Sure, I'll help you match the algebraic expressions to the verbal descriptions step-by-step.
1. Expression: [tex]\(\sqrt{x^2 - 11}\)[/tex]:
- Verbal Description: "the square root of the difference of a number squared and 11"
- Explanation: The expression [tex]\(\sqrt{x^2 - 11}\)[/tex] translates to taking the square root of the difference between a number squared ( [tex]\(x^2\)[/tex] ) and 11.
2. Expression: [tex]\(\frac{2x}{11}\)[/tex]:
- Verbal Description: "the quotient of two times a number and 11"
- Explanation: The expression [tex]\(\frac{2x}{11}\)[/tex] translates to the quotient (which means division) of two times a number ( [tex]\(2x\)[/tex] ) and 11.
3. Expression: [tex]\(\sqrt{2x} + 11\)[/tex]:
- Verbal Description: "the sum of the square root of two times a number and 11"
- Explanation: The expression [tex]\(\sqrt{2x} + 11\)[/tex] translates to the sum (addition) of the square root of two times a number ( [tex]\(2x\)[/tex] ) and 11.
Therefore, the correct matches are:
- the square root of the difference of a number squared and 11 [tex]\(\leftrightarrow \sqrt{x^2 - 11}\)[/tex]
- the quotient of two times a number and 11 [tex]\(\leftrightarrow \frac{2 x}{11}\)[/tex]
- the sum of the square root of two times a number and 11 [tex]\(\leftrightarrow \sqrt{2 x} + 11\)[/tex]
I hope this helps! If you have any more questions, feel free to ask!
