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Akimi4 [234]
3 years ago
9

X2 -20x + y^2 - 10y+25=0 identify center of the circle and radius

Mathematics
1 answer:
nlexa [21]3 years ago
5 0

Answer:

Center of the circle = (10, 5)

Radius = 10

Step-by-step explanation:

Look at the picture

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<span>Answers:
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aliya0001 [1]
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1 - 4x + 4x² - 4x + 16x² - 16x³ + 4x² - 16x³ + 16x⁴
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One equation in a system of linear equations is y=2x+1
Rufina [12.5K]

Step-by-step explanation:

<u>Given equation:</u>

  • y = 2x + 1

a. write a second equation so that (1,3) is the only solution of the system

To have only one solution the equation must have a different slope.

<u>Let it be 10, then the y-intercept of y = 10x + b is:</u>

  • 3 = 1*10 + b ⇒ b = -7

<u>And the equation:</u>

  • y = 10x - 7

b. Write a second equation so that the system has infinitely many solutions

<u>To have infinitely many solutions, both equations must be same:</u>

  • y = 2x + 1

c. Write a second equation so that the system has no solutions.

<u>To have no solutions, the equations must have same slope but different y-intercepts:</u>

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3 0
3 years ago
Scores on a final exam taken by 1200 students have a bell shaped distribution with mean=72 and standard deviation=9
SVETLANKA909090 [29]

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean $ \pm $ Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 = $ \frac{68}{100} \times 1200 $

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean $ \pm $ 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to $ \frac{95}{2} \% $ of the values.

Therefore, Scores between 72 and 90 = $ \frac{95}{2(100)} \times 1200 = \frac{95}{200} \times 1200  $

$ \implies 95 \times 12 $ = 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 = $ \frac{2.5}{100} \times 1200 $

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

8 0
3 years ago
Can you please help me on -5(x+2)=-(-5x+1)-x
PilotLPTM [1.2K]

Answer:

x = -1

Step-by-step explanation:

<u>Step 1:  Distribute</u>

-5(x + 2) = -(-5x + 1) - x

-5x - 10 = 5x - 1 - x

<em>-5x - 10 = 4x - 1</em>

<em />

<u>Step 2:  Solve for x</u>

-5x - 10 + 5x = 4x - 1 + 5x

-10 + 1 = 9x - 1 + 1

-9 / 9 = 9x / 9

<em>-1 = x</em>

<em />

Answer:  x = -1

7 0
3 years ago
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