To solve the expression [tex]\((-5)^2 + 12 \div 3 \times 2\)[/tex] using the order of operations (PEMDAS/BODMAS), we must evaluate it step by step according to the rules: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
1. Evaluate Exponents:
[tex]\[ (-5)^2 \][/tex]
This means [tex]\((-5) \times (-5) = 25\)[/tex].
2. Evaluate Division:
[tex]\[ 12 \div 3 \][/tex]
Dividing 12 by 3 gives [tex]\(4.0\)[/tex].
3. Evaluate Multiplication:
[tex]\[ 4.0 \times 2 \][/tex]
Multiplying 4.0 by 2 gives [tex]\(8.0\)[/tex].
4. Evaluate Addition:
Now we add the result of the exponentiation to the result of the multiplication:
[tex]\[ 25 + 8.0 \][/tex]
Adding 25 and 8.0 gives [tex]\(33.0\)[/tex].
So, the correct answer to the expression [tex]\((-5)^2 + 12 \div 3 \times 2\)[/tex] is:
[tex]\[ c.) 33 \][/tex]
