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. 6a + 5b
Step-by-step explanation:
36a^2-25b^2
Rewriting as
(6a)^2 - (5b)^2
We know this is the difference of squares
(x^2 -y^2) = (x-y)(x+y)
(6a - 5b) (6a+5b)
Answer:
x=4
Step-by-step explanation:
It's a parallel line so the equation is
100+19x+4=180
19x=180-100-4
19x=76
x=76/19
x=4
Answer:
- x = -1/2(1 +√21) ≈ -2.79129
- x = -1/2(1 -√21) ≈ 1.79129
Step-by-step explanation:
We assume the middle term is supposed to be 4x.
We can remove a common factor of 4 to simplify this a bit.
x^2 +x -5 = 0
This is of the form
ax^2 +bx +c = 0
where a=1, b=1, c=-5.
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The <em>quadratic formula</em> gives the solutions as ...
Filling in the given coefficients, we have ...
x = (-1 ±√(1^2 -4·1·(-5)))/(2·1)
x = (-1±√21)/2
The solutions are x = -1/2(1 +√21) and -1/2(1 -√21).
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<em>If what you wrote is what you intend</em>, then the equation simplifies to 4x^2 -16 = 0.
Dividing by 4 and factoring the difference of squares gives ...
x^2 -4 = 0
(x -2)(x +2) = 0
These factors are zero (hence their product is 0) for the values x = 2 and x = -2.
The solutions are x=2 and x=-2.
Answer:
Triangle 1 - 
(if they want simplest radical form) or 5.4 (if they want to the nearest tenth)
Triangle 2- i couldnt figure this one out- may not be true
Pythagorean Theorem is... C) true for all right triangles
Step-by-step explanation:
