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AlladinOne [14]
1 year ago
7

What is the radius of circle c

Mathematics
1 answer:
Oxana [17]1 year ago
7 0

Answer:

radius = 13

Step-by-step explanation:

Look at the attached picture below. We can calculate radius with the help of the Pythagorean theorem. But first we have to find out the values of the two legs.

First let's find the shorter leg.

<u>Equidistant Chords Theorem</u>

Two chords are congruent if they are equidistant from the center.

Chords in the picture are congruent and that means that the distance from the center to each of them is the same!

Let's calculate the distance. But to get the distance we have to find x first.

Since the distances are the same:

x + 3 = 2x + 1\\2 = x

Therefore:

\text{distance (short leg)} = 2x + 1 = 2\cdot2 + 1 = 5

Let's focus on the longer leg. Since part of the radius is perpendicular to the chord, it actually bisects the chord! That means that the long leg is going to be a half of the length of the chord.

Therefore:

\text{long leg} = \frac{\text{chord}}{2} = \frac{24}{2} = 12

All that is left is the Pythagorean Theorem in the right triangle.

<u>Pythagorean Theorem</u>

\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2

Hypotenuse in our case is the radius.

\text{radius}^2 = 5^2 + 12^2\\\text{radius}^2 = 25 + 144\\\text{radius}^2 = 169\\\text{radius} = 13

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Answer:

D

Step-by-step explanation:

Since there are two types of values here: tokens and dollars, we will need to use the same value across numerators and denominators in the ratio.

Choice D has 11 tokens over $2 equals to t tokens over $16. In both fractions the numerator is tokens and denominator is dollars.

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3 years ago
18/24 = b/12 <br><br> Solve the proportion:
Lemur [1.5K]

Answer:

b=9

Step-by-step explanation:

18/24=3/4

3/4=b/12

cross product

4*b=3*12

4b=36

b=36/4

b=9

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3 years ago
Drug steps in order to correctly solve the equation X -27 equals 62 for X
Norma-Jean [14]

If it’s X-27=62, you have to isolate X. So you would put your -27 on the other side but in doing that you have to change your negative 27 to a positive as it is switching sides. So it would now be, X=62+27, which is 89. Final answer, X=89

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2 years ago
Is it ever possible that sin (A+B)= sin⁡ A+sin⁡ B? If so, explain how. If not, explain why not.
Contact [7]

The formula for the sine sum is

\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)

So, equation

\sin(a)\cos(b)+\cos(a)\sin(b) = \sin(a)+\sin(b)

Cannot be solved with standard ways. However, we can build special cases to make it work.

The most trivial example would be A=B=0. In this case, we have

\sin(0+0)=0 \sin(0) = 0,\quad\sin(0)+\sin(0)=0+0=0

If we work on this idea a little bit, we can produce examples like

A=2k_1\pi,\quad B=2k_2\pi

And again we have

\sin(A+B)=\sin(2\pi(k_1+k_2))=0

\sin(A)+\sin(B)=\sin(2k_1\pi)+\sin(2k_2\pi)=0+0=0

So, yes, it is possible that \sin(A+B)=\sin(A)+\sin(B), although solving the equation directly would be quite difficult.

5 0
3 years ago
Read 2 more answers
Alvin and Simon shared £540 in the ratio 4:5. Alvin gave half of his share to Theo. Simon gave a tenth of his share to Theo. Wha
Liono4ka [1.6K]

Answer:

\frac{5}{18}

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

Divide the amount by 9 to find the value of one part of the ratio

£540 ÷ 9 = £60 ← value of 1 part of the ratio , thus

4 parts = 4 × £60 = £240 ← Alvin's share

5 parts = 5 × £60 = £300 ← Simon's share

\frac{1}{2} × £240 = £120

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Theo receives £120 + £30 = £150 , which as a fraction is

\frac{150}{540} ( divide numerator/ denominator by 30 )

= \frac{5}{18} ← in simplest form

8 0
2 years ago
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