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klio [65]
3 years ago
10

Prove that the two circles shown below are similar. (10 points) Circle C is shown with a center at negative 3, 1 and a radius of

4. Circle E is shown with a center of 4, 9 and a radius of 3.

Mathematics
1 answer:
Tanya [424]3 years ago
5 0

Answer:

Well, in reality, all circles are similar to each other. They will all have the same angles, and they don't really have side lengths. So, they are similar.

But to PROVE they are similar, we will transform Circle C to match circle E.

Circle C has a center at (-3, 1), and Circle E has a center of (4, 9). For Circle C to have the same center as Circle E, we will translate Circle C 7 units to the right, and 8 units up.

Since Circle C has a radius of 4, and Circle E has a radius of 3, dilate Circle C by a factor of 3/4. That way, the radius is 3 units as well.

And there you go! The two circles will map perfectly on top of each other.

Hope this helps!

You might be interested in
How can I create a sine graph that has a period of 2π and an amplitude of 3?
inna [77]

Hello!


The parent function of the graph of sin is y = sin(x).


Amplitude is the maximum displacement on the graph of a function.

Period is the displacement of x at which the graph of a function begins to repeat.

The period can be found by using the formula: P = \frac{2\pi}{B}.


Since the amplitude is 3, the graph of sin is y = 3sin(x).


Given the period 2π, we can substitute this value into the given formula, P = \frac{2\pi}{B}, to find B.


2π = 2π / B (multiply B to both sides)

2π · B = 2π (divide by 2π)

B = 1


Thus, the equation is y = 3sin(x). I'll post the graph as well.

6 0
3 years ago
Karen spends $450 on monthly bills. Of this total amount, 12% is for phone service, 1/10 is for internet service, and 2/9 is for
finlep [7]
12%= 0.12 = 12/100 = 108/900
1/10 = 90/900
2/9 = 200/900

108/900 + 90/900 + 200/900 = 398/900 used

900- 398 = 502

502/900 = 251/ 450

251/450 × 450 = 251


Karen has $251 for food
4 0
3 years ago
Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word TRY. a. The number of ways
Phantasy [73]

Answer:

a) 6 ways

b) 6 ways

Step-by-step explanation:

a) for all of the letters

for the first letter, we have 3 options

for the second, we have 2 options

for the third, we have 1 option

So the number of options will be;

3 * 2 * 1 = 6

b) for the first, we have 3 options, for the second, we have 2 options

so the number of options will be 3 * 2 = 6 options

8 0
2 years ago
A study of bone density on 5 random women at a hospital produced the following results.
IRINA_888 [86]

Answer:

- 0.9503 ; r is not statistically significant ; 0.9031

Step-by-step explanation:

Given the following :

Age (X) :

37

41

57

65

73

Bone density (Y)

355

345

340

315

310

Using the pearson R value calculator :

The r value of the data % - 0.9503.

This value depicts a very strong negative correlation between age and density of bone.

Using the pearson R calculator to obtain the P- value, the P value obtained is .01332 and hence the r is not significant at P < 0.01.

The Coefficient of determination R^2 can be obtained by getting the square value of R

R^2 = - 0.9503^2

R^2 = 0.90307009

R^2 = 0.9031

8 0
3 years ago
Triangle ABC
Virty [35]

Answer:

15 cm

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

\frac{BC}{EF} =\frac{AC}{DF}.

\frac{18}{x}=\frac{12}{10}

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

\frac{18}{x}=\frac{12}{10}\\ 18*10 = x*12 \\ 180 = 12x \\ 15 = x

5 0
3 years ago
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