Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.10: Inverse Variation
Problem 8P
Related questions
Question
![### Problem:
**Solve for \( x \) to the nearest tenth.**
#### Diagram:
The diagram shows a right triangle with the following measurements:
- The length of one leg is 6 units.
- The length of the other leg is \(4 + 1 = 5\) units.
- The hypotenuse is labeled as \( x \).
#### Steps to Solve:
To find the value of \( x \), we can use the Pythagorean theorem, which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.
For the given triangle:
- \( a = 6 \)
- \( b = 5 \)
- \( c = x \)
Now, substitute the given side lengths into the Pythagorean theorem:
\[ 6^2 + 5^2 = x^2 \]
\[ 36 + 25 = x^2 \]
\[ 61 = x^2 \]
To solve for \( x \), take the square root of both sides:
\[ x = \sqrt{61} \]
\[ x \approx 7.81 \]
Rounding to the nearest tenth, we get:
\[ x \approx 7.8 \]
However, the marked correct option is 7.2 which is incorrect based on our previous calculation.
**Selecting an Answer:**
- 7.2
- 4.1
- 6.1
- 6.4
### Explanation:
Though the provided answers do not include the correct calculation as \(7.8\), marking an error out of the provided options is necessary, as the correct approximation should indeed be \(7.8\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb6a3e0a-0e9e-4eb9-b3f8-cac67ff0b1b6%2F7a653819-b430-4807-82f4-49fb1f5d58df%2Fbllomk9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem:
**Solve for \( x \) to the nearest tenth.**
#### Diagram:
The diagram shows a right triangle with the following measurements:
- The length of one leg is 6 units.
- The length of the other leg is \(4 + 1 = 5\) units.
- The hypotenuse is labeled as \( x \).
#### Steps to Solve:
To find the value of \( x \), we can use the Pythagorean theorem, which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.
For the given triangle:
- \( a = 6 \)
- \( b = 5 \)
- \( c = x \)
Now, substitute the given side lengths into the Pythagorean theorem:
\[ 6^2 + 5^2 = x^2 \]
\[ 36 + 25 = x^2 \]
\[ 61 = x^2 \]
To solve for \( x \), take the square root of both sides:
\[ x = \sqrt{61} \]
\[ x \approx 7.81 \]
Rounding to the nearest tenth, we get:
\[ x \approx 7.8 \]
However, the marked correct option is 7.2 which is incorrect based on our previous calculation.
**Selecting an Answer:**
- 7.2
- 4.1
- 6.1
- 6.4
### Explanation:
Though the provided answers do not include the correct calculation as \(7.8\), marking an error out of the provided options is necessary, as the correct approximation should indeed be \(7.8\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
