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Question 1044963: Okay so I'm in geometry and we're doing Segment Addition Postulate, here's the question: Find MN if N is between M and P, MN= 3x+2, NP= 18, and MP= 5x.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! segment addition postulate states:
In geometry, the segment addition postulate states that, given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
change the names and it becomes:
In geometry, the segment addition postulate states that given two points M and P, a third point N lies on the line segment MP if and only if the distances between the points satisfy the equation MN + NP = MP
your overall segment is mn
n is between m and p
you are given that:
mn = 3x + 2
np = 18
mp = 5x
the addition postulates says that mn + np = mp
replace mp with 5x and mn with 3x + 2 and np with 18 and you get:
3x + 2 + 18 = 5x
combine like terms to get:
3x + 20 = 5x
subtract 3x from both sides of this equation to get:
20 = 5x - 2x
combine like terms to get:
20 = 2x
solve for x to get:
x = 10
replace x with 5 and you get:
mn = 3x + 2 = 32
np = 18
mp = 5x = 50
mn + np = mp becomes 32 + 18 = 40 which becomes 50 = 50
your solution is that mn = 32
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