Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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**Problem Statement:** Given \( m \parallel n \), find the value of \( x \) and \( y \). **Diagram Explanation:** The image shows two parallel lines, \( m \) and \( n \), with a transversal line intersecting them. There are three angle expressions marked: 1. The angle between the transversal and line \( m \) is labeled as \( (5x + 9)^\circ \). 2. The angle between the transversal and line \( n \) is labeled as \( (4x + 17)^\circ \). 3. There is another angle on line \( n \) labeled as \( (y + 20)^\circ \). **Calculations:** To find the values of \( x \) and \( y \), use the properties of parallel lines and corresponding angles: - Since \( m \parallel n \), the corresponding angles are equal. Therefore, set the expressions for corresponding angles equal to each other: \[ 5x + 9 = 4x + 17 \] Solving this equation will give you the value of \( x \). - To find \( y \), use the fact that the angle \( (y + 20)^\circ \) is supplementary to the angle \( (4x + 17)^\circ \) because they are on a straight line intersected by the transversal. \[ (4x + 17) + (y + 20) = 180 \] Plug the value of \( x \) from the first equation into this equation to solve for \( y \). **Input Fields:** - \( x = \) [Input box for \( x \)] - \( y = \) [Input box for \( y \)] **Submit Button:** - [Submit Answer]
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Transcribed Image Text:**Problem Statement:** Given \( m \parallel n \), find the value of \( x \) and \( y \). **Diagram Explanation:** The image shows two parallel lines, \( m \) and \( n \), with a transversal line intersecting them. There are three angle expressions marked: 1. The angle between the transversal and line \( m \) is labeled as \( (5x + 9)^\circ \). 2. The angle between the transversal and line \( n \) is labeled as \( (4x + 17)^\circ \). 3. There is another angle on line \( n \) labeled as \( (y + 20)^\circ \). **Calculations:** To find the values of \( x \) and \( y \), use the properties of parallel lines and corresponding angles: - Since \( m \parallel n \), the corresponding angles are equal. Therefore, set the expressions for corresponding angles equal to each other: \[ 5x + 9 = 4x + 17 \] Solving this equation will give you the value of \( x \). - To find \( y \), use the fact that the angle \( (y + 20)^\circ \) is supplementary to the angle \( (4x + 17)^\circ \) because they are on a straight line intersected by the transversal. \[ (4x + 17) + (y + 20) = 180 \] Plug the value of \( x \) from the first equation into this equation to solve for \( y \). **Input Fields:** - \( x = \) [Input box for \( x \)] - \( y = \) [Input box for \( y \)] **Submit Button:** - [Submit Answer]
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