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

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