She argued 'convincingly' [='persuasively'] that more money should be given to public schools.
There is no 'convincing' evidence to support his theory.
Your argument/story isn't very 'convincing'.
(..) You better go back into the Senate. I hit him from the floor with everything I knew. I haven't got the stomach for it. If he starts convincing those senators, you might as well blow your brains out! This is the works! Either we're out of business or bigger than ever before. (..)1939 Mr. Smith Goes to Washington