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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Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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**Parallel Lines and Angles - Educational Explanation** **Question:** What value of \( x \) would prove \( a \parallel b \)? **Diagram Description:** - There are two horizontal lines labeled as \( a \) and \( b \). - A transversal intersects lines \( a \) and \( b \). - The angle formed between the transversal and line \( a \) is expressed as \( 12x + 3 \). - The angle formed between the transversal and line \( b \) is expressed as \( 21x - 51 \). **Options:** a. \( x = 6.9 \) b. \( x = 6 \) c. \( x = 12 \) d. \( x = 4.2 \) For the lines \( a \) and \( b \) to be parallel, the corresponding angles need to be equal. Therefore, set the expressions equal to each other and solve for \( x \): \[ 12x + 3 = 21x - 51 \] Subtract \( 12x \) from both sides: \[ 3 = 9x - 51 \] Add 51 to both sides: \[ 54 = 9x \] Divide by 9: \[ x = 6 \] Therefore, the correct value of \( x \) that proves \( a \parallel b \) is found in option b: **Answer:** \( x = 6 \)
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Transcribed Image Text:**Parallel Lines and Angles - Educational Explanation** **Question:** What value of \( x \) would prove \( a \parallel b \)? **Diagram Description:** - There are two horizontal lines labeled as \( a \) and \( b \). - A transversal intersects lines \( a \) and \( b \). - The angle formed between the transversal and line \( a \) is expressed as \( 12x + 3 \). - The angle formed between the transversal and line \( b \) is expressed as \( 21x - 51 \). **Options:** a. \( x = 6.9 \) b. \( x = 6 \) c. \( x = 12 \) d. \( x = 4.2 \) For the lines \( a \) and \( b \) to be parallel, the corresponding angles need to be equal. Therefore, set the expressions equal to each other and solve for \( x \): \[ 12x + 3 = 21x - 51 \] Subtract \( 12x \) from both sides: \[ 3 = 9x - 51 \] Add 51 to both sides: \[ 54 = 9x \] Divide by 9: \[ x = 6 \] Therefore, the correct value of \( x \) that proves \( a \parallel b \) is found in option b: **Answer:** \( x = 6 \)
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