Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
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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![### Algebraic Equations: Solving Square Root Equations
#### Problem 1: Solving for x
Consider the following algebraic equation involving square roots:
\[ \frac{\sqrt{x}}{3x - 5} = \frac{6}{\sqrt{x}} \]
**Question:**
What is the value of \( x \) when this equation is satisfied?
#### Multiple Choice Answers:
- A) \( \frac{15}{8} \)
- B) \( \frac{5}{17} \)
- C) \( \frac{30}{17} \)
- D) \( \frac{11}{3} \)
To solve this problem, follow these steps:
1. **Isolate the square roots:** Multiply both sides by \( \sqrt{x}(3x - 5) \) to eliminate the fractions.
2. **Simplify the equation:** Combine like terms and solve for \( x \).
3. **Verify the solution:** Ensure the solution satisfies the original equation by substituting \( x \) back into the equation.
Choose the correct answer from the given options.
**Solution Steps:**
1. Start by cross-multiplying to get rid of the fractions:
\[ \sqrt{x} \cdot \sqrt{x} = 6 \cdot (3x - 5) \]
2. We know that \(\sqrt{x} \cdot \sqrt{x} = x\), so:
\[ x = 6(3x - 5) \]
3. Distribute the 6:
\[ x = 18x - 30 \]
4. Move all terms involving \( x \) to one side of the equation:
\[ x - 18x = -30 \]
\[ -17x = -30 \]
5. Divide both sides by -17:
\[ x = \frac{30}{17} \]
Thus, the value of \( x \) is \(\frac{30}{17}\).
Therefore, the correct answer is:
- C) \( \frac{30}{17} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffda00417-b7b2-4353-8e1a-cc43c4365f92%2F20374bc6-f5e9-4725-be2f-a4243377f710%2F27ndatj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Algebraic Equations: Solving Square Root Equations
#### Problem 1: Solving for x
Consider the following algebraic equation involving square roots:
\[ \frac{\sqrt{x}}{3x - 5} = \frac{6}{\sqrt{x}} \]
**Question:**
What is the value of \( x \) when this equation is satisfied?
#### Multiple Choice Answers:
- A) \( \frac{15}{8} \)
- B) \( \frac{5}{17} \)
- C) \( \frac{30}{17} \)
- D) \( \frac{11}{3} \)
To solve this problem, follow these steps:
1. **Isolate the square roots:** Multiply both sides by \( \sqrt{x}(3x - 5) \) to eliminate the fractions.
2. **Simplify the equation:** Combine like terms and solve for \( x \).
3. **Verify the solution:** Ensure the solution satisfies the original equation by substituting \( x \) back into the equation.
Choose the correct answer from the given options.
**Solution Steps:**
1. Start by cross-multiplying to get rid of the fractions:
\[ \sqrt{x} \cdot \sqrt{x} = 6 \cdot (3x - 5) \]
2. We know that \(\sqrt{x} \cdot \sqrt{x} = x\), so:
\[ x = 6(3x - 5) \]
3. Distribute the 6:
\[ x = 18x - 30 \]
4. Move all terms involving \( x \) to one side of the equation:
\[ x - 18x = -30 \]
\[ -17x = -30 \]
5. Divide both sides by -17:
\[ x = \frac{30}{17} \]
Thus, the value of \( x \) is \(\frac{30}{17}\).
Therefore, the correct answer is:
- C) \( \frac{30}{17} \)
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