To find the distance between her home and her latest position:
According to the question, the diagram is,
Consider the right triangle,
AB=120 km
BC=50 km
To find AC:
Using Pythagoras theorem,
![\begin{gathered} AC^2=AB^2+BC^2_{} \\ =120^2+50^2 \\ =14400+2500 \\ =16900 \\ =130\text{ km} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20AC%5E2%3DAB%5E2%2BBC%5E2_%7B%7D%20%5C%5C%20%3D120%5E2%2B50%5E2%20%5C%5C%20%3D14400%2B2500%20%5C%5C%20%3D16900%20%5C%5C%20%3D130%5Ctext%7B%20km%7D%20%5Cend%7Bgathered%7D)
Hence, the distance between the new position and her home is 130 km.
Answer:
um.......but where is Math translation ?
Answer:
k=8192
Step-by-step explanation:
The number of teams,t remaining after each round, r, can be expressed as:
![t=65,536(\frac{1}{2})^r](https://tex.z-dn.net/?f=t%3D65%2C536%28%5Cfrac%7B1%7D%7B2%7D%29%5Er)
- 8 Teams will advance to the quarterfinals.
First, we determine the round,r at which there will be 8 teams left.
![t=65,536(\frac{1}{2})^r\\8=65536*0.5^r\\0.5^r=8 \div 65536\\2^{-1r}=2^{-13}\\-r=-13\\r=13](https://tex.z-dn.net/?f=t%3D65%2C536%28%5Cfrac%7B1%7D%7B2%7D%29%5Er%5C%5C8%3D65536%2A0.5%5Er%5C%5C0.5%5Er%3D8%20%5Cdiv%2065536%5C%5C2%5E%7B-1r%7D%3D2%5E%7B-13%7D%5C%5C-r%3D-13%5C%5Cr%3D13)
Using this value of r
![If \: r=\frac{Log\frac{1}{k}}{Log\frac{1}{2}} \\Since\: r=13\\13=\frac{Log\frac{1}{k}}{Log\frac{1}{2}}\\$Cross Multiply$\\Log\frac{1}{k}=13 X Log 0.5\\ $Using a Log b=Log $b^{a}\\Log\frac{1}{k}= Log 0.5^{13}\\\frac{1}{k}=0.5^{13}\\\frac{1}{k}=\frac{1}{8192}\\k=8192](https://tex.z-dn.net/?f=If%20%5C%3A%20r%3D%5Cfrac%7BLog%5Cfrac%7B1%7D%7Bk%7D%7D%7BLog%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5CSince%5C%3A%20r%3D13%5C%5C13%3D%5Cfrac%7BLog%5Cfrac%7B1%7D%7Bk%7D%7D%7BLog%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%24Cross%20Multiply%24%5C%5CLog%5Cfrac%7B1%7D%7Bk%7D%3D13%20X%20Log%200.5%5C%5C%20%24Using%20a%20Log%20b%3DLog%20%24b%5E%7Ba%7D%5C%5CLog%5Cfrac%7B1%7D%7Bk%7D%3D%20Log%200.5%5E%7B13%7D%5C%5C%5Cfrac%7B1%7D%7Bk%7D%3D0.5%5E%7B13%7D%5C%5C%5Cfrac%7B1%7D%7Bk%7D%3D%5Cfrac%7B1%7D%7B8192%7D%5C%5Ck%3D8192)
Answer:
-20
Step-by-step explanation:
-3x - 7y = -5
Multiply each side by 4
4(-3x - 7y) = -5*4
-12x -28y = -20
Answer:
A
Step-by-step explanation:
there cannot be 2 different points on the same x coordinate