s = standard version amount
h = high quality version amount
we know that there were 1090 downloads of the song, meaning s + h = 1090.
we also know that the total amount of MBs downloaded was 3353 MBs, and since the standard is 2.1 MBs and the high quality is 4.9MBs, then 2.1s + 4.9h = 3353.
![\begin{cases} s+h=1090\\ 2.1s + 4.9h = 3353\\[-0.5em] \hrulefill\\ h = 1090 - s \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{2.1s+4.9(1090-s) = 3353} \\\\\\ 2.1s + 5341 - 4.9s = 3353\implies -2.8s + 5341 = 3353 \\\\\\ -2.8s=-1988\implies s = \cfrac{-1988}{-2.8}\implies \boxed{s = 710}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20s%2Bh%3D1090%5C%5C%202.1s%20%2B%204.9h%20%3D%203353%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20h%20%3D%201090%20-%20s%20%5Cend%7Bcases%7D%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20on%20the%202nd%20equation%7D%7D%7B2.1s%2B4.9%281090-s%29%20%3D%203353%7D%20%5C%5C%5C%5C%5C%5C%202.1s%20%2B%205341%20-%204.9s%20%3D%203353%5Cimplies%20-2.8s%20%2B%205341%20%3D%203353%20%5C%5C%5C%5C%5C%5C%20-2.8s%3D-1988%5Cimplies%20s%20%3D%20%5Ccfrac%7B-1988%7D%7B-2.8%7D%5Cimplies%20%5Cboxed%7Bs%20%3D%20710%7D)
Solution: Check the picture I uploaded.
Answer:
60.65
Step-by-step explanation:
The Law of Cosines can help you figure this out. Call the given sides "a" and "b" and the given angle "C". Then the third side, "c" will satisfy the relation ...
c² = a² + b² -2ab·cos(C)
= 33² +37² -2·33·37·cos(120°) = 3679
c = √3679 ≈ 60.65476 ≈ 60.65
The length of the third side is about 60.65 units.
Answer:
0 = a
Step-by-step explanation:
The first thing to do is subtract 5 from both sides.
a + 5 = 5a + 5
- 5 - 5
The 5's cancel out.
Now we have a + 0 = 5a
You next subtract the a from both sides.
a + 0 = 5a
-a -a
0 = 4a
Lastly would to get a by itself so then we divide 4 from both sides
0 = 4a
_ _
4 4
0 = a