Answer:
Option C
Step-by-step explanation:
I took this before
To find avg downstream is 39/3 = 13 mph
upstream is 20/4 = 5mph
the average of the 2 is the still water speed which is 8 mph
Step-by-step explanation:
x - 5 < 2 (y - 8) • 1/4
x - 5 < (y - 8) / 2
2 (x - 5) < y - 8
2x - 10 < y - 8
2x - 10 + 8 < y
y > 2x - 2
graph 2x - 2 and shade the section above
Kate would have borrowed $68.32
Answer:
![3^2=x+5](https://tex.z-dn.net/?f=3%5E2%3Dx%2B5)
Step-by-step explanation:
Given equation:
![\log_3(x+5)=2](https://tex.z-dn.net/?f=%5Clog_3%28x%2B5%29%3D2)
<u>Method 1</u>
![\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b](https://tex.z-dn.net/?f=%5Ctextsf%7BUsing%20the%20Log%20law%3A%7D%20%5Cquad%20%5Clog_ab%3Dc%20%5C%3A%5C%3A%20%5CLongleftrightarrow%20%5C%3A%5C%3A%20a%5Ec%3Db)
![\implies \log_3(x+5)=2](https://tex.z-dn.net/?f=%5Cimplies%20%5Clog_3%28x%2B5%29%3D2)
![\implies 3^2=x+5](https://tex.z-dn.net/?f=%5Cimplies%203%5E2%3Dx%2B5)
<u>Method 2</u>
Make both sides of the equation the index to base 3:
![\implies \log_3(x+5)=2](https://tex.z-dn.net/?f=%5Cimplies%20%5Clog_3%28x%2B5%29%3D2)
![\implies 3^{\log_3(x+5)}=3^2](https://tex.z-dn.net/?f=%5Cimplies%203%5E%7B%5Clog_3%28x%2B5%29%7D%3D3%5E2)
Apply the log law
:
![\implies x+5=3^2](https://tex.z-dn.net/?f=%5Cimplies%20x%2B5%3D3%5E2)
Swap sides:
![\implies 3^2=x+5](https://tex.z-dn.net/?f=%5Cimplies%203%5E2%3Dx%2B5)
<u>Solve for x</u>
Although the question hasn't asked to <u>solve for x</u>, here is the solution:
![\implies 3^2=x+5](https://tex.z-dn.net/?f=%5Cimplies%203%5E2%3Dx%2B5)
![\implies 9=x+5](https://tex.z-dn.net/?f=%5Cimplies%209%3Dx%2B5)
![\implies x=9-5](https://tex.z-dn.net/?f=%5Cimplies%20x%3D9-5)
![\implies x=4](https://tex.z-dn.net/?f=%5Cimplies%20x%3D4)
<u>Check</u>
Substitute the found value of x into the original equation:
![x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}](https://tex.z-dn.net/?f=x%3D4%20%5Cimplies%20%5Clog_3%284%2B5%29%3D%5Clog_39%3D2%20%5Cquad%20%5Cleftarrow%5Ctextsf%7Bcorrect%7D)