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ivanzaharov [21]
3 years ago
13

Solve for x ‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎ ‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎ ‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎ ‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎​

Mathematics
1 answer:
FromTheMoon [43]3 years ago
6 0

Answer:

x = 15.2

Step-by-step explanation:

you can use the Pythagorean Theorem on either half of the large triangle because you know one leg is 29/2 and the hypotenuse is 21

(29/2)² + x² = 21²

210.25 + x² = 441

x² = 230.75

x = \sqrt{230.75}

x = 15.2

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5. Find the volume of the composite space figure to the nearest whole number. (1 point)
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Answer:

  (d)  944 mm³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the distance between bases.

__

<h3>base area</h3>

Here, the base of the prism is a rectangle with a semicircle on top. The circle has a diameter of 9 mm, so a radius of 4.5 mm. The area of the semicircle is ...

  A = 1/2πr² = 1/2π(4.5 mm)² ≈ 31.809 mm²

The area of the rectangle is the product of its length and width.

  A = LW = (9 mm)(6 mm) = 54 mm²

So, the total base area is ...

  31.809 mm² +54 mm² = 85.809 mm²

<h3>prism volume</h3>

The prism volume is this area multiplied by the length of the figure:

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The volume of the figure is about 944 mm³.

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