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Romashka-Z-Leto [24]
3 years ago
5

Drag the phrases into the box to match each expression. 3/4x+1/2 ​ 3/4−1/2x ​ ​ 3/4−(x+1/2) ​ 20 pointss!!! i know i must be cra

zy!!!!!!!
Mathematics
1 answer:
fomenos3 years ago
6 0

Answer:

\frac{3}{4}x + \frac{1}{2} = One-half more than three-fourths of a number

\frac{3}{4}-\frac{1}{2}x = Three-fourths minus one-half of a number

\frac{3}{4}-(x+\frac{1}{2}) = three-fourths minus the sum of a number and one-half

Step-by-step explanation:

Suppose x be an unknown number.

∵ 3/4th of a number = \frac{3}{4}x

\frac{3}{4}x + \frac{1}{2} = One-half more than three-fourths of a number

Now, half of a number = \frac{1}{2}x

\frac{3}{4}-\frac{1}{2}x = Three-fourths minus one-half of a number

Sum of a number and one-half = x+\frac{1}{2}

\frac{3}{4}-(x+\frac{1}{2}) = three-fourths minus the sum of a number and one-half

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The area of the shaded region is  \rm (150\sqrt{3} \ - 75\pi ) \ feet^2 option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

<h3>What is a circle?</h3>

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

\rm A = \frac{3\sqrt{3} }{2} a^2  where a is the side length.

\rm A = \frac{3\sqrt{3} }{2} 10^2 ⇒ 150\sqrt{3} \rm feet^2

We have the shortest length = x feet and from the figure:

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x = 5 feet

The radius of the circle r = longer leg

\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3} feet

The area of the circle a = \pi r^2  ⇒ \pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2  

The area of the shaded region = A - a

\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2

Thus, the area of the shaded region is  \rm (150\sqrt{3} \ - 75\pi ) \ feet^2

Learn more about circle here:

brainly.com/question/11833983

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