Hydra Slayer

You are facing a nine-headed hydra. Your flaming longsword cuts five heads in each swipe (no more, no less), which will kill a five-headed hydra, but a larger one will regrow two heads after each swipe. Your storm scythe cuts exactly seven heads, but it makes ten heads grow back if the hydra is not dead.

Is it possible to kill the hydra? What if you also had a silver dagger, which cuts just one head, but makes five heads grow back?