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?
29,45 250 1
O A. f(x) =
| 35x, x > 250)
B. f(x)=
29.x < 250
129+ 35x, x > 250)
O C. f(x)={ 29, x>250
129+. 35x, x5 250
29,7 $250
O D. f(x) =
129+.35(x-250),x > 250)

Step-by-step explanation:

If we call "x" the number of call minutes used with this plan, the piecewise function used to describe it must represent;

a) a constant value of 29 for any x value smaller than or equal to 250

b) a line with positive slope of 0.35 for the region with x larger than 250. The mathematical representation of such increasing straight line, should be given by a line of slope m = 0.35, and containing the point (250, 29) which is the starting point for this right hand side portion of the domain:

So the function should look like:

or as shown above, in a more simplified form:

answer: i can’t tell you that

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204