Question

geometry
here is a figure that looks like the letter a, along with several other figures. which figures are scaled copies of the original a? explain how you know.
expressions and equations
solve the equation below. use the hanger to help you solve it. explain how you know.
2x + 3 = 7

Explanation:

Step1: Check similarity for scaled - copies

For two figures to be scaled copies, the ratios of corresponding side - lengths must be equal and the angles must be the same. In the given figures:

• Figure 1: The shape and the ratios of side - lengths are the same as the original 'A'. The angles are also the same.
• Figure 2: The shape and the ratios of side - lengths are the same as the original 'A'. The angles are also the same.
• Figure 3: The shape is different from the original 'A' as the orientation and the ratios of side - lengths are not in proportion to the original 'A'.
• Figure 4: The shape and the ratios of side - lengths are the same as the original 'A'. The angles are also the same.

Step2: Solve the equation

We have the equation \(2x + 3=7\).
Subtract 3 from both sides of the equation to isolate the term with \(x\).
\(2x+3 - 3=7 - 3\), which simplifies to \(2x = 4\).
Then divide both sides by 2 to solve for \(x\). \(\frac{2x}{2}=\frac{4}{2}\), so \(x = 2\).

Answer:

• The scaled copies of the original 'A' are Figure 1, Figure 2, and Figure 4 because they have the same shape, with equal - angle measures and proportional side - lengths.
• For the equation \(2x + 3 = 7\), \(x = 2\). We first subtracted 3 from both sides to get \(2x=4\), then divided both sides by 2 to find \(x\).