**Mathematics Problem: Determining Values in a Parallelogram****Problem Statement:**If \(ON = 7x - 5\), \(LM = 6x + 3\), \(NM = x - 4\), and \(OL = 2y + 5\), find the values of \(x\) and \(y\) given that \(LMNO\) is a parallelogram.**Solution Approach:**A parallelogram is a quadrilateral with opposite sides that are equal and parallel. Therefore, in \(LMNO\):1. \(ON = LM\)2. \(NM = OL\)Using the given equations:1. For the sides \(ON\) and \(LM\): \[ ON = 7x - 5 \] \[ LM = 6x + 3 \] Since \(ON = LM\): \[ 7x - 5 = 6x + 3 \] Simplifying this equation to solve for \(x\): \[ 7x - 6x = 3 + 5 \] \[ x = 8 \]2. For the sides \(NM\) and \(OL\): \[ NM = x - 4 \] \[ OL = 2y + 5 \] Substituting \(x = 8\) in \(NM\): \[ NM = 8 - 4 = 4 \] Since \(NM = OL\): \[ 4 = 2y + 5 \] Solving for \(y\): \[ 4 - 5 = 2y \] \[ -1 = 2y \] \[ y = -\frac{1}{2} \]**Solution:**Thus, the values of \(x\) and \(y\) are:\[x = 8\]\[y = -\frac{1}{2}\]

Name: **Mathematics Problem: Determining Values in a Parallelogram****Probl
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Mathematics Problem: Determining Values in a Parallelogram****Problem Statement:**If \(ON = 7x - 5\), \(LM = 6x + 3\), \(NM = x - 4\), and \(OL = 2y + 5\), find the values of \(x\) and \(y\) given that \(LMNO\) is a parallelogram.**Solution Approa