Q11. - Algebra 2

Question

If $\overline{AC}$ is 2 units, what is the value of t?

Step-by-Step Solution

Answer

The value of t is 0.25. 

Step-1 – Apply the concept of line segment

The line segment is a line with two end points. It can be breakdown into small line segments.

Step-2 –Construct the expression

Consider the provided line segment $\overline{AC}$. The length of $\overline{AC}$ is 2 units.

The line segment $\overline{AC}$ is the sum of line segments $\overline{AB}\text{ and }\overline{BC}$.

$\overline{AC}=\overline{AB}+\overline{BC}$

The length of line segment $\overline{AB}$ is 3t and of line segment $\overline{BC}$ is 5t.

Step-3 –Evaluate the expression

The mathematical expression for $\overline{AC}=\overline{AB}+\overline{BC}$ is provided below.

$\begin{array}{c}\overline{AC}=\overline{AB}+\overline{BC}\\ 2=3t+5t\\ 2=8t\\ \frac{2}{8}=t\end{array}$

Divide and simplify.

$t=0.25$

Thus, the value of t is $0.25$.