Deirdre works for a moving company. Her job includes giving clients a price for their move. Deirdre has one function, h(r) = 4r, which gives the number of hours h to pack up a number of rooms r. She has a second function, c(h) = 40h, that gives the price c for the number of hours of packing h. What is the function that gives the price c for a number of rooms r?

The function that gives the price for a number of rooms is .

Step-by-step explanation:

This problem shows a case of composition between two function, which is defined as follows:

(Eq. 1)

Where:

 - Price, measured in US dollars.

- Packing time, measured in hours.

- Number of rooms, dimensionless.

If we know that and , then the composite function is:

(Eq. 2)

The function that gives the price for a number of rooms is .

step-by-step explanation:

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the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is