The amount of energy a microwave oven uses (in the form of electricity) is given by the function f (x) = 5x+9, where x is the amount of time the microwave is turned on. The amount of energy the microwave puts out is modeled by the function g (x) = -x^2+3x+1, where x is the amount of time the microwave is turned on.

What is the difference between the amount of energy the microwave uses and the amount it puts out?

(x) = x^2+2x+8

f (x) = -x^2-2x-8

f (x) = -x^2+8x+10

f (x) = x^2-8x-10

The difference between the amount of energy the microwave uses and the amount it puts out is x² + 2x + 8 ⇒ first answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The amount of energy a microwave oven uses is given by the

function f (x) = 5x + 9

- The amount of energy the microwave puts out is given by the

function g (x) = - x² + 3x + 1

- x is the amount of time the microwave is turned on in

both functions

- To find the difference between the amount of energy the

microwave uses and the amount it puts out we will subtract

g (x) from f (x)

* Lets do that

∵ f (x) = 5x + 9

∵ g (x) = - x² + 3x + 1

∴ The difference = 5x + 9 - (-x² + 3x + 1) ⇒ multiply the bracket by (-)

- Remember that (-) (-) = (+) and (-) (+) = (-)

∴ The difference = 5x + 9 + x² - 3x - 1 ⇒ Add the like terms

∴ The difference = x² + (5x - 3x) + (9 - 1)

∴ The difference = x² + 2x + 8

* The difference between the amount of energy the microwave uses

and the amount it puts out is x² + 2x + 8