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alex41 [277]
3 years ago
10

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Mathematics
2 answers:
Vsevolod [243]3 years ago
8 0

<u>Answer:</u>

(x-5)^2+(y+4)^2 = 10^2

<u>Step-by-step explanation:</u>

The formula for the equation of a circle centered at the origin (0, 0) is x^2+y^2 = r^2 but when the center of the circle is not the origin, then you move it back to the center mathematically.

So we have:

(x-5)^2+(y+4)^2 = r^2

Finding the radius r by calculating the distance from the center to the given point:

r= \sqrt{(5-(-3))^2+(-4-2)^2} = \sqrt{64+36} = \sqrt{100} = 10

Therefore, the equation of this circle will be:

(x-5)^2+(y+4)^2 = 10^2


KATRIN_1 [288]3 years ago
5 0

By definition, the equation of a circle, centered at point (a, b) is


(x-a) ^ 2 + (y-b) ^ 2 = r ^ 2


Where r is the radius of the circumference, and is calculated as the distance from the center to any point belonging to the circumference.



We have the center (5, -4) and the point through which the circumference passes (-3, 2), then:

a = 5\\b = -4\\r = \sqrt {(- 3-5) ^ 2 + (2 + 4) ^ 2}\\r = 10


Finally, the equation of the circumference is:

(x-5) ^ 2 + (y + 4) ^ 2 = 10 ^ 2

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The measure of one angle is six more than half the measure of another angle. If the angles are complementary, find both measures
DiKsa [7]

Answer:

The measure of the angles are 34° and 56°

Step-by-step explanation:

Let

x -----> the measure of one angle

y -----> the measure of another angle

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

x+y=90° -----> equation A

x=0.5y+6 ----> equation B

substitute equation B in equation A and solve for y

0.5y+6+y=90

1.5y=90-6

1.5y=84

y=56°

Find the value of x

x=0.5(56)+6=34°

therefore

The measure of the angles are 34° and 56°

8 0
3 years ago
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marusya05 [52]

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3 0
3 years ago
What is the positive solution of x^2 – 36 = 5x
Radda [10]

Answer: 9

Step-by-step explanation:

The equation x^2 - 36 = 5x is a quadratic equation and can be solved thus: x^2 - 36 = 5x x^2 - 5x - 36 = 0 x^2 + 4x - 9x - 36 = 0 x(x + 4) - 9(x + 4) = 0 (x - 9)(x + 4) = 0 x - 9 = 0 or x + 4 = 0 x = 9 or x = -4 Therefore, the positive solution of x^2 - 36 = 5x? is 9.

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3 years ago
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(07.04)<br> The solution to 8x = 32 is x =<br> 3<br> 4<br> 5<br> 6
Elenna [48]
The answer would be 4 after dividing both sides by 8.
4 0
3 years ago
What is the mean absolute deviation for 3 3 4 5 5 4
nikitadnepr [17]

Answer as a fraction = 2/3

Answer in decimal form = 0.667 (approximate)

=======================================================

Explanation:

The first thing we need is to find the mean. Add up the values to get 3+3+4+5+5+4 = 24. Then divide by n = 6 since there are 6 values.

24/n = 24/6 = 4

The mean is 4

Now subtract the mean from each value

  • 3-4 = -1
  • 3-4 = -1
  • 4-4 = 0
  • 5-4 = 1
  • 5-4 = 1
  • 4-4 = 0

Apply absolute value to each result so that the difference is not negative.

We get this new list: {1, 1, 0, 1, 1, 0}

Now compute the mean of that new list to get the final answer

1+1+0+1+1+0 = 4

4/n = 4/6 = 2/3 = 0.667 approximately

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