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Mila [183]
3 years ago
6

Line segment MN is shown below. If point P(x,y) partitions the line segment

Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0

Answer:

P (-1 , 0)

Step-by-step explanation:

M (-6 , 2)      N (9 , -4)     P (x , y)

horizontal distance of M and N = 9 - (-6) = 15

vertical distance of M and N = 2 - (-4) = 6

1/3 from x coordinate of M (-6): -6 + 15/3 = -1    This is x coordinate of point P

1/3 from y coordinate of M (2): 2 - 6/3 = 0    This is y coordinate of point P

P (x , y)  i.e P (-1 , 0)

check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385

distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77

MP / PN = 5.385 / 10.77 = 0.5 = 1/2

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a certain triangle has a perimeter of 3067 mi. the shortest side measures 71 mi less than the middle side and the longest side m
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Answer:

The measure of the shortest side is 851 miles

Step-by-step explanation:

Let

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y ---> the measure of the middle side

z ---> the measure of the longest side

we know that

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P=x+y+z

P=3,067\ mi

so

3,067=x+y+z ----> equation A

the shortest side measures 71 mi less than the middle side

so

x=y-71 ----> equation B

the longest side measures 372 mi more the the middle side

so

z=y+372 ----> equation C

substitute equation B and equation C in equation A

3,067=(y-71)+y+(y+372)

solve for y

3,067=3y+301\\3y=2,766\\y=922

Find the value of x

x=y-71\\x=922-71\\x=851

therefore

The measure of the shortest side is 851 miles

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Answer:

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