Let's evaluate each of the statements one by one to determine their truthfulness.
Statement #1: \( 3 \cdot 20 = 4(6 + 9) \)
Calculating the left-hand side: \[ 3 \cdot 20 = 60 \]
Calculating the right-hand side: \[ 4(6 + 9) = 4 \cdot 15 = 60 \]
Since both sides are equal, statement #1 is true.
Statement #2: \( 4 \cdot 12 = 6 \cdot (8 \cdot 2) \) and \( 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8 \)
Calculating the first part:
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Left-hand side: \[ 4 \cdot 12 = 48 \]
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Right-hand side: \[ 6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96 \]
Since \( 48 \neq 96 \), the first part of statement #2 is false.
Now let's look at the second part:
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Left-hand side: \[ 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \]
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Right-hand side: \[ 2 \cdot 4 \cdot 8 = 64 \]
Since \( 60 \neq 64 \), the second part is also false.
So, statement #2 is false.
Statement #3: \( 4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8 \)
Calculating the left-hand side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]
Calculating the right-hand side: \[ 42 + 4 \cdot 8 = 42 + 32 = 74 \]
Since \( 48 \neq 74 \), statement #3 is false.
Conclusion
The only true statement is statement #1. Thus, the true responses are:
1 and 3 (but only #1 is true)
1 answer