Which of the following mathematical expressions is equivalent to the verbal expression ''A number, c, squared is 52 more than the product of c and 11''?

Options

A. `2c=52+11c`
B. `2c=52c+11c`
C. `c^(2)=52-11c`
D. `c^(2)=52+11c`

Answer

To convert the verbal expression "A number, c, squared is 52 more than the product of c and 11" into a mathematical expression, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the components of the verbal expression**:
- "A number, c, squared" refers to \( c^2 \).
- "the product of c and 11" refers to \( 11c \).
- "is 52 more than" indicates that we will add 52 to the product.

2. **Translate the verbal expression into a mathematical equation**:
- The phrase "is 52 more than" means we will take the product \( 11c \) and add 52 to it.
- Therefore, we can write the equation as:
\[ c^2 = 11c + 52 \]

3. **Rearranging the equation**:
- To express it in a standard form, we can rearrange it:
\[ c^2 - 11c - 52 = 0 \]
- However, the original question asks for an expression equivalent to the verbal statement, not necessarily in standard form.

4. **Identify the correct option**:
- From the options given, we can see that the expression \( c^2 = 52 + 11c \) matches our derived equation.
- Therefore, the correct answer is:
\[ c^2 = 52 + 11c \]

### Final Answer:
The mathematical expression equivalent to the verbal expression is:
\[ c^2 = 52 + 11c \]