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Volgvan
2 years ago
13

A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is

84 square inches. Write an equation you can use to find the width (in inches).

Mathematics
1 answer:
Virty [35]2 years ago
8 0

Answer:

  • See below

Step-by-step explanation:

<u>The side of the square is w/2, then its area is:</u>

  • A = (w/2)² = w²/4

<u>The shaded area is the difference of areas of the rectangle and the square:</u>

  • 14w - w²/4 = 84

<u>This can be simplified:</u>

  • 56w - w² = 336
  • w² - 56w + 336 = 0

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For this case we propose a system of equations:

x: Let the variable representing the quantity of Granny Smith apples

y: Let the variable representing the number of Gala apples

According to the statement we have:

x + y = 19\\0.25x + 0.30y = 5.10

From the first equation we have to:

x = 19-y

replacing in the second equation:

0.25 (19-y) + 0.30y = 5.10\\4.75-0.25y + 0.30y = 5.10\\4.75 + 0.05y = 5.10\\0.05y = 5.10-4.75\\0.05y = 0.35\\y = \frac {0.35} {0.05}\\y = 7

So, Carl bought 7 Gala apples

On the other hand:

x = 19-7 = 12

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Answer:

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Answer:

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116x=100×39.32

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divide both sides by 116

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

Source: https://www.tutoreye.com/blog/what-is-the-scope-of-statistics


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