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20 July, 08:11

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

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Answers (1)
  1. 20 July, 11:19
    0
    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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