2. If LM = 10 and PS = 11, what is KN? ls 3. If PS = 2x + 4 and KN = 5x+ 2, and LM =-3x + 8, what is x?

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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The image depicts a geometric figure consisting of two interconnected trapezoids. Here's a detailed description:

1. **Upper Trapezoid**: The shape is a trapezoid with vertices labeled L, M, P, and S. The line segment LM serves as the top base, while PS is the bottom base. The legs, LP and MS, are the non-parallel sides that connect the two bases. This trapezoid is oriented with its longer base (PS) on the bottom.

2. **Lower Trapezoid**: Below the upper trapezoid, there is another trapezoid with vertices labeled P, S, K, and N. The same line segment PS now serves as the top base for the lower trapezoid, and KN is the bottom base. The non-parallel sides, PK and SN, connect the two trapezoids.

The diagram highlights the connection between two trapezoids sharing a common base, PS.
Transcribed Image Text:The image depicts a geometric figure consisting of two interconnected trapezoids. Here's a detailed description: 1. **Upper Trapezoid**: The shape is a trapezoid with vertices labeled L, M, P, and S. The line segment LM serves as the top base, while PS is the bottom base. The legs, LP and MS, are the non-parallel sides that connect the two bases. This trapezoid is oriented with its longer base (PS) on the bottom. 2. **Lower Trapezoid**: Below the upper trapezoid, there is another trapezoid with vertices labeled P, S, K, and N. The same line segment PS now serves as the top base for the lower trapezoid, and KN is the bottom base. The non-parallel sides, PK and SN, connect the two trapezoids. The diagram highlights the connection between two trapezoids sharing a common base, PS.
Certainly! Here is the transcribed text with explanations for educational use:

---

**Example Questions:**

2. If \( LM = 10 \) and \( PS = 11 \), what is \( KN \)?

3. If \( PS = 2x + 4 \) and \( KN = 5x + 2 \), and \( LM = -3x + 8 \), what is \( x \)?

---

These questions involve solving equations based on given expressions. For question 2, you need to find the value of \( KN \) when specific values are given for \( LM \) and \( PS \).

For question 3, solve for \( x \) using the given expressions for \( PS \), \( KN \), and \( LM \). This requires setting up an equation based on relationships implied or illustrated in the corresponding example referred to in the text.
Transcribed Image Text:Certainly! Here is the transcribed text with explanations for educational use: --- **Example Questions:** 2. If \( LM = 10 \) and \( PS = 11 \), what is \( KN \)? 3. If \( PS = 2x + 4 \) and \( KN = 5x + 2 \), and \( LM = -3x + 8 \), what is \( x \)? --- These questions involve solving equations based on given expressions. For question 2, you need to find the value of \( KN \) when specific values are given for \( LM \) and \( PS \). For question 3, solve for \( x \) using the given expressions for \( PS \), \( KN \), and \( LM \). This requires setting up an equation based on relationships implied or illustrated in the corresponding example referred to in the text.
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