Use completing the square to find the equation of the following circle in standard form.

3x^2 + 3y^2 - 12x + 36y - 48 = 0

Group of answer choices

(x - 4)^2 + (y + 12)^2 = 176

(x - 2)^2 + (y + 6)^2 = LaTeX: \sqrt{56} 56

(x - 2)^2 + (y + 6)^2 = 56

(x - 2)^2 + (y + 6)^2 = 16

(x + 2)^2 + (y - 6)^2 = 56

(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

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step-by-step explanation:

at each of the parallel lines adjacent angles are supplementary. the angles have special names identifying their positions with respect to the parallel lines and transversal. they are corresponding angles, alternate interior angles, or alternate exterior angles. an angles is congruent to its matched angle.