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vazorg [7]
2 years ago
8

Which of the following points lies on the circle whose center is at the origin and whose radius is 10?

Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
6 0

The equation is: \frac{(x - 0)^{2} }{10^{2} } + \frac{(y - 0)^{2} }{10^{2} } = 1

= \frac{x^{2} }{10^{2} } + \frac{y^{2} }{10^{2} } = 1

A) \frac{(\sqrt{10}) ^{2} }{10^{2} } + \frac{(0)^{2} }{10^{2} } = 1

⇒ \frac{10}{100} + 0 = 1   FALSE

B) \frac{(0) ^{2} }{10^{2} } + \frac{(2\sqrt{5})^{2} }{10^{2} } = 1

⇒ 0 + \frac{20}{100} = 1   FALSE

C) \frac{(5\sqrt{2}) ^{2} }{10^{2} } + \frac{(5\sqrt{2})^{2} }{10^{2} } = 1

⇒ \frac{50}{100} + \frac{50}{100} = 1   TRUE

Answer: C


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Describe and correct the error in finding the measure of the angle
DerKrebs [107]

Sorry, it's late, and I'm a bad explainer.

The error is adding (2x-12) with x and 30. This is wrong because you are adding the angles inside the triangle and you are assuming that (2x - 12) is the unlabeled angle INSIDE the triangle, when it is the exterior angle/outside of the triangle.

A straight line is also 180°.

(2x - 12) + ? = 180

30 + x + ? = 180

If you look at the equations, and put parentheses around 30 + x, (30 + x) and (2x - 12) should be the SAME NUMBER. So you could set them equal to each other to find x. (or you could also look at the picture and see that they both need/are missing the same angle)

2x - 12 = 30 + x

x = 42

Now you plug 42 into the exterior angle equation

2(42) - 12 = 84 - 12 = 72°

5 0
3 years ago
Find the first term and common difference of an AP, whose 7th term is 29/6 and 15th term is 11/2.​
777dan777 [17]

Answer:

The first term is 13/3 and the common difference is d = 1/12

The formula is a(n) = 13/3 + (1/12)(n - 1)        

Step-by-step explanation:

The general equation for an arithmetic progression is:

a(n) = a(1) + d(n - 1), where d is the common difference/

Case 1:  n = 7:  29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)

Case 2:  n = 15:  11/2 = a(1) + d(15 - 1) =  a(1) + d(14)

Then our system of linear equations is:

a(1) + 6d = 29/6

a(1) + 14d = 11/2

Let's solve this by elimination by addition and subtraction.  Subtract the first equation from the second.  We get:

                                                             

Substituting 1/12 for d in the first equation, we get:

a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)

Then a(1) = 66/12 - 14/12 = 52/12 = 13/3

The first term is 13/3 and the common difference is d = 1/12

The arithmetic sequence formula for this problem is thus:

a(n) = 13/3 + (1/12)(n - 1)                                                                          8

5 0
3 years ago
B is the midpoint of AC and E' is the midpoint of BD. If A(-9,-4), C(-1, 6), and E(-4,-3), find the coordinates of D.
Ipatiy [6.2K]
The coordinates for D are (-4, -7)

First we must locate point B as it is vital to finding the midpoint of BD. To do this, we take the average of the endpoints AC since B is its midpoint. 

x values = -9 + 1 = -8
Then divide by 2 for the average -8/2 = -4

y values = -4 + 6 = 2
Then divide by 2 for the average 2/2 = 1

Therefore B must be (-4, 1)

Now we know the values of E must be the average of B and D. So we can write equations for each coordinate since we know they are averages. 

x - values = (Bx + Dx)/2 = Ex
(-4 + Dx)/2 = -4 ---> multiply both sides by 2
-4 + Dx = -8 ---> add -4 to both sides
Dx = -4

y - values = (By + Dy)/2 = Ey
(1 + Dy)/2 = -3 ---> multiply both sides by 2
1 + Dy = -6 ---> subtract 1 from both side
Dy = -7

So the coordinates for D must be (-4, -7)
5 0
3 years ago
Read 2 more answers
2x + 7 = 27 or 3 + 3x = 30
Leokris [45]

Step-by-step explanation:

2x + 7 = 27 OR 3 + 3x = 30.

2x = 27 - 7 OR 3x = 30 - 3

2x = 20 OR 3x = 27

x = 20/2 OR x = 27/3

x = 10 OR x = 9

5 0
2 years ago
Find each percentage of 75 explain your reasoning 1.what Is 10%of 75% 2. What is 1% of 75%
kozerog [31]
1. 7.5 because Y/75 X 10/100 = 750 /100 = 7.5
2. .75 because Y/75 X 1/100 = 75/100 = .75
4 0
3 years ago
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