Suppose the circle with equation (x-2)2 +(y+4)2 = 7 is translated by (x, y)➡️(x + 3,y - 1). What is the equation of the image of the
circle? Explain.

The answer to your question is    (x - 5)² + (y + 5)² = 7      

Step-by-step explanation:

Data

Circle equation      (x - 2)² + (y + 4)² = 7

translated (x,y)  (x + 3, y - 1)

Process

1.- Find the center of the circle

Remember that the center is represented as (h, k)

From the standard equation

                                (x - 2)² + (y + 4)² = 7

h = 2

k = -4

Center = (2, -4)

This is the point that is going to change its position

2.- Determine the new coordinates of the center

New center = (2 + 3, -4 - 1)

                   = (5, -5)

3.- Find the new equation of the circle

                       (x - 5)² + (y + 5)² = 7              

mean, 40.6

step-by-step explanation:

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a