Answer
Smaller
Step-by-step explanation:
The closer it is the 0 the smaller
Prime factor if 8 is 2
Prime factors of 12 are 3 and 4
Answer:
![\boxed{\ell = 12}.](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cell%20%3D%2012%7D.)
Step-by-step explanation:
Let
denote the length of the missing side. Since
and
share one vertex and
, these triangles are similar. This means that:
![\dfrac{AX}{AB} = \dfrac{AY}{AC} \iff \dfrac{\ell}{18+\ell} = \dfrac{14}{14+21} \iff\dfrac{\ell}{18+\ell} = \dfrac{14}{35}.](https://tex.z-dn.net/?f=%5Cdfrac%7BAX%7D%7BAB%7D%20%3D%20%5Cdfrac%7BAY%7D%7BAC%7D%20%5Ciff%20%5Cdfrac%7B%5Cell%7D%7B18%2B%5Cell%7D%20%3D%20%5Cdfrac%7B14%7D%7B14%2B21%7D%20%5Ciff%5Cdfrac%7B%5Cell%7D%7B18%2B%5Cell%7D%20%3D%20%5Cdfrac%7B14%7D%7B35%7D.)
We now multiply both sides by
and solve the equation:
![\dfrac{\ell}{18+\ell} = \dfrac{14}{35} \iff \ell = \dfrac{36}{5} + \dfrac{14}{35}\ell \iff \ell \left(1-\dfrac{14}{35}\right) = \dfrac{36}{5} \iff \dfrac{3}{5}\ell = \dfrac{36}{5}.](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cell%7D%7B18%2B%5Cell%7D%20%3D%20%5Cdfrac%7B14%7D%7B35%7D%20%5Ciff%20%5Cell%20%3D%20%5Cdfrac%7B36%7D%7B5%7D%20%2B%20%5Cdfrac%7B14%7D%7B35%7D%5Cell%20%5Ciff%20%5Cell%20%5Cleft%281-%5Cdfrac%7B14%7D%7B35%7D%5Cright%29%20%3D%20%5Cdfrac%7B36%7D%7B5%7D%20%5Ciff%20%5Cdfrac%7B3%7D%7B5%7D%5Cell%20%3D%20%5Cdfrac%7B36%7D%7B5%7D.)
So we now simply get:
![\boxed{\ell = \dfrac{36}{3} = 12}.](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cell%20%3D%20%5Cdfrac%7B36%7D%7B3%7D%20%3D%2012%7D.)
Answer:
280 miles
Step-by-step explanation:
First you multiply 15 x 4= 60 gallons. You then multiply 4 x 70=280 miles
Hope this helps!