What is the value of n? <br><br> n=__

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

Evgen [1.6K]

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contain the point (-5 , -3) and has a center at (-2 , 1)

Step-by-step explanation:

The equation of a circle of center (h , k) and radius r is:

(x - h)² + (y - k)² = r²

The given is:

The center of the circle is (-2 , 1)
The circle passes through point (-5 , -3)

The length of the radius is the distance from the center of the circle

to a point on the circle

∵ The formula of the distance is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∵ The center of the circle is (-2 , 1)

∵ The circle passes through point (-5 , -3)

∴ $r=\sqrt{[(-5)-(-2)]^{2}+[(-3)-(1)]^{2}}$

∴ $r=\sqrt{[-3]^{2}+[-4]^{2}}$

∴ $r=\sqrt{9+16}$

∴ $r=\sqrt{25}$

∴ r = 5

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ The center of the circle is (-2 , 1)

∴ h = -2 and k = 1

∵ r = 5

∴ r² = (5)² = 25

- Substitute the values of h , k , r² in the equation of the circle

∴ (x - -2)² + (y - 1)² = 25

∴ (x + 2)² + (y - 1)² = 25

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contains

the point (-5 , -3) and has a center at (-2 , 1)

Learn more:

You can learn more about the equation of the circle in brainly.com/question/9510228

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7 0

3 years ago

Solve the following equation for m.<br> F=mv^2 / r

aleksklad [387]

Answer:

Step-by-step explanation:

F = $\frac{mv^2}{r}$

mv² = Fr

m = $\frac{Fr}{v^2}$

8 0

2 years ago

How many 7 digit phone numbers are there assuming the first digit can't be a 0 or a 1?

Anettt [7]

The first digit can be any one of the numbers 2-9 That a total of 8 numbers.

The next 6 digits can be any permutation of 6 from the numbers 0 to 9.
(10 numbers)

nPr = n! / r!

so here we have 10P6 = 10! / 6! = 10*9*8*7 = 5040

So final answer is 8 * 5040 = 40,320

7 0

3 years ago

Please help me, worth LOTS of points

Aliun [14]

Answer:

a) $91\,+\,0.14 \,x \leq 140$ where " $x$ " stands for the number of miles driven.

b) He can drive as far as 250 miles to keep the rental cost limited to $140.

Step-by-step explanation:

a) Robert wants to make sure that the addition of the costs coming from the car rental per week ($91) plus the amount paid for the coverage of "x" number of miles (which goes as $0.14 times x) does not exceed $140 (which is the same as saying that this total cost must be smaller than or equal to $140.

In math terms, such is written as:

$91\,+\,0.14 \,x \leq 140$

where "x" stands for the number of miles driven.

b) the total number of miles (x) he is allowed to cover given the $140 restriction is obtained by solving for "x" (the number of driven miles) in the inequality of part a):

$91\,+\,0.14 \,x \leq 140\\0.14\,x\leq 140-91\\0.14\,x\leq 49\\x\leq \frac{49}{0.14} \\x\leq 350$

which tells us that the number of driven miles (x) has to be smaller or equal to 350 miles. Then he can drive as far as 250 miles to keep the rental cost limited to $140.

4 0

3 years ago

if possible,find the missing side length labeled with a question mark. if not possible, explain why. on the left at here are 6 i

Lady bird [3.3K]

Answer:

10 inches

Step-by-step explanation:

They're 36 degrees, so corresponding angles are the same, so the middle line is parallel to the bottom line of the triangle.

But the middle line bisects one of the waist lines of the triangle, so this is the middle line, which is equal to half the length of the bottom line

3 0

2 years ago

Read 2 more answers

What is the value of n? n=___cm