The height of the doorway is 7 feet less than 5 times its width. if the area is 24 square feet, find the dimensions of the door

(use polynomials)

i feel like it’s 8 and 3 but i don’t know if it’s right or if im even doing it right in the first place

  height: 8 ft

  width: 3 ft

Step-by-step explanation:

You can check your answer against the problem criteria:

  area = (8 ft)(3 ft) = 24 ft^2

  height = -7 +5(3) = -7 +15 = 8 . . . . your height

Your numbers match the requirements.

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The problem statement asks you to "use polynomials." You have not shown work, so we don't know whether you did. (I like to use a graphing calculator.)

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Let x represent the width and y represent the height, both in feet.

  y = -7 +5x . . . . . height is 7 ft less than 5 times width

  xy = 24 . . . . . . . area is 24 square feet

Using the first equation to substitute for y in the second equation, we have ...

  x(-7+5x) = 24

  5x^2 -7x -24 = 0 . . . . . put in standard form (the required polynomial)

  5x^2 -15x +8x -24 = 0 . . . . . facilitate factoring by grouping*

  5x(x -3) +8(x -3) = 0

  (5x +8)(x -3) = 0

The positive solution is x = 3. Then y = 24/3 = 8.

The dimensions are 3 ft wide by 8 ft high.

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* To factor this, we look for factors of 5·(-24) = -120 that sum to -7. Those factors are -15 and +8. There are several ways to get to the binomial factors once you have these numbers, but the "factor by grouping" method is the most easily explained.

it depends on the weather. because i have flown to seattle when it was pouring down rain and there was one time i flew to ohio when it was snowing hard. whats your situation.

step-by-step explanation: