Question
Evaluate the two sums and determine which statement is true. Enter the correct number associated with your response. Column A Column B 0.5+34 3–√+25 Statement #1: Only Column A has a rational sum. Statement #2: Only Column B has a rational sum. Statement #3: Column A and Column B both have rational sums. (1 point) The simplified values of both columns indicate that Statement # is true.
Answers
GPT-4o mini
Let's evaluate both sums in Column A and Column B.
**Column A:**
\[ 0.5 + 34 = 34.5 \]
**Column B:**
\[ 3 - \sqrt{3} + 25 \]
First, simplify \( 3 - \sqrt{3} + 25 \):
\[ = 28 - \sqrt{3} \]
Now, let's determine whether each sum is rational or not.
- **Column A (34.5)**: This is a rational number because it can be expressed as \( \frac{69}{2} \).
- **Column B (28 - \sqrt{3})**: Since \( \sqrt{3} \) is an irrational number, \( 28 - \sqrt{3} \) is also irrational.
Now looking at the statements:
- **Statement #1**: Only Column A has a rational sum. (True)
- **Statement #2**: Only Column B has a rational sum. (False)
- **Statement #3**: Column A and Column B both have rational sums. (False)
Thus, the correct answer is Statement #1 is true.
The final answer is **1**.
**Column A:**
\[ 0.5 + 34 = 34.5 \]
**Column B:**
\[ 3 - \sqrt{3} + 25 \]
First, simplify \( 3 - \sqrt{3} + 25 \):
\[ = 28 - \sqrt{3} \]
Now, let's determine whether each sum is rational or not.
- **Column A (34.5)**: This is a rational number because it can be expressed as \( \frac{69}{2} \).
- **Column B (28 - \sqrt{3})**: Since \( \sqrt{3} \) is an irrational number, \( 28 - \sqrt{3} \) is also irrational.
Now looking at the statements:
- **Statement #1**: Only Column A has a rational sum. (True)
- **Statement #2**: Only Column B has a rational sum. (False)
- **Statement #3**: Column A and Column B both have rational sums. (False)
Thus, the correct answer is Statement #1 is true.
The final answer is **1**.