Point U is on line segment start overline, T, V, end overline
TV
. Given T, V, equals, x, plus, 10, commaTV=x+10, T, U, equals, 3, x, minus, 8, commaTU=3x−8, and U, V, equals, 10, commaUV=10, determine the numerical length of start overline, T, V, end overline, .
TV
.
First, we know that the length of TV is x + 10 and the length of UV is 10. Therefore, the total length of TV is x + 10 + 10 = x + 20.
Next, we know that U is on the line segment TV, so the sum of lengths TU and UV should be equal to the length TV.
Therefore, TU + UV = TV
(3x - 8) + 10 = x + 20
3x - 8 + 10 = x + 20
3x + 2 = x + 20
2x = 18
x = 9
Now that we have found the value of x, we can substitute it back into the expression for the length of TV:
TV = x + 20
TV = 9 + 20
TV = 29
Therefore, the numerical length of TV is 29 units.