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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step-by-step explanation:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.