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What is the equation of the circle with center (−3, 1) that passes through the point (−5, 3)?

Mariulka [41]

Answer:

( x + 3)^2 + ( y - 1)^2 = 8

Step-by-step explanation:

The equation of a circle with a center and a point

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

( x , y) - any point on the circle

( a, b) - center of the circle

r^2 - radius of the circle

( -3 , 1) - center - ( a, b)

a = -3

b = 1

( -5 , 3) - point - ( x, y)

x = -5

y = 3

Step 1: substitute the center into the equation

( x -(-3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + ( y - 1)^2 = r^2

Step 2 : sub the point into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( -5 + 3)^2 + ( 3 - 1)^2 = r^2

(-2)^2 + 2^2 = r^2

4 + 4 = r^2

8 = r^2

Step 3 : sub the radius into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + (y - 1)^2 = 8

Therefore, the equation of the circle is

( x + 3)^2 + (y - 1)^2 = 8

6 0

3 years ago

Identify the conclusion in a hypothesis test of the following claim and sample data:

Anarel [89]

Answer:

C

Step-by-step explanation:

Firstly, we set up the null and alternative hypothesis as follows;

The null hypothesis is;

H0: μ ≥ 12

The alternative hypothesis is;

Ha : μ < 12

Next step is to calculate the test statistic z

Mathematically;

z = (x - μ )/ σ /√n

= (11.58 - 12) /1.93/√(80

Test statistic z = -1.92

Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel

P(z < -1.92) = 0.0274

P-value = 0.0274

alpha = 0.05

From the above, we can see that

P-value < alpha

And because of this, we are going to reject the null hypothesis and therefore accept the alternative.

We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."

7 0

3 years ago

Jill invested $500 in an account with a compound interest rate of 6%. cheryl invests $600 in an account with a compound interest

34kurt

The time taken by Jill and Cheryl to double their money is 12 years and 18 years respectively.

<h3>What is Algebra?</h3>

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

Jill invested $500 in an account with a compound interest rate of 6%.

Cheryl invests $600 in an account with a compound interest rate of 4%.

The number of years each doubles their money. Using the relation of 72.

$\rm t = \dfrac{72}{r}$

where r is the interest rate and t be the time

The time for the Jill will be

$\rm t = \dfrac{72}{6}\\\\t = 12\\$

The time for the Cheryl will be

$\rm t = \dfrac{72}{4}\\\\t = 18\\$

More about the Algebra link is given below.

brainly.com/question/953809

4 0

1 year ago

Solve the formula v+f−e=2 for e

Bess [88]

Add e to both sides and subtract 2 from both sides :: v+f-2=e

8 0

3 years ago

Sara opens a bank account with $200. The account accrues 2% interest compounded annually.

AleksAgata [21]

<span>A=P(1+rn)nt
A=200(1+.02)^3
A=200(1.02)^3
A=200(1.061208)
A=</span><span>212.2416
which u round to 212.24</span>

5 0

3 years ago