Let's evaluate each expression step-by-step to determine which one equals 46.
### Option (A): [tex]\(5(9-3) + (6 \cdot 2)\)[/tex]
1. Evaluate inside the parentheses first:
[tex]\[
9 - 3 = 6
\][/tex]
2. Substitute back into the expression:
[tex]\[
5 \cdot 6 + (6 \cdot 2)
\][/tex]
3. Perform the multiplications:
[tex]\[
5 \cdot 6 = 30
\][/tex]
[tex]\[
6 \cdot 2 = 12
\][/tex]
4. Add the results:
[tex]\[
30 + 12 = 42
\][/tex]
Thus, option (A) evaluates to 42.
### Option (B): [tex]\(3(4+8) + (2 \cdot 5)\)[/tex]
1. Evaluate inside the parentheses first:
[tex]\[
4 + 8 = 12
\][/tex]
2. Substitute back into the expression:
[tex]\[
3 \cdot 12 + (2 \cdot 5)
\][/tex]
3. Perform the multiplications:
[tex]\[
3 \cdot 12 = 36
\][/tex]
[tex]\[
2 \cdot 5 = 10
\][/tex]
4. Add the results:
[tex]\[
36 + 10 = 46
\][/tex]
Thus, option (B) evaluates to 46.
### Option (C): [tex]\(7(3 + 3) + 7\)[/tex]
1. Evaluate inside the parentheses first:
[tex]\[
3 + 3 = 6
\][/tex]
2. Substitute back into the expression:
[tex]\[
7 \cdot 6 + 7
\][/tex]
3. Perform the multiplication:
[tex]\[
7 \cdot 6 = 42
\][/tex]
4. Add the results:
[tex]\[
42 + 7 = 49
\][/tex]
Thus, option (C) evaluates to 49.
### Option (D): [tex]\(2(10 + 5) + 6\)[/tex]
1. Evaluate inside the parentheses first:
[tex]\[
10 + 5 = 15
\][/tex]
2. Substitute back into the expression:
[tex]\[
2 \cdot 15 + 6
\][/tex]
3. Perform the multiplication:
[tex]\[
2 \cdot 15 = 30
\][/tex]
4. Add the results:
[tex]\[
30 + 6 = 36
\][/tex]
Thus, option (D) evaluates to 36.
### Final Answer
The expression that equals 46 is:
[tex]\[
\boxed{B}
\][/tex]
