Hi there!
The question here is basically asking us to use ratios to find the length of the missing side. To do this, we must first construct a ratio. The best one would be -

Now, just cross multiply and solve for x.



Therefore, the length of the missing side would be
8. Hope this helped!
Answer:
Step-by-step explanation:
If our ratio is apple juice to orange juice, then the proportion will be

If we are looking for how much orange juice she needs if she uses 32 ounces of apple juice, then 32 goes on top of a new ratio and x goes on bottom:

That's the proportion. If you need to solve it, cross multiply to get
8x = 128 so
x = 16 ounces of orange juice
For this case, the first thing we are going to do is define the following variable:
x = unknown number
We now write the following inequality:
5-3x <= 11
We clear x:
5-11 <= 3x
-6 <= 3x
-6/3 <= x
-2 <= x
The solution set is:
[-2, inf)
Answer:
the solution set is:
[-2, inf)
Answer:
9 hours at 9 dollars an hour is 81 dollars so therefore he needs to work 9 weeks in order to raise the money.
Step-by-step explanation:
Answer:
number of terms=9
Step-by-step explanation:
![t_{1}=6\\t_{5}=18\\\\t_{n}=t_{1}+(n-1)d\\18=6+(5-1)d\\18-6=4d\\4d=12\\d=12/4=3\\s_{n}=162\\s_{n}=\frac{n}{2}[2t_{1}+(n-1)d]\\162=\frac{n}{2}[2(6)+(n-1)3]\\162 \times 2=n(12+3n-3)\\324=n(3n+9)\\3n^2+9n-324=0\\n^2+3n-108=0\\n^2+12n-9n-108=0\\n(n+12)-9(n+12)=0\\(n+12)(n-9)=0\\n=-12,9\\n=-12 (rejected)](https://tex.z-dn.net/?f=t_%7B1%7D%3D6%5C%5Ct_%7B5%7D%3D18%5C%5C%5C%5Ct_%7Bn%7D%3Dt_%7B1%7D%2B%28n-1%29d%5C%5C18%3D6%2B%285-1%29d%5C%5C18-6%3D4d%5C%5C4d%3D12%5C%5Cd%3D12%2F4%3D3%5C%5Cs_%7Bn%7D%3D162%5C%5Cs_%7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D%5B2t_%7B1%7D%2B%28n-1%29d%5D%5C%5C162%3D%5Cfrac%7Bn%7D%7B2%7D%5B2%286%29%2B%28n-1%293%5D%5C%5C162%20%5Ctimes%202%3Dn%2812%2B3n-3%29%5C%5C324%3Dn%283n%2B9%29%5C%5C3n%5E2%2B9n-324%3D0%5C%5Cn%5E2%2B3n-108%3D0%5C%5Cn%5E2%2B12n-9n-108%3D0%5C%5Cn%28n%2B12%29-9%28n%2B12%29%3D0%5C%5C%28n%2B12%29%28n-9%29%3D0%5C%5Cn%3D-12%2C9%5C%5Cn%3D-12%20%28rejected%29)
as number of terms can't be negative.