Question

this part of the quiz is not on the computer but you must do them for a pr or ad grade.

1. polygon n is a scaled copy of polygon m.
2. solve each equation.

a. \\(\frac{6}{13} = \frac{y}{39}\\)
s the value of y?
b. what is the scale factor?

Explanation:

Part 1: Solve the proportion \(\frac{6}{13}=\frac{y}{39}\)

Step 1: Cross - multiply

To solve the proportion \(\frac{6}{13}=\frac{y}{39}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\). Here, \(a = 6\), \(b = 13\), \(c = y\), and \(d = 39\). So we have \(6\times39=13\times y\).

Step 2: Simplify and solve for \(y\)

First, calculate \(6\times39 = 234\). So the equation becomes \(234 = 13y\). Then, divide both sides of the equation by 13: \(y=\frac{234}{13}\). Since \(234\div13 = 18\), we get \(y = 18\).

Step 1: Identify corresponding sides

Polygon \(N\) is a scaled copy of Polygon \(M\). The height of Polygon \(M\) is 8 and the height of Polygon \(N\) is 12.

Step 2: Calculate the scale factor

The scale factor \(k\) from \(M\) to \(N\) is the ratio of the length of a side of \(N\) to the corresponding side of \(M\). So \(k=\frac{12}{8}=\frac{3}{2}\).

Answer:

\(y = 18\)

Part 2: Find the scale factor