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.
Topic Video
Question
![### Solve for \( x \).
Below is an image of a circle with two intersecting chords forming a cross inside the circle. The lengths of the segments are given as follows:
- One chord divides into two segments of lengths 8 and 10.
- The other chord is divided into segments of lengths 17 and \( x \), where \( x \) is the segment to be solved for.
According to the intersecting chords theorem (also known as the power of a point theorem), for two intersecting chords in a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Therefore, we can set up the following equation:
\[ (8) \times (10) = (17) \times (x) \]
The equation is derived from multiplying the length segments:
\[ 80 = 17x \]
### Steps to Solve for \( x \):
1. Set up the equation from the given segment lengths:
\[ 8 \times 10 = 17 \times x \]
2. Simplify the left-hand side:
\[ 80 = 17x \]
3. Solve for \( x \) by dividing both sides by 17:
\[ x = \frac{80}{17} \]
So the exact value for \( x \) is:
\[ x = \frac{80}{17} \]
You can insert your answer in the box provided below the diagram.
**Answer:**
\( x = \frac{80}{17} \)
Click the "Submit Answer" button to check your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f20aeac-3658-4125-82ac-c012d50c949f%2F91409b4e-cca3-4d07-9ee8-8557d1fb5d58%2Fz89cay_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solve for \( x \).
Below is an image of a circle with two intersecting chords forming a cross inside the circle. The lengths of the segments are given as follows:
- One chord divides into two segments of lengths 8 and 10.
- The other chord is divided into segments of lengths 17 and \( x \), where \( x \) is the segment to be solved for.
According to the intersecting chords theorem (also known as the power of a point theorem), for two intersecting chords in a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Therefore, we can set up the following equation:
\[ (8) \times (10) = (17) \times (x) \]
The equation is derived from multiplying the length segments:
\[ 80 = 17x \]
### Steps to Solve for \( x \):
1. Set up the equation from the given segment lengths:
\[ 8 \times 10 = 17 \times x \]
2. Simplify the left-hand side:
\[ 80 = 17x \]
3. Solve for \( x \) by dividing both sides by 17:
\[ x = \frac{80}{17} \]
So the exact value for \( x \) is:
\[ x = \frac{80}{17} \]
You can insert your answer in the box provided below the diagram.
**Answer:**
\( x = \frac{80}{17} \)
Click the "Submit Answer" button to check your solution.
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