Question

Select all that are true.
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.**