Determine which of the following statements is/are true:

Question

#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

2 and 3
2 and 3

1
1

1 and 2
1 and 2

1 and 3
1 and 3

Answer 1

To determine which statements are true, let's evaluate each 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:

\(4 \cdot 12 = 6 \cdot (8 \cdot 2) + 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8\)

Calculating each part:

• Left side: \(4 \cdot 12 = 48\)
• Right side: \[ 6 \cdot (8 \cdot 2) + 12 + 6 \cdot \sqrt{64} = 6 \cdot 16 + 12 + 6 \cdot 8 \] \[ = 96 + 12 + 48 = 156 \] This does not equal \(48\), so Statement #2 is false.

Statement #3:

\(4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8\)

Calculating both sides:

• Left side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]
• Right side: \[ 42 + 4 \cdot 8 = 42 + 32 = 74 \] This does not equal \(48\), so Statement #3 is false.

Conclusion:

Only Statement #1 is true.

The correct response is: 1