To determine the location of the point that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex], follow these steps:
1. Compute the difference between [tex]\(B\)[/tex] and [tex]\(A\)[/tex]:
[tex]\[
B - A = 6 - 31 = -25
\][/tex]
This indicates that [tex]\(B\)[/tex] is 25 units back from [tex]\(A\)[/tex].
2. Identify the desired fraction of the distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
We want to find a point that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex].
3. Calculate [tex]\(\frac{2}{5}\)[/tex] of the difference:
[tex]\[
\frac{2}{5} \times (-25) = -10
\][/tex]
This means that we need to move 10 units back from [tex]\(A\)[/tex].
4. Add this calculated difference to the initial point [tex]\(A\)[/tex]:
[tex]\[
A + (-10) = 31 - 10 = 21
\][/tex]
Therefore, the location on the number line that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex] is at 21.
Thus, the correct answer is:
A. 21
