Answer:
The distance between (-3, 2) and (0,3) is √10.
Step-by-step explanation:
As we go from (-3,2) to (0,3), x increases by 3 and y increases by 1.
Think of a triangle with base 3 and height 1. Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):
distance = √(3² + 1²) = √10
The distance between (-3, 2) and (0,3) is √10.
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:
1/64
Step-by-step explanation:
4^(-3)
1/4³
1/64
Answer:
Hello! answer: 25
Step-by-step explanation:
x = 56 because... 56 - 31 = 25 56 + 43 = 99 and x = 56 so 56 + 25 + 99 = 180 Hope that helps!
Answer:
Answer should be 1/4, since it's not there I would suggest 1/2.
Step-by-step explanation:
Its rise/run therefore it going up one and moving four.
