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Thread: proof

  1. #1
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    proof

    (ax + by)/(a + b) = z


    (ax + by)/(a + b) = z
    then it will be true that the distances to the mean are inversely proportional to the weights:
    (z - x)/(y - z) = b/a
    so that
    a(z - x) = b(y - z)

    How can we show this to be true algebraically?
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  2. #2
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    Re: proof

    Pretty straight forward:
    From (ax+ by)/(a+ b)= z,
    ax+ by= (a+ b)z= az+ bz.

    ax- az= a(x- z)= bz- by= b(z- y)

    (x- z)/(z- y)= b/a
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  3. #3
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    Re: proof

    Many Thanks
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