Answer:
10
Step-by-step explanation:
Answer:
![f(x) = 2[\frac{3^x}{9}] + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%5B%5Cfrac%7B3%5Ex%7D%7B9%7D%5D%20%2B%202)
![f(x) = 8(4)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%208%284%29%5Ex)
Step-by-step explanation:
Given
![f(x) = 2(3)^{x-2} + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%283%29%5E%7Bx-2%7D%20%2B%202)
![f(x) = \frac{1}{2}(4)^{x+2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284%29%5E%7Bx%2B2%7D)
Required
Remove the h component
In a function, the h component is highlighted as:
![f(x) = a^{x+h}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20a%5E%7Bx%2Bh%7D)
So, we have:
![f(x) = 2(3)^{x-2} + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%283%29%5E%7Bx-2%7D%20%2B%202)
Split the exponents using the following law of indices:
![a^m/a^n = a^{m-n}](https://tex.z-dn.net/?f=a%5Em%2Fa%5En%20%3D%20a%5E%7Bm-n%7D)
![f(x) = 2*\frac{3^x}{3^2} + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%2A%5Cfrac%7B3%5Ex%7D%7B3%5E2%7D%20%2B%202)
![f(x) = 2*\frac{3^x}{9} + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%2A%5Cfrac%7B3%5Ex%7D%7B9%7D%20%2B%202)
![f(x) = 2[\frac{3^x}{9}] + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%5B%5Cfrac%7B3%5Ex%7D%7B9%7D%5D%20%2B%202)
<em>The h component has been removed</em>
![f(x) = \frac{1}{2}(4)^{x+2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284%29%5E%7Bx%2B2%7D)
Split the exponent using the following law of indices
![a^{m+n} =a^m * a^n](https://tex.z-dn.net/?f=a%5E%7Bm%2Bn%7D%20%3Da%5Em%20%2A%20a%5En)
So, we have:
![f(x) = \frac{1}{2}(4)^x * 4^2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284%29%5Ex%20%2A%204%5E2)
Express 4^2 as 16
![f(x) = \frac{1}{2}(4)^x * 16](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%284%29%5Ex%20%2A%2016)
Divide 16 by 2
![f(x) = 8(4)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%208%284%29%5Ex)
Answer:
Each hotdog costs $1.65
Each juice drink costs $1.05
Step-by-step explanation:
Let's begin by letting
represent the number of hot dogs and
the number of juice drinks.
The Baxter family bought 6 hot dogs and 4 juices for $14.10.
![6x + 4y = 14.10](https://tex.z-dn.net/?f=6x%20%2B%204y%20%3D%2014.10)
The Farley family bought 3 hot dogs and 4 juices for $9.15.
![3x + 4y = 9.15](https://tex.z-dn.net/?f=3x%20%2B%204y%20%3D%209.15)
Now, we subtract these equations.
![6x + 4y = 14.10\\- (3x + 4y = 9.15)](https://tex.z-dn.net/?f=6x%20%2B%204y%20%3D%2014.10%5C%5C-%20%283x%20%2B%204y%20%3D%209.15%29)
Since
has reversed coefficients, it gets eliminated. Now solve for x.
![6x+4y-3x-4y=14.1-9.15\\3x = 4.95\\\frac{3x}{3} = \frac{4.95}{3}](https://tex.z-dn.net/?f=6x%2B4y-3x-4y%3D14.1-9.15%5C%5C3x%20%3D%204.95%5C%5C%5Cfrac%7B3x%7D%7B3%7D%20%3D%20%5Cfrac%7B4.95%7D%7B3%7D)
![\frac{4.95}{3} = 1.65](https://tex.z-dn.net/?f=%5Cfrac%7B4.95%7D%7B3%7D%20%3D%201.65)
![x = 1.65](https://tex.z-dn.net/?f=x%20%3D%201.65)
NOW, we find y by substituting x with 1.65 (in either equation).
We'll use the first equation.
![6x + 4y = 14.10](https://tex.z-dn.net/?f=6x%20%2B%204y%20%3D%2014.10)
![6(1.65) + 4y = 14.10](https://tex.z-dn.net/?f=6%281.65%29%20%2B%204y%20%3D%2014.10)
![9.9 + 4y = 14.10\\4y = 14.1 - 9.9\\4y = 4.2](https://tex.z-dn.net/?f=9.9%20%2B%204y%20%3D%2014.10%5C%5C4y%20%3D%2014.1%20-%209.9%5C%5C4y%20%3D%204.2)
![\frac{4y}{4} = \frac{4.2}{4} \\y = 1.05](https://tex.z-dn.net/?f=%5Cfrac%7B4y%7D%7B4%7D%20%3D%20%5Cfrac%7B4.2%7D%7B4%7D%20%5C%5Cy%20%3D%201.05)
= 1.65
= 1.05
represents hotdogs and
represents juice drinks.
Therefore, each hotdog costs $1.65 and each juice drink costs $1.05.
<em> I hope this helps! :)</em>
Answer:
3 divided by 1/2
Step-by-step explanation:
turn 3 into 3/1 then flip 1/2 into 2/1 and multiply which is <u><em>6</em></u>
Kcf
Keep
Change
Flip
The right answer is <u>Many kids went directly from grammar school to special vocational schools sponsored by private agencies. . .</u>
I hope it helps :)