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 2 and 3 2 and 3 1 1 1 and 3 1 and 3 1 and 2 1 and 2

Answer 1

so is only #1 true or 1 and 3?

Answer 2

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:
- Left-hand side:
\[ 4 \cdot 12 = 48 \]

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

- 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)**

Answer 3

I apologize for any confusion in my previous response. To clarify:

- **Statement #1** is **true**:
\[ 3 \cdot 20 = 60 \quad \text{and} \quad 4(6 + 9) = 4 \cdot 15 = 60 \]

- **Statement #2** is **false**:
\[ 4 \cdot 12 = 48 \quad \text{and} \quad 6 \cdot (8 \cdot 2) = 96 \quad (48 \neq 96) \]
Additionally, the other part of this statement also did not hold true.

- **Statement #3** is **false**:
\[ 4 \cdot 18 - 4 \cdot 6 = 48 \quad \text{and} \quad 42 + 4 \cdot 8 = 74 \quad (48 \neq 74) \]

Therefore, only **Statement #1** is true.

The accurate statement is that only statement **#1** is true. Thank you for your patience!