Answer: The correct option is (D) 36 units.
Step-by-step explanation: Given that point V lies between points U and W on UW, where
[tex]UV=2x-4,~~VW=4x+10~~~\textup{and}~~~UW=9x-9.[/tex]
We are to find the length of UW in units.
Since point V lies on the line segment UW, so we must have
[tex]UV+VW=UW\\\\\Rightarrow (2x-4)+(4x+10)=9x-9\\\\\Rightarrow 6x+6=9x-9\\\\\Rightarrow 9x-6x=6+9\\\\\Rightarrow 3x=15\\\\\Rightarrow x=5.[/tex]
Therefore, the length of UW is
[tex]UW=9x-9=9\times5-9=45-9=36~\textup{units}.[/tex]
Thus, the length of UW is 36 units.
Option (D) is correct.
