Answer: m∠F=67°
Step-by-step explanation:
Given the right triangle FHG and the lengths of all its sides:
![FG=5\\HG=12\\FH=13](https://tex.z-dn.net/?f=FG%3D5%5C%5CHG%3D12%5C%5CFH%3D13)
You can calculate the measure of the angle identified as m∠F with:
![\alpha=arctan(\frac{opposite}{adjacent})](https://tex.z-dn.net/?f=%5Calpha%3Darctan%28%5Cfrac%7Bopposite%7D%7Badjacent%7D%29)
Where the opposite side is 12, the adjacent side is 5 and the angle
is m∠F.
Then, substituting values into
:
![F=arctan(\frac{12}{5})\\F=67.38\°](https://tex.z-dn.net/?f=F%3Darctan%28%5Cfrac%7B12%7D%7B5%7D%29%5C%5CF%3D67.38%5C%C2%B0)
To the nearest degree:
m∠F=67°
The last one because he has negative money so he has a liability to pay that money back
Answer:
Step-by-step explanation:
The phrase "twice as much lemonade" tells you that if Mark sold 2 gallons and Regan sold twice as much as Mark, then Regan sold 2 * 2 which is 4 gallons, right? It's the same with the "2/3 as much". But since 2/3 is less than 1, the amount after you multiply some number by 2/3 is going to be less than the original number.
If Mark sold 2 7/8 gallons and Regan sold 2/3 as much, then Regan sold
![2\frac{7}{8}*\frac{2}{3}](https://tex.z-dn.net/?f=2%5Cfrac%7B7%7D%7B8%7D%2A%5Cfrac%7B2%7D%7B3%7D)
I teach my algebra students to change that mixed fraction into an improper to make the multiplication easier:
![\frac{23}{8}*\frac{2}{3}=\frac{46}{24}=\frac{23}{12}=1\frac{11}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B23%7D%7B8%7D%2A%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B46%7D%7B24%7D%3D%5Cfrac%7B23%7D%7B12%7D%3D1%5Cfrac%7B11%7D%7B12%7D)