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irina [24]
3 years ago
10

Points X and Z are on a number line, and point Y partitions

Mathematics
1 answer:
abruzzese [7]3 years ago
6 0

Answer:

The coordinate of Z is 13.36.

Step-by-step explanation:

According to the statement, we have the following information:

\frac{XY}{XZ} = \frac{5}{12} (1)

\frac{YZ}{XZ} = \frac{7}{12} (2)

X = 0.4 (3)

Y = 5.8 (4)

From (2), we have the following expression:

YZ = \frac{7}{12}\cdot XZ

Y-Z =\frac{7}{12}\cdot (X-Z)

Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z

Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z

\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X

5\cdot Z = 12\cdot Y-7\cdot X

Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X (5)

If we know that Y = 5.8 and X = 0.4, then the coordinate of Z is:

Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)

Z = 13.36

The coordinate of Z is 13.36.

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