Question Determine which of the following statements is/are true: #1: 3⋅20=4(6+9) #2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8 #3: 4⋅18−4⋅6=42+4⋅8 (1 point) Responses 1 and 2 1 and 2 1 and 3 1 and 3 2 and 3 2 and 3 1 1 Skip to navigation

Answer 1

Let's evaluate each statement one by one:

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

Calculating both sides:

• Left side: \( 3 \cdot 20 = 60 \)
• Right side: \( 4(6 + 9) = 4 \cdot 15 = 60 \)

Both sides are equal, so Statement #1 is true.

Statement #2: \( 4 \times 12 = 6 \times (8 \times 2) + 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8 \)

Now calculate the left side:

• Left side: \( 4 \times 12 = 48 \)

Now evaluate the right side:

• Right side:
  • \( 6 \times (8 \times 2) = 6 \times 16 = 96 \)
  • \( 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \)

Combining the two parts of the right side:

• \( 96 + 60 = 156 \)

Clearly, \( 48 \neq 156 \). Therefore, Statement #2 is false.

Statement #3: \( 4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8 \)

Calculate the left side:

• \( 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \)

Now calculate the right side:

• \( 42 + 4 \cdot 8 = 42 + 32 = 74 \)

Since \( 48 \neq 74 \), Statement #3 is false.

Conclusion:

Only Statement #1 is true. The correct response is: 1.