Answer:
Step-by-step explanation:
The average rate of change is given by [g(x_2) - g(x_1)]/(x_2 - x_1). Here, we have x_1 = -2, x_2 = -2 + h, and g(x) = 4/x, so we get:
Average rate of change
= [g(x_2) - g(x_1)]/(x_2 - x_1)
= [4/(-2 + h) - 4/(-2)]/[(-2 + h) - (-2)]
= [4/(-2 + h) + 4/2]/(-2 + h + 2)
= [4/(-2 + h) + 2]/h
To simplfiy this, we combine fractions in the numerator:
[4/(-2 + h) + 2]/h
= [4/(-2 + h) + 2(-2 + h)/(-2 + h)]/h
= {[4 + 2(-2 + h)]/(-2 + h)]}/h
= [(4 - 4 + 2h)/(-2 + h)]/h
= [2h/(-2 + h)]/h
= 2/(-2 + h)
So the average rate of change of g(x) = 4/x between x = -2 and x = -2 + h is 2/(-2 + h).
I hope this helps!
In the form
... y = a(x - h)2 + v
the vertex coordinates are (h, v). These are given in your problem statement as (2, -2).
h = 2
v = -2
Answer:
(2,-1.5)
Step-by-step explanation:
6x-4y=18
-x-6y=7
Switch the second equation from standard form to y=mx+b form
-x-6y=7→ -x=7+6y → multiply both sides by -1→ x=-7-6y
Substitute all of the things that equal x into the other equation into x
6x-4y=18→ 6(-7-6y)-4y=18
Simplify
-42-36y-4y=18
Bring - 42 to the other side and add like terms
-42-36y-4y=18→ -40y= 60
Solve for y
y=-1.5
Choose an equation and plug y in it.
-x-6(-1.5)=7
-x+9=7
-x=-2
Multiply both sides by -1
x=2
6 with and remainder of 2