Option A: [tex]\frac{3}{3+5} (2-(-14))+(-14)[/tex] is the expression that correctly uses the formula [tex]\frac{m}{m+n} (x_2-x_1)+x_1[/tex]
Explanation:
It is given that, the number line segment from Q to S has endpoints Q at –14 and S at 2.
Point R partitions the directed line segment from Q to S in a 3:5 ratio.
Thus, we have,
[tex]x_1=-14[/tex] , [tex]x_2=2[/tex] , [tex]m=3[/tex] and [tex]n=5[/tex]
The location of point R can be determined using the formula,
[tex]\frac{m}{m+n} (x_2-x_1)+x_1[/tex]
Substituting the values, we get,
[tex]\frac{3}{3+5} (2-(-14))+(-14)[/tex]
Hence, substituting the values [tex]x_1=-14[/tex] , [tex]x_2=2[/tex] , [tex]m=3[/tex] and [tex]n=5[/tex] in the formula [tex]\frac{m}{m+n} (x_2-x_1)+x_1[/tex], we get, [tex]\frac{3}{3+5} (2-(-14))+(-14)[/tex]
Thus, the expression that correctly uses the formula is [tex]\frac{3}{3+5} (2-(-14))+(-14)[/tex]
Therefore, Option A is the correct answer.
Answer:
A
Step-by-step explanation:
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