To find the point on the number line that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex], let's follow these steps:
1. Determine the direction and the distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
- The distance from [tex]\(A\)[/tex] to [tex]\(B\)[/tex] is calculated as [tex]\(B - A\)[/tex].
- So, [tex]\(B - A = 6 - 31 = -25\)[/tex].
2. Calculate the fraction of this distance:
- We need to find the point that is [tex]\(\frac{2}{5}\)[/tex] of this distance.
- The fraction of the distance is [tex]\(\frac{2}{5} \times -25\)[/tex].
3. Compute [tex]\(\frac{2}{5} \times -25\)[/tex]:
- [tex]\(\frac{2}{5} \times -25 = -10\)[/tex].
4. Find the location of the point by starting at [tex]\(A\)[/tex] and moving this fraction of the distance:
- Starting at [tex]\(A = 31\)[/tex], we move [tex]\(-10\)[/tex], as calculated above.
- Therefore, the location of the point is [tex]\(31 + (-10) = 21\)[/tex].
So, the point that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex] is located at 21.
Thus, the correct answer is:
C. 21
