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Find y in the parallelogram below. 2y + 4 2x+2/ 3x-3 O 11 7 O 5 O 6 y + 10

Find y in the parallelogram below. 2y + 4 2x+2/ 3x-3 O 11 7 O 5 O 6 y + 10

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Educational Content on Parallelograms #### Problem Description **Find \( y \) in the parallelogram below.** [Image Description] - The image depicts a parallelogram with expressions on its sides: - The left side of the parallelogram is labeled as \( 2x + 2 \). - The right side of the parallelogram is labeled as \( 3x - 3 \). - The top side of the parallelogram is labeled as \( 2y + 4 \). - The bottom side of the parallelogram is labeled as \( y + 10 \). Below the image, multiple-choice options are provided for the value of \( y \): - O 11 - O 7 - O 5 - O 6 #### Explanation: In a parallelogram, opposite sides are equal in length. This forms the basis for setting up our equations: 1. **Equating Vertical Sides**: \[ 2x + 2 = 3x - 3 \] 2. **Solving for \( x \)**: - Subtract \( 2x \) from both sides: \[ 2 = x - 3 \] - Add 3 to both sides: \[ x = 5 \] 3. **Equating Horizontal Sides**: \[ 2y + 4 = y + 10 \] 4. **Solving for \( y \)**: - Subtract \( y \) from both sides: \[ y + 4 = 10 \] - Subtract 4 from both sides: \[ y = 6 \] Thus, the correct value for \( y \) is \( 6 \). ### Answer Choices - O 11 - O 7 - O 5 - **O 6** Correct Answer: **6**
Transcribed Image Text:### Educational Content on Parallelograms #### Problem Description **Find \( y \) in the parallelogram below.** [Image Description] - The image depicts a parallelogram with expressions on its sides: - The left side of the parallelogram is labeled as \( 2x + 2 \). - The right side of the parallelogram is labeled as \( 3x - 3 \). - The top side of the parallelogram is labeled as \( 2y + 4 \). - The bottom side of the parallelogram is labeled as \( y + 10 \). Below the image, multiple-choice options are provided for the value of \( y \): - O 11 - O 7 - O 5 - O 6 #### Explanation: In a parallelogram, opposite sides are equal in length. This forms the basis for setting up our equations: 1. **Equating Vertical Sides**: \[ 2x + 2 = 3x - 3 \] 2. **Solving for \( x \)**: - Subtract \( 2x \) from both sides: \[ 2 = x - 3 \] - Add 3 to both sides: \[ x = 5 \] 3. **Equating Horizontal Sides**: \[ 2y + 4 = y + 10 \] 4. **Solving for \( y \)**: - Subtract \( y \) from both sides: \[ y + 4 = 10 \] - Subtract 4 from both sides: \[ y = 6 \] Thus, the correct value for \( y \) is \( 6 \). ### Answer Choices - O 11 - O 7 - O 5 - **O 6** Correct Answer: **6**
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