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storchak [24]
3 years ago
14

If point P is Four-sevenths of the distance from M to N, what ratio does the point P partition the directed line segment from M

to N into? 4:1 4:3 4:7 4:10
Mathematics
2 answers:
vovangra [49]3 years ago
9 0

Answer:   B. 4 : 3

edg 2021

Step-by-step explanation:

andrew-mc [135]3 years ago
3 0

Answer: Point P partitioned the line segment MN into 4:3.

Step-by-step explanation:

Point P is \dfrac47of the distance from M to N.

Let the distance between M to N =x.

MP=\dfrac47x

Point P partition the directed line segment from M to N .

MN = MP+PN

\Rightarrow\ x=\dfrac47 x+PN\\\\\Rightarrow\ PN =x-\dfrac47 x\\\\\Rightarrow\ PN=\dfrac37 x

Ratio of MP to PN = =\dfrac{\dfrac{4}{7}x}{\dfrac{3}{7}x}=\dfrac43

∴ Point P partitioned the line segment MN into 4:3.

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The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

<h3>How to find the sum of consecutive integers?</h3>

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\sum_{i=r}^s  (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b

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For the given case, the considered summation can be written symbolically as:

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\sum_{n=1}^{14}  (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14}  (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14}  (3n + 2) = 3 \times 105 + 28 = 343\\

Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

Learn more about summation here:

brainly.com/question/14322177

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