Answer:
2
Step-by-step explanation:
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.
Answer:
3x=21
X=7
Step-by-step explanation:
Step-by-step explanation:
This is a probability related problem.
Probability is the likelihood of an event to occur;
Pr = 
The sample space here is from 1 to 25 which is 25
A.
Pr of a card marked 8; we have just 1 possible outcome;
Pr(8) = 
B.
Pr of drawing a card that is a multiple of 5;
Multiples of 5 = 5, 10, 15 and 25
Pr (multiples of 5) = 
C.
Pr of drawing a card with odd numbers:
Number of odd numbers between 1 and 25 = 13
Pr(odd numbers) = 
D.
Pr of drawing a number with square number on it;
Square numbers between 1 and 25 = 1, 4, 9, 16 and 25
Pr(square numbers) = 
= 
