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 and 3
1 and 3

1 and 2
1 and 2

1

Answer 1

To determine which of the statements are true, let's evaluate each one individually.

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

Calculating the left side: \[ 3 \cdot 20 = 60 \] Calculating the right side: \[ 4(6 + 9) = 4 \cdot 15 = 60 \] Since both sides equal 60, Statement #1 is true.

Statement #2: \(4 \cdot 12 = 6 \cdot (8 \cdot 2) 12 + 6 \cdot 64^{-1} = 2 \cdot 4 \cdot 8\)

First, calculate \(4 \cdot 12\): \[ 4 \cdot 12 = 48 \] Now consider \(6 \cdot (8 \cdot 2)\): \[ 8 \cdot 2 = 16 \Rightarrow 6 \cdot 16 = 96 \] Then we interpret \( (96) 12 \) as a misinterpretation; \( 6 \cdot 64^{-1} = 6 \cdot \frac{1}{64} = \frac{6}{64} = \frac{3}{32} \rightarrow\) which is likely irrelevant to equality as it's based on accessing an incorrect expression of 'equals'.

Lastly, calculate \(2 \cdot 4 \cdot 8\): \[ 2 \cdot 4 \cdot 8 = 64 \]

Since \(48 \neq 96 + \text{something small}\), Statement #2 is false.

Statement #3: \(4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8\)

Calculating the left side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]

Calculating the right side: \[ 42 + 4 \cdot 8 = 42 + 32 = 74 \] Since \(48 \neq 74\), Statement #3 is false.

Based on this analysis, the only statement that is true is Statement #1.

Therefore, the correct answer is: 1

Answer 2

Which expression is A, in order to have a true equation A=5−113?(1 point)
Responses

A=−123+13
negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=153+13
Start Fraction 15 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=123−13
1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=123+13

Answer 3

To determine which expression equals \( A \) such that \( A = 5 - \frac{11}{3} \), we first calculate \( 5 - \frac{11}{3} \).

1. Convert \( 5 \) to a fraction with a denominator of \( 3 \): \[ 5 = \frac{15}{3} \]

2. Subtract the fractions: \[ A = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]

Now, we have found that \( A = \frac{4}{3} \).

Next, let's evaluate each of the provided expressions to see which one equals \( A \):

1. Expression 1: \( A = -\frac{2}{3} + \frac{1}{3} \) \[ = -\frac{2}{3} + \frac{1}{3} = -\frac{2 - 1}{3} = -\frac{1}{3} \quad (\text{not } \frac{4}{3}) \]

2. Expression 2: \( A = \frac{15}{3} + \frac{1}{3} \) \[ = \frac{15 + 1}{3} = \frac{16}{3} \quad (\text{not } \frac{4}{3}) \]

3. Expression 3: \( A = \frac{12}{3} - \frac{1}{3} \) \[ = \frac{12 - 1}{3} = \frac{11}{3} \quad (\text{not } \frac{4}{3}) \]

4. Expression 4: \( A = \frac{12}{3} + \frac{1}{3} \) \[ = \frac{12 + 1}{3} = \frac{13}{3} \quad (\text{not } \frac{4}{3}) \]

None of the expressions provided match \( A = \frac{4}{3} \).

If the options provided are incorrect for some values, it might be an issue in the options or the original equation \( A = 5 - \frac{11}{3} \) not aligning with the choices.

Let me know if you need further assistance!