Which of the following is a result of shifting a circle with equation (x + 3)2 + (y - 2)2 = 36 right 3 units?

a. the y-coordinate of the center of the circle decreases by 3.
b. the y-coordinate of the center of the circle increases by 3.
c. the x-coordinate of the center of the circle increases by 3.
d. both the x- and y-coordinates of the center of the circle increase by 3.

Option C is correct that is the x-coordinate of the center of the circle increases by 3.

Step-by-step explanation:

The given equation is:

Since, the circle is shifted right 3 units

There, will be no change in y-axis because it is horizontal change.

So, Option A,B and D are discarded.

Therefore, Option C is correct that is the x-coordinate of the center of the circle increases by 3.

9/16

Step-by-step explanation:

Solve for x over the real numbers:

2 x^2 + 3 x - 3 = 0

Divide both sides by 2:

x^2 + (3 x)/2 - 3/2 = 0

Add 3/2 to both sides:

x^2 + (3 x)/2 = 3/2

Add 9/16 to both sides:

x^2 + (3 x)/2 + 9/16 = 33/16

Write the left hand side as a square:

(x + 3/4)^2 = 33/16

Take the square root of both sides:

x + 3/4 = sqrt(33)/4 or x + 3/4 = -sqrt(33)/4

Subtract 3/4 from both sides:

x = sqrt(33)/4 - 3/4 or x + 3/4 = -sqrt(33)/4

Subtract 3/4 from both sides:

 x = sqrt(33)/4 - 3/4 or x = -3/4 - sqrt(33)/4