Question

Given the expressions (a^2 + 6^2) and (a - b), if (a = -3) and (b = -5), evaluate each expression using the variable replacements.

A. (a^2 + 6^2 = 9) and (a - b = 2)
B. (a^2 + 6^2 = 27) and (a - b = -2)
C. (a^2 + 6^2 = 45) and (a - b = 8)
D. (a^2 + 6^2 = 63) and (a - b = 12)

Answer 1

After substituting -3 for a and -5 for b, the expression (a^2 + 6^2) evaluates to 45, and the expression (a - b) evaluates to 2. The correct answer is not listed exactly, as there appears to be a typo in the provided options.

Step-by-step explanation:

To evaluate the expressions (a^2 + 6^2) and (a - b) using the variable replacements where a = -3 and b = -5, we will substitute these values into the expressions and simplify.

For the first expression (a^2 + 6^2), we substitute a = -3:

• (-3)^2 + 6^2 = 9 + 36 = 45

For the second expression (a - b), we substitute a = -3 and b = -5:

• (-3) - (-5) = -3 + 5 = 2

So, the correct evaluations for the expressions are:

• (a^2 + 6^2) = 45
• (a - b) = 2

Therefore, the answer is C. (a^2 + 6^2 = 45) and (a - b = 8), though there seems to be a discrepancy with the second part as it should be 2 instead of 8, indicating a possible typo in the options provided.