The statement that best explains the impact of Greek and Roman democracies on how the U.S. legislative, judiciary, and executive branches function is:
"The writers of the US constitution took inspiration from Greece and Rome but adapted the ancient ideas to create a mixed government system of their own."
This reflects the fact that while the Founding Fathers were influenced by ancient Greek democracy and Roman republicanism, they recognized the complexities of governance and made modifications to create a balanced system that included elements of democracy, republicanism, and checks and balances among the three branches of government.