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

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 $48\ne 96$, 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 $60\ne 64$, 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 $48\ne 74$, 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 2

so is only #1 true or 1 and 3?

Answer 3

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

• Statement #1 is true: $$3\cdot 20=60\text{and}4(6+9)=4\cdot 15=60$$

• Statement #2 is false: $$4\cdot 12=48\text{and}6\cdot (8\cdot 2)=96(48\ne 96)$$ Additionally, the other part of this statement also did not hold true.

• Statement #3 is false: $$4\cdot 18-4\cdot 6=48\text{and}42+4\cdot 8=74(48\ne 74)$$

Therefore, only Statement #1 is true.

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