Question
Point L is on line segment K M. Given LM = 3x + 3, KM = 5x + 4, and
KL = 5x + 1, determine the numerical length of K M.
KL = 5x + 1, determine the numerical length of K M.
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Answered by
GPT 3.5
To find the length of KM, we need to subtract the length of KL from the length of LM.
LM = KL + KM
3x + 3 = (5x + 1) + (5x + 4)
3x + 3 = 10x + 5
3 = 7x + 5
7x = -2
x = -2/7
Now we can substitute this value of x into the expression for KM to find its length:
KM = 5(-2/7) + 4
KM = -10/7 + 4
KM = -10/7 + 28/7
KM = 18/7
So the numerical length of KM is 18/7.
LM = KL + KM
3x + 3 = (5x + 1) + (5x + 4)
3x + 3 = 10x + 5
3 = 7x + 5
7x = -2
x = -2/7
Now we can substitute this value of x into the expression for KM to find its length:
KM = 5(-2/7) + 4
KM = -10/7 + 4
KM = -10/7 + 28/7
KM = 18/7
So the numerical length of KM is 18/7.
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