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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which statements are true, we need to evaluate the expressions on both sides of the equation and see if they are equal.

#1: 3⋅20=4(6+9)
60=4(15)
60=60
This statement is true.

#2: 4×12=6×(8×2)
48=6×16
48=96
This statement is false.

#3: 4⋅18−4⋅6=42+4⋅8
72-24=42+32
48=74
This statement is false.

Therefore, the true statement is only #1: 3⋅20=4(6+9).

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's evaluate each statement separately to determine if they are true or not:

#1: 3⋅20=4(6+9)
First, we simplify the right side of the equation:
4(6+9) = 4(15) = 60

Now, we can compare both sides of the equation:
3⋅20 = 60

Since the left side is equal to the right side, statement #1 is true.

#2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8
Let's evaluate each part of the statement separately:

- 4×12 = 48
- 6×(8×2) = 6×16 = 96

48 does not equal 96, so the first part of the statement is false.

Now, let's evaluate the second part:
12+6⋅64−−√ = 12 + 6√64 = 12 + 6×8 = 12 + 48 = 60

2⋅4⋅8 = 2×32 = 64

60 does not equal 64, so the second part of the statement is also false.

Therefore, statement #2 is false.

#3: 4⋅18−4⋅6=42+4⋅8
calculate each side of the equation:

- 4⋅18 = 72
- 4⋅6 = 24
- 42+4⋅8 = 42 + 32 = 74

72 does not equal 74, so statement #3 is false.

Therefore, statement #1 is true, while statement #2 and statement #3 are false.