To determine which expressions are equivalent to [tex]\((14+4) \div 6\)[/tex], we need to evaluate each option and compare the results. Here is a detailed analysis of each expression:
1. Evaluate [tex]\((14 + 4) \div 6\)[/tex]:
[tex]\[
(14 + 4) \div 6 = 18 \div 6 = 3
\][/tex]
2. Evaluate each provided expression:
- A. [tex]\((14 + 6) \div 4\)[/tex]:
[tex]\[
(14 + 6) \div 4 = 20 \div 4 = 5
\][/tex]
This results in 5, which is not equivalent to 3.
- B. [tex]\((4 + 14) \div 6\)[/tex]:
[tex]\[
(4 + 14) \div 6 = 18 \div 6 = 3
\][/tex]
This results in 3, which is equivalent to 3.
- C. [tex]\(14 \cdot (4 + 6)\)[/tex]:
[tex]\[
14 \cdot (4 + 6) = 14 \cdot 10 = 140
\][/tex]
This results in 140, which is not equivalent to 3.
- D. [tex]\((4 + 6) \cdot (14 + 6)\)[/tex]:
[tex]\[
(4 + 6) \cdot (14 + 6) = 10 \cdot 20 = 200
\][/tex]
This results in 200, which is not equivalent to 3.
Based on the evaluations, the expressions equivalent to [tex]\((14+4) \div 6\)[/tex] are:
- B. [tex]\((4 + 14) \div 6\)[/tex]
Therefore, the correct answer is:
```
B. [tex]\((4 + 14) \div 6\)[/tex]
```
