Question

1. solve 2x + 3(x - 5) = 15 2. evaluate for 7x + 5 + x² name the property that is illustrated. 4. if ∠g ≅ ∠h, then ∠h ≅ ∠g. 5. if ab = cd and cd = xy, then ab = xy. 6. ∠a ≅ ∠a complete the proof using the correct reason. (1) congruent segments, (2) given, (3) congruent angles, (4) symmetric, (5) reflexive given: $overline{ab}congoverline{cd}$ prove: $overline{cd}congoverline{ab}$ statements reasons 7. 8. 9.

Explanation:

Step1: Expand the equation

$2x + 3(x - 5)=2x+3x - 15$
So the equation becomes $2x + 3x-15 = 15$.

Step2: Combine like - terms

$(2x + 3x)-15 = 15$, which simplifies to $5x-15 = 15$.

Step3: Add 15 to both sides

$5x-15 + 15=15 + 15$, resulting in $5x=30$.

Step4: Divide both sides by 5

$\frac{5x}{5}=\frac{30}{5}$, so $x = 6$.

For the second part, we need to find the value of $7x + 5+x^{2}$ when $x = 6$.

Step1: Substitute $x = 6$ into the expression

$7(6)+5 + 6^{2}$.

Step2: Calculate each part

$7\times6=42$, $6^{2}=36$.

Step3: Add them together

$42+5 + 36=83$.

1. If $\angle G\cong\angle H$, then $\angle H\cong\angle G$ illustrates the symmetric property of congruence.
2. If $AB = CD$ and $CD = XY$, then $AB = XY$ illustrates the transitive property of equality.
3. $\angle A\cong\angle A$ illustrates the reflexive property of congruence.

For the proof:
Given $\overline{AB}\cong\overline{CD}$, to prove $\overline{CD}\cong\overline{AB}$.

Step1: State the given

Statement 1: $\overline{AB}\cong\overline{CD}$, Reason: Given.

Step2: Use the symmetric property

Statement 2: $\overline{CD}\cong\overline{AB}$, Reason: Symmetric property of congruence.

Answer:

$x = 6$