Answer:
![x=1](https://tex.z-dn.net/?f=x%3D1)
Step-by-step explanation:
A direct variation equation has the following format:
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Where k is a constant.
We know that y is 12 when x is -2. Thus, substitute:
![12=-2k](https://tex.z-dn.net/?f=12%3D-2k)
Divide both sides by -2:
![k=-6](https://tex.z-dn.net/?f=k%3D-6)
So, our direct variation equations is:
![y=-6x](https://tex.z-dn.net/?f=y%3D-6x)
To find what x is when y equals -6, substitute in -6 for y:
![-6=-6x](https://tex.z-dn.net/?f=-6%3D-6x)
Divide both sides by -6:
![x=1](https://tex.z-dn.net/?f=x%3D1)
So, our answer is 1 :)
What’s da problem that u have?
Answer:
A. (55 x 5) - (40 x 5)
Step-by-step explanation:
You are solving how much miles (further along) would the second car be after 5 hours.
The first car averages 40 miles per hour. 5 hours later, it will have averaged about 200 miles in 5 hours (40 x 5 = 200).
The second car averages 55 miles per hour. 5 hours later, it will have averaged about 275 miles in 5 hours (55 x 5 = 275)
Subtract: 275 - 200 = 75
The second car would have averaged 75 more miles than the first car.
~
We have
.
To find inverse function
we substitute x with
and vice-versa to get
![x=\dfrac{f^{-1}(x)+5}{3f^{-1}(x)-1}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7Bf%5E%7B-1%7D%28x%29%2B5%7D%7B3f%5E%7B-1%7D%28x%29-1%7D)
Now solve for
. Note that I will use
instead.
![x=\dfrac{j+5}{3j-1} \\x(3j-1)=j+5 \\3jx-x=j+5 \\3jx-x-j-5=0 \\3jx-j=x+5 \\j(3x-1)=x+5 \\j=\dfrac{x+5}{3x-1}](https://tex.z-dn.net/?f=%3C%2Fp%3E%3Cp%3Ex%3D%5Cdfrac%7Bj%2B5%7D%7B3j-1%7D%20%5C%5C%3C%2Fp%3E%3Cp%3Ex%283j-1%29%3Dj%2B5%20%5C%5C%3C%2Fp%3E%3Cp%3E3jx-x%3Dj%2B5%20%5C%5C%3C%2Fp%3E%3Cp%3E3jx-x-j-5%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3E3jx-j%3Dx%2B5%20%5C%5C%3C%2Fp%3E%3Cp%3Ej%283x-1%29%3Dx%2B5%20%5C%5C%3C%2Fp%3E%3Cp%3Ej%3D%5Cdfrac%7Bx%2B5%7D%7B3x-1%7D%3C%2Fp%3E%3Cp%3E)
So we find that
.
Hope this helps.
Let's say imput is i and that output is o.
The formula is 2 ^ i = o
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
Notice how the numbers match?
Hope this helped :)