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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![Solve for \( x \).
[Image Description]
The image contains a circle with two chords intersecting inside it. The intersection forms two line segments which divide each chord into two parts. The parts of the chords are labeled as follows:
- One chord is divided into segments labeled 8 and \( x \).
- The other chord is divided into segments labeled 5 and 20.
[Detailed Explanation]
This diagram represents a classic problem involving intersecting chords in a circle. According to the intersecting chords theorem, when two chords intersect, the products of the lengths of the segments of each chord are equal. That is, if two chords intersect at a point, forming four segments \( a \), \( b \), \( c \), and \( d \), then \( a \times b = c \times d \).
In this specific example:
- The first chord is divided into segments of length 8 and \( x \).
- The second chord is divided into segments of length 5 and 20.
The equation according to the intersecting chords theorem is:
\[ 8 \times x = 5 \times 20 \]
Simplifying the right-hand side:
\[ 8x = 100 \]
Solving for \( x \):
\[ x = \frac{100}{8} \]
\[ x = 12.5 \]
Answer: \( x \)
[Answer Input Box]
Answer: [____________]
Submit Answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53198e60-c01b-4c66-91c6-7d18bef4fe43%2F09e8295d-c8d5-4a63-9002-6290ebfe6773%2Fv29bbq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve for \( x \).
[Image Description]
The image contains a circle with two chords intersecting inside it. The intersection forms two line segments which divide each chord into two parts. The parts of the chords are labeled as follows:
- One chord is divided into segments labeled 8 and \( x \).
- The other chord is divided into segments labeled 5 and 20.
[Detailed Explanation]
This diagram represents a classic problem involving intersecting chords in a circle. According to the intersecting chords theorem, when two chords intersect, the products of the lengths of the segments of each chord are equal. That is, if two chords intersect at a point, forming four segments \( a \), \( b \), \( c \), and \( d \), then \( a \times b = c \times d \).
In this specific example:
- The first chord is divided into segments of length 8 and \( x \).
- The second chord is divided into segments of length 5 and 20.
The equation according to the intersecting chords theorem is:
\[ 8 \times x = 5 \times 20 \]
Simplifying the right-hand side:
\[ 8x = 100 \]
Solving for \( x \):
\[ x = \frac{100}{8} \]
\[ x = 12.5 \]
Answer: \( x \)
[Answer Input Box]
Answer: [____________]
Submit Answer
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