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:
C
Step-by-step explanation:
look up rules of multiplying radicals.
You can multiply the radicands (the number inside the square root) then take the square root of the new number.
3*21 = 63
Factor 63 into 3*3*7
Pull out 3^2 from inside the square root
leaves you with 3sqrt7 or answer C
Answer: Here.
The Solid formed by the net will be a rectangular pyramid.
There are TWO sets of opposite congruent triangular faces.
The base has an area of 30m2
Step-by-step explanation: Don't listen to the B and C dude.
Answer: Our required probability is 
Step-by-step explanation:
Since we have given that
Number of coins = 3
Number of coin has 2 heads = 1
Number of fair coins = 2
Probability of getting one of the coin among 3 = 
So, Probability of getting head from fair coin =
Probability of getting head from baised coin = 1
Using "Bayes theorem" we will find the probability that it is the two headed coin is given by
Hence, our required probability is
No, the answer is not
