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:
Step-by-step explanation:
we are given equation as
Since, we have to solve it by using complete square
so, firstly we will complete square
and then we can solve for x
step-1:
Factor 2 from both sides
step-2:
Simplify it
step-3:
Add both sides 3^2
now, we can complete square
step-4:
Take sqrt both sides
step-5:
Add both sides by 3
we get
Answer:
14 feet and 5 inches
Step-by-step explanation:
11 feet + 2 feet= 13 feet
9 inches + 8 inches = 17 inches
17 inches = 1 foot and 5 inches
13 + 1 = 14 feet
5 inches + 0 inches = 5 inches
9514 1404 393
Answer:
x < -2 or 3 < x
Step-by-step explanation:
<u>6x -4 > 14</u>
6x > 18 . . . . add 4
x > 3 . . . . . . divide by 6
<u>3x +10 < 4</u>
3x < -6 . . . . subtract 10
x < -2 . . . . . divide by 3
The solution is the union of disjoint sets:
x < -2 or x > 3
93 in base 10 converted into base 4 would 1131
