What is the center of the circle given by the equation below?

a. (-4 , -8)
b. (4 , -8)
c. (4 , 8)
d. (-4 , 8)

C:  (4, 8)

Step-by-step explanation:

Rewrite the given equation x² - 8x = -y² + 16y - 44 in std. form:

                                              x² - 8x + 16 - 16 + y² - 16y + 64 =  64 - 44,  or

                                                 (x - 4)²  + (y - 8)² = 64 - 44 + 16

         Comparing this to            (x - h)² + (y - k)² = 6²

we see that h = 4 and k = 8.  The radius is 6.  The center is at (4, 8) (Answer C).

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

26?

step-by-step explanation: