Question

name date 1. which number sentences are true? choose all that apply. a. $9 = 4^2 + 1$ b. $9 + 1 + 3 = 13$ c. $16 = 3 \cdot 3 \cdot 10$ d. $\frac{5 + 13}{6} = \frac{1}{2}(5 + 3)$ e. $3^2 + 4 = 2^4 - 3$ 2. consider the numbers 3, 5, 8, and 11. which of these numbers, if any, satisfy $\frac{1}{2}(2x + 6) = 14$? justify your answer.

Explanation:

Step1: Evaluate Option A

Calculate right-hand side: $4^2 + 1 = 16 + 1 = 17$. Compare to left-hand side $9$. $9
eq 17$, so A is false.

Step2: Evaluate Option B

Calculate left-hand side: $9 + 1 + 3 = 13$. Compare to right-hand side $13$. $13 = 13$, so B is true.

Step3: Evaluate Option C

Calculate right-hand side: $3 \cdot 3 \cdot 10 = 90$. Compare to left-hand side $16$. $16
eq 90$, so C is false.

Step4: Evaluate Option D

Calculate left-hand side: $\frac{5+13}{6} = \frac{18}{6} = 3$. Calculate right-hand side: $\frac{1}{2}(5+3) = \frac{1}{2} \cdot 8 = 4$. $3
eq 4$, so D is false.

Step5: Evaluate Option E

Calculate left-hand side: $3^2 + 4 = 9 + 4 = 13$. Calculate right-hand side: $2^4 - 3 = 16 - 3 = 13$. $13 = 13$, so E is true.

Step6: Solve the equation for Q2

Start with $\frac{1}{2}(2x + 6) = 14$. Multiply both sides by 2: $2x + 6 = 28$. Subtract 6: $2x = 22$. Divide by 2: $x = 11$. Verify with given numbers: 11 is in {3,5,8,11}.

Answer:

1. B. $9 + 1 + 3 = 13$, E. $3^2 + 4 = 2^4 - 3$
2. 11