Respuesta :

Considering that y is between x and z, we have that:

  • The value of k is of k = 6.
  • The length of yz is 46 units.

How to find the value of k and of yz?

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

  • xz = 4k + 38.
  • xy = 3k - 2.
  • yz = 7k + 4.

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

A similar problem, in which the length of a line segment is found, is given by https://brainly.com/question/24778489

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