Which is an equation of a circle with the center (-5, -7) and radius 6?

A.) (x - 5)^2 + (y - 7)^2 = 6

B.) (x + 7)^2 + (y + 5)^2 = 36

C.) (x + 5)^2 + (y + 7)^2 = 6

D.) (x + 5)^2 + (y + 7)^2 = 36

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Step-by-step explanation:

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Note : a circle with center (a , b) and radius r has an equation of the form:

(x - a)² + (y - b)² = r²

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and according to the provided informations

a = -5

b = -7

r = 6

therefore

the equation of the circle is :

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:)

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240