Answer:
y = -2x + 8/5
Step-by-step explanation:
3 and 1 are the factors of 3 duhhh lol
n(A) = 26
Solution:
Let us first define the cardinal number of the set.
Cardinal number of the set:
The number of distinct elements in a finite set is called its cardinal number. It is denoted as n(A).
Given set: A = {a, b, c, .... z}
We know that, there are 26 elements in the alphabet "a to z".
Number of elements in the set A = 26
Hence n(A) = 26.
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:
x = 0
Step-by-step explanation:
To 'solve' means to find the x values that make the equation equal zero, so
0 = (3x)/[(x + 5)(x - 4)
Multiply both sides by the denominator to get rid of the fraction
0[(x + 5)(x - 4)] = [(3x)(x + 5)(x - 4)]/[(x + 5)(x - 4)]
0 = 3x
0 = x (divide both sides by 3)
So x = 0 is the solution for this equation
