In the diagram below, $RT:TS = 1:2$ and $SR = PQ = 20$. Find $UV$.

It's pretty easy not college levlel just some simple high school geomerty.

12

Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.

Because $ST/SR = 2/3$ and $PQ = SR$, we have

\[\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\]Since $UQ/US = 3/2$, we have $UQ/QS = 3/5$.

We have $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

answer: give more info

step-by-step explanation: