A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost, ƒ(m) is a function of the number of miles, m, that the car is driven. In addition to a flat fee of $75, Plan A offers a rate of $0.20 per mile for an unlimited number of miles. Plan B offers a higher mileage rate of $0.35 per mile but does not charge a flat fee for the rental. Create a system of linear functions modeling the cost of the car rental plans, A and B, as a function of the miles driven. For how many miles, m, will the rental fee be the same under both plans A and B?

System of lynear functions:

Plan A: f(m) = 0.20m+75

Plan B: f(m) = 0.35m

Where m, is the number of driven miles.

The rental fee is the same for m = 500 miles

Step-by-step explanation:

We know that plan A offers a rate of $0.20 per mile and a flat fee of $75, so for plan A the function f(m) is defined as:

f(m)=0.20m+75

As we see, if we drive zero miles, the plan A cost $75, which is the flat fee, as the problem says.

We also know plan B offer a rate of $0.35 per miles without any flat fee. So for the plan B the function f(m) is defined as:

f(m)=0.35m

Finally, we need to know for how many miles will the rental fee be the same under both plans A and B. Then, we need to match the functions for plan A and plan B, and clear the value of m:

0.20m + 75 = 0.35m

75 = 0.35m - 0.20m

75 = 0.15m

m = 75/0.15

m = 500 miles

We can probe this result replacing the value of m in both equations, and we obtain that:

For plan A:

f(m=500 miles)=(0.20$/mile)(500miles) + $75

f(m=500 miles)= $175

For plan B:

f(m=500 miles)=(0.35$/mile)(500miles)

f(m=500 miles)= $175

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

idk

step-by-step explanation:

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