Question

A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.07x^2 + 34x − 140, and the cost of distributing by truck can be modeled as −0.03x^2 + 29x − 150, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.

Answer 1

`f(x) = -0.04x^(2) + 5x+10`

Explanation:

Cost of distributing by train =
`-0.07x^(2) +34x-140`

Cost of distributing by truck =
`-0.03x^(2) + 29x-150`

Let the polynomial = f(x)

f(x) = Cost of distributing by train - Cost of distributing by truck

`f(x) = -0.07x^(2) + 34x -140 -(-0.03x^(2) +29x-150)\\\\f(x) = -0.07x^(2) + 34x -140 + 0.03x^(2) -29x+150\\\\f(x) = -0.07x^(2)+ 0.03x^(2)+ 34x-29x-140+150\\\\f(x) = -0.04x^(2) + 5x+10`