How many sides does a regular polygon have if each exterior angle measures<br> 20?

Ayden earned a grade of 89% on his multiple choice history final that had a total of

Genrish500 [490]

Answer:

178

Step-by-step explanation:

Method 1: Set up a proportion

Set up an equation of the form:

\frac{\color{red}{\text{part}}}{\color{orange}{\text{whole}}}=

whole

part

=

\,\,\frac{\color{blue}{\text{percent}}}{100}

100

percent

Assign the variable xx to the unknown value:

\color{red}{x}=

x=

\,\,\color{red}{\text{part}}

part

The question asks what \textit{part}part of the total questions is 89%

Substitute the known values with the numbers given in the problem, and the unknown value with xx:

\frac{\color{red}{x}}{\color{orange}{200}}=

200

x

=

\,\,\frac{\color{blue}{89}}{100}

100

89

Solve for xx:

100\cdot\color{red}{x}=

100⋅x=

\,\,\color{orange}{200}\cdot\color{blue}{89}

200⋅89

Cross multiply

\frac{100x}{100}=

100

100x

=

\,\,\frac{17800}{100}

100

17800

Divide both sides by 100

178

Simplify

Method 2: Convert to decimal and multiply

{89}{100}=0.89

89%=

100

89

=0.89

Move decimal 2 places to the left

{Multiply result by the total:}

Multiply result by the total:

0.89{200}=

0.89⋅200=

178

number

percent

178

89%

200

100%

4 0

3 years ago

Read 2 more answers

Find all excluded values for the expression.

ZanzabumX [31]

Answer:

-3

Step-by-step explanation:

For an expression to be undefined,. the denominator must be equal to 0

Therefore, in order to make that expression undefined, we must equate the denominator to 0

6 + 2v = 0

2v = 0 - 6

2v = -6

v = -6/2

v = -3

So in order to make the expression to be equal to 0, v must be -3

6 0

3 years ago

I need help on this question

Cloud [144]

Answer:

D

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form

ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

$A_s=\frac{\theta}{360}*\pi r^2$ where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

$A_s=\frac{60}{360}*\pi (\sqrt{3})^2$ which simplifies a bit to

$A_s=\frac{1}{6}*\pi(3)$ which simplifies a bit further to

$A_s=\frac{1}{2}\pi$ which of course is the same as

$A_s=\frac{\pi}{2}$

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is $\frac{\sqrt{3} }{2}$ . Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

$A=\frac{1}{2}bh$ . There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

$(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2$ which simplifies to

$3=h^2+\frac{3}{4}$ and

$3-\frac{3}{4}=h^2$ and

$\frac{12}{4} -\frac{3}{4} =h^2$ and

$\frac{9}{4} =h^2$

Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!

$A=\frac{1}{2}(\sqrt{3})(\frac{3}{2})$ which simplifies to