Answer:
The coordinate of [tex]Z[/tex] is 13.36.
Step-by-step explanation:
According to the statement, we have the following information:
[tex]\frac{XY}{XZ} = \frac{5}{12}[/tex] (1)
[tex]\frac{YZ}{XZ} = \frac{7}{12}[/tex] (2)
[tex]X = 0.4[/tex] (3)
[tex]Y = 5.8[/tex] (4)
From (2), we have the following expression:
[tex]YZ = \frac{7}{12}\cdot XZ[/tex]
[tex]Y-Z =\frac{7}{12}\cdot (X-Z)[/tex]
[tex]Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z[/tex]
[tex]Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z[/tex]
[tex]\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X[/tex]
[tex]5\cdot Z = 12\cdot Y-7\cdot X[/tex]
[tex]Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X[/tex] (5)
If we know that [tex]Y = 5.8[/tex] and [tex]X = 0.4[/tex], then the coordinate of [tex]Z[/tex] is:
[tex]Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)[/tex]
[tex]Z = 13.36[/tex]
The coordinate of [tex]Z[/tex] is 13.36.
