Question

use the graphic organizer that represents the real - number system for questions 11 and 12.

1. which of the following could be included in section d?

a. $sqrt{99}$ b. $\frac{60}{15}$ c. - 20 d. 9.2

1. which of the following could not be included in section b?

a. $9+sqrt{72}$ b. $-\frac{42}{6}$ c. $2sqrt{100}$ d. 8

Explanation:

Step1: Analyze section D elements

Section D is likely the innermost part of the real - number system graphic organizer, which usually represents the most specific type of real numbers, like integers.

Step2: Evaluate option A for question 11

$\sqrt{99}\approx9.95$, it is an irrational number.

Step3: Evaluate option B for question 11

$\frac{60}{15}=4$, which is an integer.

Step4: Evaluate option C for question 11

$- 20$ is an integer.

Step5: Evaluate option D for question 11

$9.2$ is a non - integer rational number. Integers are more likely to be in the innermost part, so for question 11, options B and C are possible. But since we need one answer, and assuming the innermost is integers, $-20$ is a valid choice.

Step6: Analyze section B elements

Section B is likely a larger set that includes non - integers and integers. Irrational numbers are not part of the set of rational numbers which might be represented by B.

Step7: Evaluate option A for question 12

$9+\sqrt{72}=9 + 6\sqrt{2}$, it is an irrational number.

Step8: Evaluate option B for question 12

$-\frac{42}{6}=-7$, which is an integer (a type of rational number).

Step9: Evaluate option C for question 12

$2\sqrt{100}=2\times10 = 20$, which is an integer (a type of rational number).

Step10: Evaluate option D for question 12

$8$ is an integer (a type of rational number). So for question 12, the number that could not be in section B is $9+\sqrt{72}$ as it is irrational.

Answer:

1. C. -20
2. A. $9+\sqrt{72}$