Answer:
[tex]y=8[/tex]
RS: 77
ST: 46
Step-by-step explanation:
We know that RS and ST together make the line RT. This means the sum of their lengths will be equal to RT.
Since RT is 123, we can create the equation [tex]9y+5+5y+6=123[/tex].
Combining like terms gets us [tex]14y+11=123[/tex]
We can now solve for y by isolating the variable on one side of the equation.
[tex]14y + 11 - 11 = 123-11\\\\14y=112\\\\14y\div14 = 112\div14\\\\y=8[/tex]
Now we know the value of y. We can now substitute this into the expressions for RS and ST to find their values.
RS = [tex]9y+5\\\\(9\cdot8)+5\\\\72+5\\\\77[/tex]
ST = [tex]5y+6\\\\(5\cdot8)+6\\\\40+6\\\\46[/tex]
We can confirm this is correct because [tex]46+77=123[/tex].
Hope this helped!
