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What is the quotient when dividing 56r/ 4t + -12/4t

7 answers

To simplify the expression \( \frac{56r}{4t} + \frac{-12}{4t} \), we can first simplify each term separately.

  1. For the first term \( \frac{56r}{4t} \): \[ \frac{56r}{4t} = \frac{56}{4} \cdot \frac{r}{t} = 14 \cdot \frac{r}{t} = \frac{14r}{t} \]

  2. For the second term \( \frac{-12}{4t} \): \[ \frac{-12}{4t} = \frac{-12}{4} \cdot \frac{1}{t} = -3 \cdot \frac{1}{t} = \frac{-3}{t} \]

Now we can combine the two terms: \[ \frac{14r}{t} + \frac{-3}{t} = \frac{14r - 3}{t} \]

Thus, the final result of the expression is: \[ \frac{14r - 3}{t} \]

Therefore, the quotient when dividing \( \frac{56r}{4t} + \frac{-12}{4t} \) simplifies to \( \frac{14r - 3}{t} \).

When dividing 4x/2b + 2y/2b + −8/2b , how many variables will be present in the quotient?(1 point)

To simplify the expression \( \frac{4x}{2b} + \frac{2y}{2b} + \frac{-8}{2b} \), we can first simplify each term:

  1. For the first term \( \frac{4x}{2b} \): \[ \frac{4x}{2b} = \frac{4}{2} \cdot \frac{x}{b} = 2 \cdot \frac{x}{b} = \frac{2x}{b} \]

  2. For the second term \( \frac{2y}{2b} \): \[ \frac{2y}{2b} = \frac{2}{2} \cdot \frac{y}{b} = 1 \cdot \frac{y}{b} = \frac{y}{b} \]

  3. For the third term \( \frac{-8}{2b} \): \[ \frac{-8}{2b} = \frac{-8}{2} \cdot \frac{1}{b} = -4 \cdot \frac{1}{b} = \frac{-4}{b} \]

Now we can combine the simplified terms: \[ \frac{2x}{b} + \frac{y}{b} + \frac{-4}{b} = \frac{2x + y - 4}{b} \]

Now, in the expression \( \frac{2x + y - 4}{b} \):

  • The variables present in the numerator \( 2x + y - 4 \) are \( x \) and \( y \).

Thus, there are 2 variables present in the quotient: \( x \) and \( y \).

Divide 4a^2+4ab−2 by 2a . What is the quotient?(1 point)

To divide the expression \( 4a^2 + 4ab - 2 \) by \( 2a \), we can divide each term of the numerator by \( 2a \).

  1. Divide the first term: \[ \frac{4a^2}{2a} = \frac{4}{2} \cdot \frac{a^2}{a} = 2a \]

  2. Divide the second term: \[ \frac{4ab}{2a} = \frac{4}{2} \cdot \frac{ab}{a} = 2b \]

  3. Divide the third term: \[ \frac{-2}{2a} = -\frac{2}{2a} = -\frac{1}{a} \]

Now, combine all the results: \[ 2a + 2b - \frac{1}{a} \]

Thus, the quotient when dividing \( 4a^2 + 4ab - 2 \) by \( 2a \) is: \[ 2a + 2b - \frac{1}{a} \]

What is the quotient of 64x2−488 ?(1 point)
Responses

8x−16
8 x minus Start Fraction 1 over 6 End Fraction

8x2−6
8 x squared minus 6

2x2
2 x squared

8x−6

To find the quotient of \( 64x^2 - 488 \), we first notice that we can factor out a common factor from the expression.

  1. We will first factor out \( 8 \) from \( 64x^2 - 488 \):

\[ 64x^2 - 488 = 8(8x^2 - 61) \]

We can see this expression \( 8(8x^2 - 61) \) does not simplify further with respect to division, but if the question is asking to find the expression after factoring (in terms of finding the quotient when divided by \( 8 \)), we can divide both sides by 8.

The quotient would be:

\[ 8x^2 - 61 \]

However, if we look at the provided responses, the one that fits better in terms of a typical expression is:

\[ 8x - 6 \]

It seems I misunderstood your request. There may be other interpretations in your responses. Can you please clarify? If you are looking specifically for polynomial long division or trying to match with one of the provided options, let me know for further assistance!