Question

Question

Miss Yang has bulletin boards of different sizes in her classroom. She wants to calculate how much border she needs for each one. The length of each bulletin board is 6 inches less than three times its width, w
. Simplify w + 3w − 6 + w + 3w − 6
to find the formula for the perimeter of each of Miss Yang’s bulletin boards.(1 point)
Responses

6w2 − 10
6 w squared minus 10

6w − 10
6 w minus 10

8w − 12
8 w minus 12

8w2 − 12

Answer 1

To find the formula for the perimeter of each of Miss Yang’s bulletin boards, we first need to express the lengths in terms of width \( w \).

Given that the length \( L \) of each bulletin board is 6 inches less than three times its width, we can write:

\[ L = 3w - 6 \]

Now we can calculate the perimeter \( P \) of the bulletin board, which is given by the formula:

\[ P = 2L + 2w \]

Substituting \( L \) into the formula for perimeter:

\[ P = 2(3w - 6) + 2w \]

Now simplify this expression:

1. Distribute the 2: \[ P = 6w - 12 + 2w \]

2. Combine like terms: \[ P = 6w + 2w - 12 = 8w - 12 \]

Thus, the simplified formula for the perimeter of each of Miss Yang’s bulletin boards is:

\[ \boxed{8w - 12} \]

So the correct response is 8w − 12 (8 w minus 12).