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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. 11
B. 9
C. 10
D. 12


Sagot :

To find 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], follow these steps:

1. Calculate the difference between [tex]\(B\)[/tex] and [tex]\(A\)[/tex]:

[tex]\[ B - A = 17 - 2 = 15 \][/tex]

2. Determine the fraction of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]:

Since we need [tex]\(\frac{3}{5}\)[/tex] of the way, we multiply the difference by [tex]\(\frac{3}{5}\)[/tex].

[tex]\[ \text{Position from } A = 15 \times \frac{3}{5} = 15 \times 0.6 = 9 \][/tex]

3. Calculate the actual position on the number line:

To find the exact point, add the calculated position from [tex]\(A\)[/tex] to [tex]\(A\)[/tex] itself:

[tex]\[ \text{Position on line} = A + 9 = 2 + 9 = 11 \][/tex]

Hence, 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] is [tex]\(\boxed{11}\)[/tex].