Question

Use your understandinh of rational functiosn to answer the followinh wuestions about the relationship of concert profit

Answer 1

Question:

Use your understanding of rational functions to answer the following question about the relationship of concert profit P(x)=-25x^2+875x-4750 to concert operating expenses c(x)=4750-125x.

Write an algebraic rule for the function T(x), which gives the ratio of profit to operating expenses, that is, the number of dollars earned for every dollar spent by the concert promoters.

Answer:

$T(x) = \frac{x^2-35x+190}{5x-190}$

Step-by-step explanation:

Given

$P(x)=-25x^2+875x-4750$ --- concert profit

$c(x)=4750-125x.$ --- concert operating exercise

Solving (a): An expression for T(x)

T(x) is the ratio of P(x) to c(x)

So:

$T(x) = \frac{P(x)}{c(x)}$

$T(x) = \frac{-25x^2+875x-4750}{4750-125x}$

Factorize

$T(x) = \frac{-25(x^2-35x+190)}{-25(-190+5x)}$

$T(x) = \frac{x^2-35x+190}{-190+5x}$

Rewrite as:

$T(x) = \frac{x^2-35x+190}{5x-190}$