Help please

Tracy has a cell phone plan that provides 250 free minutes each month for a flat rate of $29. For any minutes over 250, Tracy is charged $0.35 per minute. Which of the following piecewise functions represents charges based on Tracy's cell phone plan?

A. f(x)={29,x less than or equal to 250} {20+.35x,x>250}
B. f(x)={29,x>250} {20+.35x,xless than or equal to 250}
C. f(x)={29,xless than or equal to 250} {.35x,x>250}
D. f(x)={29,xless than or eual to 250} {29+.35(x-250),x>250}

The correct answer is D.

Tracy's cell phone plan has two different charges depending on the number of minutes used. For the first 250 minutes, Tracy is charged a flat rate of $29, and for any minutes beyond that, Tracy is charged $0.35 per minute.

Therefore, the piecewise function that represents Tracy's charges would be:

f(x) = 29, for x ≤ 250 (charging $29 for the first 250 minutes)
f(x) = 29 + 0.35(x - 250), for x > 250 (charging $29 for the first 250 minutes, and then an additional $0.35 for each additional minute)

So, the correct function is D.

To determine which piecewise function represents Tracy's cell phone charges, we need to consider the conditions given in the problem.

Let's break down the information provided:

- Tracy has 250 free minutes each month for a flat rate of $29.
- For any minutes over 250, Tracy is charged $0.35 per minute.

Now, let's analyze each option:

A. f(x) = {29, x ≤ 250} {20 + 0.35x, x > 250}
This function assigns a flat rate of $29 for all usage up to 250 minutes, which is correct. However, for minutes over 250, it charges $20 + $0.35x, which isn't accurate. It should be charging $0.35 per minute, not adding the total minutes.

B. f(x) = {29, x > 250} {20 + 0.35x, x ≤ 250}
This function assigns a flat rate of $29 for minutes over 250, which is incorrect. The flat rate should be applied up to 250 minutes. It also incorrectly charges $20 + $0.35x for minutes less than or equal to 250.

C. f(x) = {29, x ≤ 250} {0.35x, x > 250}
This function correctly assigns a flat rate of $29 for minutes up to 250. For minutes above 250, it charges $0.35 per minute, which is correct.

D. f(x) = {29, x ≤ 250} {29 + 0.35(x - 250), x > 250}
This function assigns a flat rate of $29 for minutes up to 250, which is correct. For minutes over 250, it charges $29 + $0.35(x - 250), which is accurate. This additional term ensures that the $0.35 per minute charge is applied only to the excess minutes over 250.

Based on the given information, option D. f(x) = {29, x ≤ 250} {29 + 0.35(x - 250), x > 250} represents the charges based on Tracy's cell phone plan.

Not A. It charges double for minutes over 250

Not B. flat rate up till x=250

Not C. Drops the $29 for x>250

Clearly D. Only charges the .35 for those minutes over 250.