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Helen [10]
3 years ago
10

Find the value of the variable and YZ if Y is between X and Z. XY=4n+3, YZ=2n-7,XZ=22

Mathematics
1 answer:
ruslelena [56]3 years ago
7 0

Answer:

\large \boxed{n = \dfrac{13}{3}; YZ = \dfrac{5}{3}}}

Step-by-step explanation:

I think you have the situation shown in the diagram below.

1. Calculate the value of n

\begin{array}{rcl}XY + YZ & = & XZ\\4n+ 3 + 2n - 7 & = & 22\\6n - 4 & = & 22\\6n & = & 26\\n & = & \dfrac{26}{6}\\\\& = & \mathbf{\dfrac{13}{3}}\\\end{array}\\\large \boxed{\mathbf{n = \dfrac{13}{3}}}

2. Calculate the value of YZ

\begin{array}{rcl}YZ & = & 2n - 7\\& = & 2\left (\dfrac{13}{3}\right ) - 7 \\\\& = & \dfrac{26}{3} - 7\\\\& = & \dfrac{26}{3} - \dfrac{21}{3}\\\\& = & \dfrac{5}{3} \\\\\end{array}\\\large \boxed{YZ = \mathbf{ \dfrac{5}{3}}}

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