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nikklg [1K]
3 years ago
6

What has two expressions that have the same value?

Mathematics
1 answer:
Dmitrij [34]3 years ago
4 0
<span>equivalent expressions</span>
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If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the
Brrunno [24]

Answer:

\left(100\pi - 150\sqrt{3}\right) square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be 10 inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment \sf CH be a height on side \sf AB. Since this triangle is equilateral, the size of each internal angle will be \sf 60^\circ. The length of segment

\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}.

The area (in square inches) of this equilateral triangle will be:

\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}.

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}.

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is 10 inches, the radius of this circle will also be 10 inches.

The area (in square inches) of a circle of radius 10 inches is:

\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi.

The area (in square inches) of the circle that the hexagon did not cover would be:

\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}.

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3 years ago
Evaluate 14+(-9)+(-9)
Vilka [71]
The answer to your question is -4
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Three-eighths of the teachers at Naran's school are men, and 30 of the teachers are women. (Each teacher is either a man or a wo
Vlad1618 [11]

48 teachers     30 w  18 m

5/8=30

3/8=x

5/8 x =3/8 30

remove 8 from both sides

5x=90

x=18

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2 years ago
Help meh pls- 5x(20 divided by 4)to the power of 2
vagabundo [1.1K]

Answer:

125

Step-by-step explanation:

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Describe the transformation of the parent function f(x)=x^2 to 1/2 (x+1)^2-5
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The parent function was moved left one and down five. It also opened up due to the 1/2
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