Question

1. does figure b appear to be a scale drawing of figure a? explain your thinking.
2. evaluate 2(3x + 5)+4x + 5 when x = 3.

Explanation:

Step1: Simplify the expression

First, use the distributive property on \(2(3x + 5)\):
\[

$$\begin{align*} 2(3x+5)+4x + 5&=(2\times3x+2\times5)+4x + 5\\ &=6x + 10+4x+5 \end{align*}$$

\]
Then combine like - terms:
\[

$$\begin{align*} 6x + 10+4x+5&=(6x+4x)+(10 + 5)\\ &=10x+15 \end{align*}$$

\]

Step2: Substitute \(x = 3\)

Substitute \(x = 3\) into the simplified expression \(10x+15\):
\[

$$\begin{align*} 10x+15&=10\times3+15\\ &=30 + 15\\ &=45 \end{align*}$$

\]

To determine if figure B is a scale drawing of figure A, we need to check if the ratios of corresponding lengths are equal and if the shapes are similar in orientation and proportion. Visually, if all parts of figure B are in the same ratio to the corresponding parts of figure A, it is a scale drawing. If not, it is not. Without specific measurements, a visual inspection can be made. If the overall shape, angles, and relative sizes of the elements in figure B match those of figure A in a proportional way, it may be a scale drawing.

Answer:

45

For the question "Does figure B appear to be a scale drawing of figure A? Explain your thinking.":