Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x - 4). Her steps are below:
V
1. 3x + 12 + 2 = 2 + 5x - 20
V
Use the drops-downs to justify how Heidi arrived
each step.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
2. 3x + 14 = 5x - 18
3. 14 = 2x - 18
V
4. 32 - 2x
5. 16 = x

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Ответ:

clapoint2003p3chnu

01.03.2022

Mathematics

$\triangle ABC\sim \triangle DEC\\ \\\angle B\cong \angle E\\ \\3BC=2EC$

Step-by-step explanation:

Right triangle ABC is reflected over AC to form triangle AFC.

Triangle AFC dilated by a scale factor of two-thirds to form triangle DEC.

Reflection is a rigid transformation which preserves lengths and angles, then

$\triangle ABC\cong \triangle AFC$

Dilation is a transformation which maps the triangle into similar triangle, so

$\triangle AFC \sim \triangle DEC$

Thus,

$\triangle ABC \sim \triangle DEC$

Similar triangle have congruent corresponding angles, so

$\angle B\cong \angle E$

and proportional corresponding sides

$\dfrac{BC}{EC}=\dfrac{AB}{DE}=\dfrac{2}{3}\Rightarrow \\ \\3BC=2EC\\ \\3AB=2DE$

Thus, correct options are:

$\triangle ABC\sim \triangle DEC\\ \\\angle B\cong \angle E\\ \\3BC=2EC$

Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triang

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Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x - 4). Her steps are below: V 1. 3x + 12 + 2 = 2 + 5x - 20 V Use the drops-downs to justify how Heidi arrived each step. Step 1: Step 2: Step 3: Step 4: Step 5: 2. 3x + 14 = 5x - 18 3. 14 = 2x - 18 V 4. 32 - 2x 5. 16 = x