Mulitiplication is the answer
<span>7n + 4 - 5n <= 2(n+2)
Let's simplify these expression first
2n + 4 <= 2(n + 2)
2(n +4) = 2n + 4
The LHS and RHS expressions are the same but the inequality says contrary
Hence 2n + 4 is not less than but equal to 2(n + 2).
7+ 6a >= -4(2-a) - 2a
-4(2-a) - 2a = -8 + 4a - 2a = -8 + 2a. It should be obvious that 7 +6a is greater than the RHS expression.
Suppose a= 2 then we have 7 + 6(2) = 19 while -8 + 2(2) = - 8 + 4 = -4 So it follows that 7 + 6a >= -4(2-4) -2a
4x >= 8. The expression is always true so the equal to option is out.</span>
Answer:
Slope: 2/3
Step-by-step explanation:
You have to first write the equation into slope-intercept form...
y = mx + b
So...
-2x + 3y = -6
becomes...
3y = 2x - 6
y = 2/3x - 2
Which means...
2/3 is the slope
Hope this help :)
Let me know if there are any mistakes!!
Answer:
d. The mapping represents y as a function of x, because each x-value corresponds to exactly one y-value.
Step-by-step explanation:
This would be a function as long as one x-value doesn't correspond to two y-values. If two x-values correspond to one y-value though, it still represents a function.
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.
