Find XZ, if XM = 2x + 35 and MZ = 5x - 22.?

3 Answers

Relevance
  • Pope
    Lv 7
    1 month ago

    Either MXZ is a triangle or points M, X, and Z are collinear.

    If MXZ is a triangle, |XM - MZ| < XZ < XM + MZ.

    If M, X, and Z are collinear, XZ = |XM - MZ| or XZ = XM + MZ.

    Combining the two cases,

    |XM - MZ| ≤ XZ ≤ XM + MZ

    |(2x + 35) - (5x - 22)| ≤ XZ ≤ (2x + 35) + (5x - 22)

    |57 - 3x| ≤ XZ ≤ 7x + 13

  • 1 month ago

      If XM = 2x + 35 and MZ = 5x - 22, find XZ.

      XZ = 7x + 13.

      If M is the midpoint of XZ:

      2x + 35 = 5x - 22

      3x = 57

        x = 19

     XZ = 146

  • 1 month ago

    You haven't told us anything about the relationship of X, M and Z.

    I'm going to assume they are on a line where XM + MZ = XZ

    I'm also going to assume that M is the midpoint.

    That means the two segments are equal in length.

    5x - 22 = 2x + 35

    Get like terms together:

    5x - 2x = 35 + 22

    3x = 57

    x = 57/3

    x = 19

    Now plug that into either equation:

    5x - 22

    = 5(19) - 22

    = 95 - 22

    = 73

    And the other segment would have the same length. Let's calculate it to be sure:

    2x + 35

    = 2(19) + 35

    = 38 + 35

    = 73

    Adding those together we get the length for XZ.

    XZ = XM + MZ

    XZ = 73 + 73

    XZ = 146

    P.S. Next time please provide the full information so that we don't have to guess and make assumptions. :)

Still have questions? Get your answers by asking now.