Mrs. culland is finding the center of a circle whose equation
is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. her
work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (x2 + 4y + 4) = 3 + 9 + 4

The center of the circle is (-3,-2)

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

where

(h,k) is the center

r is the radius

In this problem we have

Completing the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

therefore

The center of the circle is (-3,-2)

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

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