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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]?
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].
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