In the parallelogram shown, AE = t + 2, CE = 31 - 14, What is the length of line segment DB? %3D and DE = 21 + 8. 20 units B 24 units E 48 units 68 units D C.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 41E
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### Geometry Problem: Parallelogram Analysis

#### Problem Statement:

In the parallelogram shown, the following relationships are given:
- \( AE = t + 2 \)
- \( CE = 3t - 14 \)
- \( DE = 2t + 8 \)

The task is to find the length of line segment \( DB \).

#### Multiple Choice Options:
- 20 units
- 24 units
- 48 units
- 68 units

#### Diagram Description:
The diagram depicts a parallelogram \( ABCD \) with diagonals intersecting at point \( E \):
- Points \( A \), \( B \), \( C \), and \( D \) form the vertices of the parallelogram.
- Line segments \( AE \), \( CE \), and \( DE \) are marked.

Presence of buttons:
- "Mark this and return"
- "Save and Exit"
- "Next"
- "Submit" 

These buttons seem to be part of an online assessment interface allowing students to mark questions, navigate through the test, and submit their answers.

### Explanation:
To solve for \( DB \), utilize the properties of the parallelogram and given equations to find \( t \) first. Then use \( t \) to find the total length of \( DB \).

---

Feel free to explore more about properties of parallelograms and solving linear equations for better understanding and solution strategies!
Transcribed Image Text:### Geometry Problem: Parallelogram Analysis #### Problem Statement: In the parallelogram shown, the following relationships are given: - \( AE = t + 2 \) - \( CE = 3t - 14 \) - \( DE = 2t + 8 \) The task is to find the length of line segment \( DB \). #### Multiple Choice Options: - 20 units - 24 units - 48 units - 68 units #### Diagram Description: The diagram depicts a parallelogram \( ABCD \) with diagonals intersecting at point \( E \): - Points \( A \), \( B \), \( C \), and \( D \) form the vertices of the parallelogram. - Line segments \( AE \), \( CE \), and \( DE \) are marked. Presence of buttons: - "Mark this and return" - "Save and Exit" - "Next" - "Submit" These buttons seem to be part of an online assessment interface allowing students to mark questions, navigate through the test, and submit their answers. ### Explanation: To solve for \( DB \), utilize the properties of the parallelogram and given equations to find \( t \) first. Then use \( t \) to find the total length of \( DB \). --- Feel free to explore more about properties of parallelograms and solving linear equations for better understanding and solution strategies!
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