6/16 or 3/8 because if there are 6 blue out of 16 that it obvious. Please press thank you cuz I hope it helps.
Answer:
![x=5](https://tex.z-dn.net/?f=x%3D5)
Step-by-step explanation:
We have the equation:
![34\cdot 3^{x-2}-2\cdot 3^{x-3}=0.8\cdot 10^{x-2}+10^{x-3}](https://tex.z-dn.net/?f=34%5Ccdot%203%5E%7Bx-2%7D-2%5Ccdot%203%5E%7Bx-3%7D%3D0.8%5Ccdot%2010%5E%7Bx-2%7D%2B10%5E%7Bx-3%7D)
Let's simplify this a bit. Let
. Then
. We can substitute the exponents:
![34\cdot3^u-2\cdot 3^{u-1}=0.8\cdot 10^u+10^{u-1}](https://tex.z-dn.net/?f=34%5Ccdot3%5Eu-2%5Ccdot%203%5E%7Bu-1%7D%3D0.8%5Ccdot%2010%5Eu%2B10%5E%7Bu-1%7D)
Use the properties of exponents, we can write
. We can do the same thing on the right. So:
![34\cdot3^u-2\cdot \frac{3^u}{3}=0.8\cdot 10^u+\frac{10^u}{10}](https://tex.z-dn.net/?f=34%5Ccdot3%5Eu-2%5Ccdot%20%5Cfrac%7B3%5Eu%7D%7B3%7D%3D0.8%5Ccdot%2010%5Eu%2B%5Cfrac%7B10%5Eu%7D%7B10%7D)
We can now factor out a
from the left and a
on the right. This yields:
![3^u(34-2\cdot\frac{1}{3})=10^u(0.8+ \frac{1}{10})](https://tex.z-dn.net/?f=3%5Eu%2834-2%5Ccdot%5Cfrac%7B1%7D%7B3%7D%29%3D10%5Eu%280.8%2B%20%5Cfrac%7B1%7D%7B10%7D%29)
Evaluate the expressions within the parentheses:
![3^u(34-\frac{2}{3})=10^u(\frac{9}{10})](https://tex.z-dn.net/?f=3%5Eu%2834-%5Cfrac%7B2%7D%7B3%7D%29%3D10%5Eu%28%5Cfrac%7B9%7D%7B10%7D%29)
Evaluate:
![3^u(\frac{100}{3})=10^u(\frac{9}{10})](https://tex.z-dn.net/?f=3%5Eu%28%5Cfrac%7B100%7D%7B3%7D%29%3D10%5Eu%28%5Cfrac%7B9%7D%7B10%7D%29)
Now, let's multiply both sides by
. So:
![3^u=10^u(\frac{9}{10})(\frac{3}{100})](https://tex.z-dn.net/?f=3%5Eu%3D10%5Eu%28%5Cfrac%7B9%7D%7B10%7D%29%28%5Cfrac%7B3%7D%7B100%7D%29)
Also, let's divide both sides by
. Multiply on the right:
![\frac{3^u}{10^u}=\frac{27}{1000}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Eu%7D%7B10%5Eu%7D%3D%5Cfrac%7B27%7D%7B1000%7D)
Therefore:
![3^u=27\text{ and } 10^u=1000](https://tex.z-dn.net/?f=3%5Eu%3D27%5Ctext%7B%20and%20%7D%2010%5Eu%3D1000)
We can now substitute back u. Notice that 27 is the same as 3 cubed and 1000 is the same as 10 cubed. So:
![3^{x-2}=3^3\text{ and } 10^{x-2}=10^3](https://tex.z-dn.net/?f=3%5E%7Bx-2%7D%3D3%5E3%5Ctext%7B%20and%20%7D%2010%5E%7Bx-2%7D%3D10%5E3)
Since they have the same base, their exponents must be equal. Therefore:
![x-2=3](https://tex.z-dn.net/?f=x-2%3D3)
Add 2 to both sides:
![x=5](https://tex.z-dn.net/?f=x%3D5)
So, the value of x is 5.
And we're done!
Answer:
Graph B
Step-by-step explanation:
the "x" and "y" represent ![\frac{rise}{run}](https://tex.z-dn.net/?f=%5Cfrac%7Brise%7D%7Brun%7D)
so therefore, it's
,
,
, ![\frac{2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%7D)
you would start at (0,0) or the origin
and count over one and up one, or however many units the fraction/chart tells you to count up