Question
What is the quotient when dividing 56r−12/4t ?(1 point)
Responses
14r−3
11r/t
11
14r−3/t
Responses
14r−3
11r/t
11
14r−3/t
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{56r - 12}{4t} \), you can divide both terms in the numerator by the denominator.
1. First, separate the terms in the numerator:
\[
\frac{56r - 12}{4t} = \frac{56r}{4t} - \frac{12}{4t}
\]
2. Now simplify each term:
- For \( \frac{56r}{4t} \):
\[
\frac{56r}{4t} = \frac{56}{4} \cdot \frac{r}{t} = 14 \cdot \frac{r}{t} = \frac{14r}{t}
\]
- For \( \frac{12}{4t} \):
\[
\frac{12}{4t} = \frac{12}{4} \cdot \frac{1}{t} = 3 \cdot \frac{1}{t} = \frac{3}{t}
\]
3. Combine the simplified terms:
\[
\frac{56r - 12}{4t} = \frac{14r}{t} - \frac{3}{t} = \frac{14r - 3}{t}
\]
Thus, the final result is:
\[
\frac{14r - 3}{t}
\]
The correct response from the options you provided is \( 14r - 3/t \).
1. First, separate the terms in the numerator:
\[
\frac{56r - 12}{4t} = \frac{56r}{4t} - \frac{12}{4t}
\]
2. Now simplify each term:
- For \( \frac{56r}{4t} \):
\[
\frac{56r}{4t} = \frac{56}{4} \cdot \frac{r}{t} = 14 \cdot \frac{r}{t} = \frac{14r}{t}
\]
- For \( \frac{12}{4t} \):
\[
\frac{12}{4t} = \frac{12}{4} \cdot \frac{1}{t} = 3 \cdot \frac{1}{t} = \frac{3}{t}
\]
3. Combine the simplified terms:
\[
\frac{56r - 12}{4t} = \frac{14r}{t} - \frac{3}{t} = \frac{14r - 3}{t}
\]
Thus, the final result is:
\[
\frac{14r - 3}{t}
\]
The correct response from the options you provided is \( 14r - 3/t \).
Answer
When dividing 4x+2y−8/2b , how many variables will be present in the quotient?(1 point)
Responses
2
1
0
3
Responses
2
1
0
3
Answered by
GPT-4o mini
To analyze the expression \( \frac{4x + 2y - 8}{2b} \):
1. **Identify the numerator**: The numerator \( 4x + 2y - 8 \) consists of three terms involving the variables \( x \) and \( y \).
2. **Identify the denominator**: The denominator is \( 2b \), which involves the variable \( b \).
When you divide \( 4x + 2y - 8 \) by \( 2b \), you will distribute the division across each term in the numerator:
\[
\frac{4x}{2b} + \frac{2y}{2b} - \frac{8}{2b}
\]
This results in the following terms:
1. \( \frac{4x}{2b} = \frac{2x}{b} \)
2. \( \frac{2y}{2b} = \frac{y}{b} \)
3. \( \frac{8}{2b} = \frac{4}{b} \)
In the final expression, the variables present are \( x, y, \) and \( b \).
Thus, there are **3 variables** in total: \( x, y, \) and \( b \).
The correct response is **3**.
1. **Identify the numerator**: The numerator \( 4x + 2y - 8 \) consists of three terms involving the variables \( x \) and \( y \).
2. **Identify the denominator**: The denominator is \( 2b \), which involves the variable \( b \).
When you divide \( 4x + 2y - 8 \) by \( 2b \), you will distribute the division across each term in the numerator:
\[
\frac{4x}{2b} + \frac{2y}{2b} - \frac{8}{2b}
\]
This results in the following terms:
1. \( \frac{4x}{2b} = \frac{2x}{b} \)
2. \( \frac{2y}{2b} = \frac{y}{b} \)
3. \( \frac{8}{2b} = \frac{4}{b} \)
In the final expression, the variables present are \( x, y, \) and \( b \).
Thus, there are **3 variables** in total: \( x, y, \) and \( b \).
The correct response is **3**.
Answer
Divide 4a^2+4ab−2 by 2a. What is the quotient?(1 point)
Responses
2a+2b−1
2a+2b
2 a plus 2 b
2a+2b−1/a
2b−1/a
Responses
2a+2b−1
2a+2b
2 a plus 2 b
2a+2b−1/a
2b−1/a
Answered by
GPT-4o mini
To divide \( 4a^2 + 4ab - 2 \) by \( 2a \), we can distribute the division across each term in the numerator:
\[
\frac{4a^2 + 4ab - 2}{2a} = \frac{4a^2}{2a} + \frac{4ab}{2a} - \frac{2}{2a}
\]
Now we simplify each term:
1. **For \( \frac{4a^2}{2a} \)**:
\[
\frac{4a^2}{2a} = \frac{4}{2} \cdot \frac{a^2}{a} = 2a
\]
2. **For \( \frac{4ab}{2a} \)**:
\[
\frac{4ab}{2a} = \frac{4}{2} \cdot \frac{ab}{a} = 2b
\]
3. **For \( \frac{-2}{2a} \)**:
\[
\frac{-2}{2a} = -\frac{1}{a}
\]
Now, combining the results, we have:
\[
2a + 2b - \frac{1}{a}
\]
Therefore, the quotient is:
\[
2a + 2b - \frac{1}{a}
\]
The correct response from the options given is **2a + 2b - 1/a**.
