Certainly! Let's go through the solution step-by-step to address all necessary computations accurately.
### 1. Identifying the Distances
- Joseph’s distance: [tex]\( 12 \)[/tex] km
- Isabelle’s distance: [tex]\( 18 \)[/tex] km
### 2. Squaring the Distances
- Joseph’s distance squared:
[tex]\[
12^2 = 144
\][/tex]
- Isabelle’s distance squared:
[tex]\[
18^2 = 324
\][/tex]
### 3. Difference of Squares
- Difference in squares:
[tex]\[
144 - 324 = -180
\][/tex]
### 4. Solving for [tex]\( d \)[/tex]
- Division to find [tex]\( d \)[/tex] without taking the square root:
[tex]\[
d = \frac{-180}{2} = -90.0
\][/tex]
In summary, the correct distances, their squares, the difference of the squares, and the final computation for [tex]\( d \)[/tex] are as follows:
- Joseph’s distance: [tex]\( 12 \)[/tex] km
- Isabelle’s distance: [tex]\( 18 \)[/tex] km
- Joseph’s distance squared: [tex]\( 144 \)[/tex]
- Isabelle’s distance squared: [tex]\( 324 \)[/tex]
- Difference in squares: [tex]\( -180 \)[/tex]
- Final value of [tex]\( d \)[/tex]: [tex]\( -90.0 \)[/tex]
This breakdown ensures a complete and accurate understanding of the problem and its solution.