Which pair of numbers are not opposites? Select one: \( \begin{array}{l}\text { a. } 27 \text { and }|-27| \\ \text { b. } 72 \text { and }-72 \\ \text { c. } 171 \text { and }-7 \\ \text { d. } 27 \text { and }-27\end{array} \)

The pair of numbers that are not opposites is \(171\) and \(-7\). Opposite numbers have the same absolute value but differ in sign, so while \(27\) and \(-27\) or \(72\) and \(-72\) do have that relationship, \(171\) and \(-7\) do not, as they are vastly different in value. To put it in context, opposites are like mirror images across zero on a number line. If you imagine \(27\) on the right and \(-27\) on the left, they stand equal distance from zero but on opposite sides! That's what makes them opposites, and thus \(171\) and \(-7\) just don't belong in that club.