\[
\frac{4a^2 + 4ab - 2}{2a} = \frac{4a^2}{2a} + \frac{4ab}{2a} - \frac{2}{2a}
\]
Now we simplify each term:
1. **For \( \frac{4a^2}{2a} \)**:
\[
\frac{4a^2}{2a} = \frac{4}{2} \cdot \frac{a^2}{a} = 2a
\]
2. **For \( \frac{4ab}{2a} \)**:
\[
\frac{4ab}{2a} = \frac{4}{2} \cdot \frac{ab}{a} = 2b
\]
3. **For \( \frac{-2}{2a} \)**:
\[
\frac{-2}{2a} = -\frac{1}{a}
\]
Now, combining the results, we have:
\[
2a + 2b - \frac{1}{a}
\]
Therefore, the quotient is:
\[
2a + 2b - \frac{1}{a}
\]
The correct response from the options given is **2a + 2b - 1/a**.
Answer
What is the quotient of 64x^2−48/8 ?(1 point)
Responses
8x−1/6
2x^2
2 x squared
8x−6
8 x minus 6
8x^2−6
Responses
8x−1/6
2x^2
2 x squared
8x−6
8 x minus 6
8x^2−6
Answered by
GPT-4o mini
To find the quotient of \( \frac{64x^2 - 48}{8} \), we can divide each term in the numerator by the denominator:
1. **Separate the terms**:
\[
\frac{64x^2 - 48}{8} = \frac{64x^2}{8} - \frac{48}{8}
\]
2. **Simplify each term**:
- For \( \frac{64x^2}{8} \):
\[
\frac{64x^2}{8} = 8x^2
\]
- For \( \frac{48}{8} \):
\[
\frac{48}{8} = 6
\]
3. **Combine the results**:
\[
\frac{64x^2 - 48}{8} = 8x^2 - 6
\]
Thus, the final quotient is:
\[
8x^2 - 6
\]
The correct response from the options you provided is **8x²−6**.
1. **Separate the terms**:
\[
\frac{64x^2 - 48}{8} = \frac{64x^2}{8} - \frac{48}{8}
\]
2. **Simplify each term**:
- For \( \frac{64x^2}{8} \):
\[
\frac{64x^2}{8} = 8x^2
\]
- For \( \frac{48}{8} \):
\[
\frac{48}{8} = 6
\]
3. **Combine the results**:
\[
\frac{64x^2 - 48}{8} = 8x^2 - 6
\]
Thus, the final quotient is:
\[
8x^2 - 6
\]
The correct response from the options you provided is **8x²−6**.
Answer
Divide 28x^2+7x−7/7x^2 . What is the quotient?(1 point)
Responses
4/x^2
Start Fraction 4 over x squared End Fraction
4+1/2x
4 plus Start Fraction 1 over 2 x End Fraction
4+1/x−1/x^2
4 plus Start Fraction 1 over x End Fraction minus Start Fraction 1 over x squared End Fraction
4+1/x^2
4 plus Start Fraction 1 over x squared End Fraction
Responses
4/x^2
Start Fraction 4 over x squared End Fraction
4+1/2x
4 plus Start Fraction 1 over 2 x End Fraction
4+1/x−1/x^2
4 plus Start Fraction 1 over x End Fraction minus Start Fraction 1 over x squared End Fraction
4+1/x^2
4 plus Start Fraction 1 over x squared End Fraction
Answered by
GPT-4o mini
To divide \( \frac{28x^2 + 7x - 7}{7x^2} \), we can separate each term in the numerator and divide by the denominator:
\[
\frac{28x^2}{7x^2} + \frac{7x}{7x^2} - \frac{7}{7x^2}
\]
Now, let's simplify each term:
1. For \( \frac{28x^2}{7x^2} \):
\[
\frac{28x^2}{7x^2} = \frac{28}{7} = 4
\]
2. For \( \frac{7x}{7x^2} \):
\[
\frac{7x}{7x^2} = \frac{7}{7} \cdot \frac{x}{x^2} = 1 \cdot \frac{1}{x} = \frac{1}{x}
\]
3. For \( \frac{-7}{7x^2} \):
\[
\frac{-7}{7x^2} = -\frac{1}{x^2}
\]
Now, combine these results:
\[
4 + \frac{1}{x} - \frac{1}{x^2}
\]
Thus, the final quotient is:
\[
4 + \frac{1}{x} - \frac{1}{x^2}
\]
The correct response from the options you provided is **4 + 1/x − 1/x²**.
\[
\frac{28x^2}{7x^2} + \frac{7x}{7x^2} - \frac{7}{7x^2}
\]
Now, let's simplify each term:
1. For \( \frac{28x^2}{7x^2} \):
\[
\frac{28x^2}{7x^2} = \frac{28}{7} = 4
\]
2. For \( \frac{7x}{7x^2} \):
\[
\frac{7x}{7x^2} = \frac{7}{7} \cdot \frac{x}{x^2} = 1 \cdot \frac{1}{x} = \frac{1}{x}
\]
3. For \( \frac{-7}{7x^2} \):
\[
\frac{-7}{7x^2} = -\frac{1}{x^2}
\]
Now, combine these results:
\[
4 + \frac{1}{x} - \frac{1}{x^2}
\]
Thus, the final quotient is:
\[
4 + \frac{1}{x} - \frac{1}{x^2}
\]
The correct response from the options you provided is **4 + 1/x − 1/x²**.