To find \( k(-7) \), we simply need to substitute \(-7\) into the function \( k(t) = 10t - 19 \):
\[ k(-7) = 10(-7) - 19 \]
Calculating this step-by-step:
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Multiply \(10\) by \(-7\): \[ 10 \times -7 = -70 \]
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Subtract \(19\) from \(-70\): \[ -70 - 19 = -89 \]
Therefore, the value of \( k(-7) \) is: \[ \boxed{-89} \]