Understanding the '@' Symbol Pattern

The question presents a sequence based on a mathematical operator '@'. We need to identify the rule governing this operator using the given examples and then apply it to find the result for 7 @ 4.

Step 1: Analyze the Given Equations

We are given two instances of the operation:

• 5 @ 2 = 17
• 6 @ 3 = 27

Let's represent the operation as $a \text{ @ } b = \text{Result}$. We need to find the relationship between $a$, $b$, and the Result.

Step 2: Identify the Pattern

Let's test a potential pattern. Consider the pattern: $a \text{ @ } b = (a \times b) + (a + b)$.

Test with the first equation (5 @ 2 = 17):

• $a = 5$, $b = 2$
• $(5 \times 2) + (5 + 2) = 10 + 7 = 17$

The pattern holds true for the first equation.

Test with the second equation (6 @ 3 = 27):

• $a = 6$, $b = 3$
• $(6 \times 3) + (6 + 3) = 18 + 9 = 27$

The pattern holds true for the second equation as well. Therefore, the confirmed pattern is $a \text{ @ } b = (a \times b) + (a + b)$.

Step 3: Calculate 7 @ 4

Now, apply the confirmed pattern to find the value of 7 @ 4:

• $a = 7$, $b = 4$
• $7 \text{ @ } 4 = (7 \times 4) + (7 + 4)$
• $7 \text{ @ } 4 = 28 + 11$
• $7 \text{ @ } 4 = 39$

Conclusion

Following the identified pattern, 7 @ 4 equals 39.