I will explain you and pair two of the equations as an example to you. Then, you must pair the others.
1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
-(z + (-17)) = 12 + 17
-(z - 17) = 12 + 17
Distribute -1:
-z + 17 = 12 + 17
Subtract 17 to both sides:
-z = 12
Multiply -1 to both sides:
z = -12
Answer: 24, 44, and 66 
Step-by-step explanation:
Check all of the possible combinations of the faces:
6 × 4 = 24
11 × 4 = 44
11 × 6 = 66
So the answers are 24, 44, and 66
Answer:
here you go..............
Answer:
The answer is D
Step-by-step explanation:
Plug any x value for the y values of f(x) and g(x)
Let's do 0 since it is easier.
f(x)=-2(0)-4=-4
g(x)=-2(0)+2=2
So, g(x) is 6 greater than f(x).
Thus, g is most likely moved 6 units up from f.
Graph the 2 functions on Desmos for a better picture.
