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determine which of the following statements is/are true

1: 3 dot 20 = 4 (6+9)
2: 4 x 12 = 6 x (8 x 2) 12 + 6 dot sqrt 64 =2 dot 4 dot 8
3: 4 dot 18 - 4 dot 6 = 4^2 + 4 dot 8

1 answer

Let's analyze each statement one by one. Note that "dot" indicates multiplication.

  1. Statement 1: \(3 \cdot 20 = 4 \cdot (6 + 9)\)

    Left side: \[ 3 \cdot 20 = 60 \]

    Right side: \[ 4 \cdot (6 + 9) = 4 \cdot 15 = 60 \]

    Conclusion: True (both sides equal 60).

  1. Statement 2: \(4 \cdot 12 = 6 \cdot (8 \cdot 2) \quad \text{and} \quad 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8\)

    First part: Left side: \[ 4 \cdot 12 = 48 \]

    Right side: \[ 6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96 \]

    Here, \(4 \cdot 12\) does not equal \(6 \cdot (8 \cdot 2)\), so the first part is False.

    Second part: Left side: \[ 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \]

    Right side: \[ 2 \cdot 4 \cdot 8 = 8 \cdot 8 = 64 \]

    Here, \(12 + 6 \cdot \sqrt{64}\) does not equal \(2 \cdot 4 \cdot 8\), so the second part is also False.

    Conclusion: False (neither part is true).

  1. Statement 3: \(4 \cdot 18 - 4 \cdot 6 = 4^2 + 4 \cdot 8\)

    Left side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]

    Right side: \[ 4^2 + 4 \cdot 8 = 16 + 32 = 48 \]

    Conclusion: True (both sides equal 48).

Summary of results:

  1. True
  2. False
  3. True

So, statements 1 and 3 are true, and statement 2 is false.