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              

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x