Final answer:
In Greek mythology, Athena appeased the Furies with the gift of an olive tree, symbolizing peace and prosperity, unlike material offerings such as food, water, or jewels. The olive tree represented Athena's values of wisdom and foresight and reflected her role as the patron goddess of the city of Athens.
Step-by-step explanation:
The Furies, also known as the Eumenides in Greek mythology, were appeased by Athena with offerings that represent peace and prosperity, rather than material objects like food, water, money, or jewels.
Instead, Athena presented an olive tree, symbolizing peace and the potential for prosperity through agriculture and trade - values that would characterize the city of Athens.
This act is part of the broader narrative concerning the contest between Athena and Poseidon for the patronage of Athens, where Poseidon offered a saltwater spring, representing naval power, but the Athenians chose Athena's olive tree.
The choice of the olive tree reflects Athena's associations with wisdom and civilization, emphasizing ingenuity and the long-term benefits of wise governance. Athena's wisdom was not only seen in legends but also in the way she supported heroes like Perseus, providing him with armor and strategic advice.