 = 20t + 59 \implies 20t = -59 \implies t = -\frac{59}{20}
\]
This means there is no positive x-intercept in this context since it represents time.

3. **It costs $20 per hour to repair a laptop.**
- True. The coefficient of \( t \), which is 20, represents the hourly rate charged for repairs.

4. **A laptop that requires 3 hours of repair will cost $60.**
- False. If \( t = 3 \):
\[
c = 20(3) + 59 = 60 + 59 = 119
\]
The total cost would be $119.

Based on this analysis, the true statements are:
- The slope of the function is 20.
- It costs $20 per hour to repair a laptop.