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.

Question

Select all that are true.

Select one or more answers!

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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.