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.
The answer is approximately 8.1
Answer:
x = 55°
Step-by-step explanation:
The sum of the 3 angles in a triangle is 180°
Subtract the sum of the 2 given angles from 180 for x
x = 180° - (75 + 50)° = 180° - 125° = 55°
<h3>
Answer: choice A, graph is moved 7 units up</h3>
The plus 7 at the end will shift the graph 7 units up. Replace y with f(x).
Then we have g(x) = f(x) + 7. Adding 7 to y = f(x) will increase the y value by 7.
Answer: 8 members of the science group decided to watch the science fiction movie
Step-by-step explanation:
When a group of 40 friends goes to the movies at a multiplex, 1/5 of the group decides to watch a science friction movie. This means that the total sum of the members of the group that decided to watch the science fiction movie and the members that did not watch the science fiction movie is 40.
If 1/5 of the group decides to watch a science friction movie, that means that 1/5 of 40 watched the science fiction movie. It becomes
1/5 × 40/= 40/5 = 8
8 members of the science group decided to watch the science fiction movie.
