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What is the location of the point on the number line that is [tex]\frac{3}{5}[/tex] of the way from [tex]A = 2[/tex] to [tex]B = 17[/tex]?

A. 9
B. 10
C. 12
D. 11


Sagot :

To find the location of the point on the number line that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex], we can follow these steps:

1. Determine the distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[ \text{Distance between } A \text{ and } B = B - A \][/tex]
Substituting the given values:
[tex]\[ \text{Distance between } A \text{ and } B = 17 - 2 = 15 \][/tex]

2. Calculate [tex]\(\frac{3}{5}\)[/tex] of this distance:
[tex]\[ \text{Fraction of distance} = \frac{3}{5} \times \text{Distance between } A \text{ and } B \][/tex]
Substituting the calculated distance:
[tex]\[ \text{Fraction of distance} = \frac{3}{5} \times 15 \][/tex]
[tex]\[ \text{Fraction of distance} = 9 \][/tex]

3. Find the location of the point by starting at [tex]\(A\)[/tex] and moving this fraction of the distance towards [tex]\(B\)[/tex]:
[tex]\[ \text{Location of the point} = A + \text{Fraction of distance} \][/tex]
Substituting [tex]\(A\)[/tex] and the calculated fraction of distance:
[tex]\[ \text{Location of the point} = 2 + 9 = 11 \][/tex]

Thus, the location of the point that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex] is [tex]\(11\)[/tex].

The correct answer is:
D. 11