Question

1. which of the following is the graph of $y - 1 = \frac{1}{4}(x - 1)$? (four graphs labeled a, b, c, d)
2. which of the following is the graph of $y = |x + 1|$? (four graphs labeled a, b, c, d)
3. $\triangle tes$ is isosceles with vertex $\angle e$. find $x$.

options: a. 1, b. 2, c. 3, d. 4
(diagram: triangle with sides $5x - 4$, $3x + 2$, and base $2x + 3$)

1. find $m\angle a$. (see diagram at right)

options: a. 75, b. 41, c. 43, d. 40
(diagram: triangle with angle $40^\circ$ and exterior angles $(x - 1)^\circ$ and $(4x + 1)^\circ$)

1. in $\triangle teg$, $m\angle t = 5x + 7$, $m\angle p = 6x - 10$, and $m\angle g = x + 20$. choose the list that shows the sides correctly ordered from longest to shortest.

options: a. $eg, te, tp$, b. $tp, eg, tp$ (note: likely typo, maybe $tp, eg, te$), c. $tg, eg, te$, d. $ge, tg, te$

Explanation:

Step1: Analyze the triangle

Since \(\triangle TES\) is isosceles with vertex \(\angle E\), the sides opposite the equal angles (the legs) are equal. So, \(TE = SE\).
Given \(TE = 5x - 4\) and \(SE = 3x + 2\), we set up the equation:
\(5x - 4 = 3x + 2\)

Step2: Solve for \(x\)

Subtract \(3x\) from both sides:
\(5x - 3x - 4 = 3x - 3x + 2\)
\(2x - 4 = 2\)

Add 4 to both sides:
\(2x - 4 + 4 = 2 + 4\)
\(2x = 6\)

Divide both sides by 2:
\(x = \frac{6}{2} = 3\)

Answer:

C. 3