Answer :
Sure, let's go through the problem step by step.
The given expression is:
[tex]\[ -3b^2 + 25 \][/tex]
We need to find the value of this expression when [tex]\( b = 7 \)[/tex].
### Step-by-Step Solution
1. Start with the value of [tex]\( b \)[/tex]:
[tex]\[ b = 7 \][/tex]
2. Substitute [tex]\( b \)[/tex] into the expression:
[tex]\[ -3(7)^2 + 25 \][/tex]
3. First, calculate [tex]\( 7^2 \)[/tex]:
[tex]\[ 7^2 = 49 \][/tex]
4. Then multiply 49 by -3:
[tex]\[ -3 \cdot 49 = -147 \][/tex]
5. Now, add 25 to -147:
[tex]\[ -147 + 25 = -122 \][/tex]
Therefore, the value of the expression [tex]\(-3b^2 + 25\)[/tex] when [tex]\( b = 7 \)[/tex] is [tex]\(-122\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{-122} \][/tex]
In the list of choices given, this matches choice:
C. -122
The given expression is:
[tex]\[ -3b^2 + 25 \][/tex]
We need to find the value of this expression when [tex]\( b = 7 \)[/tex].
### Step-by-Step Solution
1. Start with the value of [tex]\( b \)[/tex]:
[tex]\[ b = 7 \][/tex]
2. Substitute [tex]\( b \)[/tex] into the expression:
[tex]\[ -3(7)^2 + 25 \][/tex]
3. First, calculate [tex]\( 7^2 \)[/tex]:
[tex]\[ 7^2 = 49 \][/tex]
4. Then multiply 49 by -3:
[tex]\[ -3 \cdot 49 = -147 \][/tex]
5. Now, add 25 to -147:
[tex]\[ -147 + 25 = -122 \][/tex]
Therefore, the value of the expression [tex]\(-3b^2 + 25\)[/tex] when [tex]\( b = 7 \)[/tex] is [tex]\(-122\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{-122} \][/tex]
In the list of choices given, this matches choice:
C. -122
