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Use the properties of operations to add 9(k+13)+10(12k−1)
.(1 point)
Responses

14k+13
14 k plus 13

14k−23
14 k minus Start Fraction 2 over 3 End Fraction

1912k−23
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

14k−7

1 answer

To simplify the expression \( 9(k + 13) + 10(12k - 1) \), we will follow the steps of distributing and combining like terms.

  1. Distribute \(9\) and \(10\):

\[ 9(k + 13) = 9k + 117 \]

\[ 10(12k - 1) = 120k - 10 \]

  1. Now, combine the results:

\[ 9k + 117 + 120k - 10 \]

  1. Combine the like terms (the \(k\) terms and the constant terms):

\[ (9k + 120k) + (117 - 10) = 129k + 107 \]

So, the final simplified expression is:

\[ 129k + 107 \]

However, none of the given options match this outcome. Let's check if additional discrepancies or if variables could lead you towards the selection.

If instead,

  1. You meant to write a case of miscalculation or shortcuts.
  2. Recheck the operations. Given you suspect certain options to be valid, then you can correlate specifics towards \(k\) adjustments; part by keeping check factorization towards both results. These might hint towards correct assembly.

But here's safely put the final derivative you derived:

\( 129k + 107 \)

Please review for exactness or if any context misses around operations' effects.