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Which expression is equivalent to 60(14x−2)+20(34y−4)

(1 point)
Responses

30xy−200
30 x y minus 200

15x+15y−200
15 x plus 15 y minus 200

15x−15y−200
15 x minus 15 y minus 200

15x+15y−64

3 answers

To simplify the expression \(60(14x−2)+20(34y−4)\), we can first distribute the constants through each parenthesis.

  1. Distributing \(60\) into \(60(14x - 2)\): \[ 60 \times 14x - 60 \times 2 = 840x - 120 \]

  2. Distributing \(20\) into \(20(34y - 4)\): \[ 20 \times 34y - 20 \times 4 = 680y - 80 \]

  3. Now, we can combine these results: \[ 840x - 120 + 680y - 80 \]

  4. Combining like terms: \[ 840x + 680y - (120 + 80) = 840x + 680y - 200 \]

Now, since none of the provided options exactly matches \(840x + 680y - 200\), we can look for an equivalent expression.

However, if we consider factoring out common terms or simplifying further based on options:

  • The expression cannot be simplified directly to fit any of the provided answers.

Of the options provided, none correctly reflect the simplified version \(840x + 680y - 200\).

  • The closest approximation for further understanding is that the first two terms might require simple integer coefficients, but based on what it is, the result remains as is.

Therefore, the expression \(60(14x−2)+20(34y−4)\) results in \(840x + 680y - 200\), and none of the provided responses accurately represent it.

If focusing on just the constant part alone from the options given: The expression simplifies correctly to an integer part of -200, but the term coefficients for \(xy\) or individually holding \(x,y\) do not carry through since there's no direct placement through transformation from variables as indicated.

So for responding to the provided formats, there isn't any valid fit based strictly on the calculation obtained as initially noted. If there’s any further context, please let me know, and details can be reconsidered.

whats the closest answer

From the original expression \(60(14x - 2) + 20(34y - 4)\), we simplified it to:

\[ 840x + 680y - 200 \]

Now let's review the provided options again:

  1. 30xy - 200
  2. 15x + 15y - 200
  3. 15x - 15y - 200
  4. 15x + 15y - 64

None of these options matches the simplified expression \(840x + 680y - 200\), but we can evaluate each.

Since the expression includes terms with \(x\) and \(y\), the only options that seem potentially similar in structure are:

  • 15x + 15y - 200
  • 15x - 15y - 200

The part -200 is common across two options, but they both significantly reduce the coefficients of \(x\) and \(y\).

Here’s how we can best approach it:

  • The expression \(15x + 15y - 200\) matches the constant term exactly, and the mixed coefficients relative to \(x\) and \(y\) can relate back by simply considering some simplification paths but might not convert through \(15x + 15y\).

So the closest answer based solely on the constant term \(-200\) would be:

15x + 15y - 200

This option accurately reflects the constant's value from the original expression after performing our simplifications.