Let's match each description with the correct algebraic expression:
1. The absolute value of twice a number increased by 11:
- Description: The term "absolute value" suggests the use of the absolute value notation, denoted by | |. The phrase "twice a number" indicates multiplying the number by 2, and "increased by 11" means adding 11. Therefore, the correct expression is [tex]\( |2x + 11| \)[/tex].
2. The square root of the difference of the square of a number and 11:
- Description: The phrase "square of a number" indicates squaring the number (i.e., [tex]\( x^2 \)[/tex]). "Difference" means subtraction, so we subtract 11, and "square root" means taking the square root of the result. Therefore, the correct expression is [tex]\( \sqrt{x^2 - 11} \)[/tex].
3. The quotient of two times a number and -11:
- Description: "Quotient" implies division. "Two times a number" means multiplying the number by 2, and the division is by -11. Therefore, the correct expression is [tex]\( -\frac{2x}{11} \)[/tex].
4. The sum of the square root of two times a number and 11:
- Description: "Two times a number" means multiplying the number by 2, "square root" means taking the square root of this product, and "sum" indicates adding 11 to it. Therefore, the correct expression is [tex]\( \sqrt{2x} + 11 \)[/tex].
So, the correct pairs are:
1. the absolute value of twice a number increased by 11: [tex]\( |2x + 11| \)[/tex]
2. the square root of the difference of the square of a number and 11: [tex]\( \sqrt{x^2 - 11} \)[/tex]
3. the quotient of two times a number and -11: [tex]\( -\frac{2x}{11} \)[/tex]
4. the sum of the square root of two times a number and 11: [tex]\( \sqrt{2x} + 11 \)[/tex]
The tile [tex]$\sqrt{2x - 11}$[/tex] is not used in these pairs.
