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
1

1 and 2
1 and 2

2 and 3
2 and 3

1 and 3

Answer 1

Let's analyze each of the statements to determine if they are true or false.

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

Calculating both sides:
- Left Side: \( 3 \cdot 20 = 60 \)
- Right Side: \( 4(6 + 9) = 4 \cdot 15 = 60 \)

Since both sides are equal, statement #1 is **true**.

#2: \( 4 \times 12 = 6 \times (8 \times 2) \)

Calculating both sides:
- Left Side: \( 4 \times 12 = 48 \)
- Right Side: \( 6 \times (8 \times 2) = 6 \times 16 = 96 \)

Since both sides are not equal, statement #2 is **false**.

#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: \( 42 + 4 \cdot 8 = 42 + 32 = 74 \)

Since both sides are not equal, statement #3 is **false**.

In conclusion:
- Statement #1 is true.
- Statement #2 is false.
- Statement #3 is false.

The correct answer is **1**.