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Yakvenalex [24]

3 years ago

13

Which pair of angles are congruent? A) 1 and 8 B) 4 and 6 C) 5 and 6 D) 1 and 7

1 answer:

taurus [48]3 years ago

6 0

Answer:

A

Step-by-step explanation:

because it makes more sense

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Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

8 0

2 years ago

If 2^3^x/8^y = 1/16, what is the value of x - y?

Ksivusya [100]

Answer: fbhgjybjgk byhhhhnkbm j hun. Hhbnbgn

Step-by-step explanation: Hvjgbkgbjh

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2 years ago

A carton has a length of 2 2/3, width of 1 1/3, and height of 1 1/2 feet. What is the volume of the carton?

Phantasy [73]

I hope this helps you

3 0

3 years ago

96 fluid ounce is greater than,less than or equal to 13 c

alekssr [168]

The answer is 96 F,O, >,< or = 13 C. Hop this helps.

7 0

2 years ago

The difference of seven halves and six quarters is multiplied by negative two fifths. Find this rational number.

malfutka [58]

First, the difference is 7/2 - 6/4 = 14/4 - 6/4 = 8/4

Now multiply it: 8/4 x (-2/5) = -16/20 = -4/5

5 0

2 years ago