Let's match each mathematical description with its corresponding algebraic expression. Here are the step-by-step solutions:
1. The absolute value of twice a number increased by 11
- Description: This describes taking twice a number, increasing it by 11, and then taking the absolute value. The absolute value symbol is represented by vertical bars.
- Expression: \(|2x + 11|\)
2. The square root of the difference of the square of a number and 11
- Description: This describes taking the square of a number, subtracting 11 from it, and then taking the square root of the result. The square root symbol is \(\sqrt{\ }\).
- Expression: \(\sqrt{x^2 - 11}\)
3. The quotient of two times a number and -11
- Description: This describes taking twice a number and dividing it by -11.
- Expression: \(- \frac{2x}{11}\)
4. The sum of the square root of two times a number and 11
- Description: This describes taking the square root of twice a number and adding 11 to the result.
- Expression: \(\sqrt{2x} + 11\)
Now let's write the pairs clearly:
- The absolute value of twice a number increased by 11:
\(|2x + 11|\)
- The square root of the difference of the square of a number and 11:
\(\sqrt{x^2 - 11}\)
- The quotient of two times a number and -11:
\(- \frac{2x}{11}\)
- The sum of the square root of two times a number and 11:
\(\sqrt{2x} + 11\)
To summarize:
- \( | 2x + 11 | \) matches "the absolute value of twice a number increased by 11"
- \( \sqrt{x^2 - 11} \) matches "the square root of the difference of the square of a number and 11"
- \( - \frac{2x}{11} \) matches "the quotient of two times a number and -11"
- [tex]\( \sqrt{2x} + 11 \)[/tex] matches "the sum of the square root of two times a number and 11"
