Find the value of `(4c^(2))/(6) - 25` when c = 12.

Options

A. 24
B. 71
C. 29
D. 35

Answer

To find the value of the expression \(\frac{4c^2}{6} - 25\) when \(c = 12\), we will follow these steps:

### Step 1: Substitute the value of \(c\)
We start by substituting \(c = 12\) into the expression:
\[ \frac{4(12)^2}{6} - 25 \]

### Step 2: Calculate \(12^2\)
Next, we calculate \(12^2\):
\[ 12^2 = 144 \]
So, we can rewrite the expression as:
\[ \frac{4 \times 144}{6} - 25 \]

### Step 3: Multiply \(4\) by \(144\)
Now, we multiply \(4\) by \(144\):
\[ 4 \times 144 = 576 \]
Now, our expression looks like this:
\[ \frac{576}{6} - 25 \]

### Step 4: Divide \(576\) by \(6\)
Next, we divide \(576\) by \(6\):
\[ \frac{576}{6} = 96 \]
So, we have:
\[ 96 - 25 \]

### Step 5: Subtract \(25\) from \(96\)
Finally, we subtract \(25\) from \(96\):
\[ 96 - 25 = 71 \]

### Conclusion
Thus, the value of the expression \(\frac{4c^2}{6} - 25\) when \(c = 12\) is:
\[ \boxed{71} \]