Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of dollars. R(x) = − x² + 6x, C(x) = x + 4.
Find the profit function. Show all work and give the profit function.

Step-by-step explanation:

Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of dollars.

Profit function = Revenue  - cost

So we get profit function by subtracting C(x) from R(x) using algebraic method of subtraction.

Profit function of x

=

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: