Question

2 - 89. simplify the following expression by combining like terms: (3x² + x - 2) - (4x² + x - 5). homework help
2 - 94. determine which similarity conditions (aa~, sss~, or sas~) could be used to establish that the following pairs of triangles are similar. list as many as you can. homework help

Explanation:

2 - 89

Step1: Remove parentheses

$(3x^{2}+x - 2)-(4x^{2}+x - 5)=3x^{2}+x - 2-4x^{2}-x + 5$

Step2: Combine like - terms

$(3x^{2}-4x^{2})+(x - x)+(-2 + 5)=-x^{2}+3$

Step1: Calculate side - length ratios

For the first pair of triangles, the side - length ratios are $\frac{3}{3.6}=\frac{5}{6}=\frac{4}{4.8}=\frac{5}{6}$. Since the ratios of the corresponding sides are equal, we use SSS~ (Side - Side - Side similarity).

Step1: Check angle - side conditions

We have two pairs of equal angles ($80^{\circ}$ and $30^{\circ}$) and the ratios of the sides including the equal - angled vertices: $\frac{2}{4}=\frac{3.5}{7}=\frac{1}{2}$. So we can use AA~ (Angle - Angle similarity) because two pairs of angles are equal, and also SAS~ (Side - Angle - Side similarity) since we have equal angles and proportional sides including those angles.

Answer:

$-x^{2}+3$

2 - 94

a.