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.
16x + 9 = 9y-2x Add 2x to both sides
18x + 9 = 9y Divide both sides by 9
2x + 1 = y Switch the sides to make it easier to read
y = 2x + 1
Answer:
C
Step-by-step explanation:
Let's find the area of each of the two circles.
First Circle:
The first circle has a diameter of 10 inches. That means the radius is 5 inches. So, its area is:
Second Circle:
The second circle has a diameter twice that of the first. So, the diameter is 20 inches. This means that the radius is 10 inches. Find the area:
Now, find the ratio between them by dividing:
Simplify:
1/4 is the same as 1:4
So, our answer is C :)
Step-by-step explanation:
just guess and see
Answer:
C) 240
Step-by-step explanation:
b = 20 cm
h = 12 cm
<h3>Area = b . h</h3>
= 20 . 12
= 240 cm²
<h3>#CMIIW</h3>
