Let's carefully break down and evaluate the expression as described in the problem step-by-step:
1. Identify the mathematical expression:
- Key words: "a number squared decreased by six."
- Using the provided replacements: "a number" with [tex]\( c \)[/tex], "squared" with exponent 2, and "decreased by" with minus (-).
2. Construct the expression:
- This translates to [tex]\( c^2 - 6 \)[/tex].
3. Evaluate the expression when [tex]\( c = 7 \)[/tex]:
- Substitute [tex]\( c \)[/tex] with 7.
- Calculate [tex]\( 7^2 - 6 \)[/tex].
4. Perform the calculation:
- [tex]\( 7^2 = 49 \)[/tex]
- Then, [tex]\( 49 - 6 = 43 \)[/tex].
Therefore, the correct expression and value when [tex]\( c = 7 \)[/tex] is:
[tex]\[ c^2 - 6; \text{ when } c=7, \text{ the value is } 43. \][/tex]
So, the correct answer is:
[tex]\[ c^2 - 6; \text{ when } c=7, \text{ the value is } 43. \][/tex]
