Can i hook a deep cycle battery up to a regular car battery for my sound system?

i have a hifonics brutus amp to power my 2 15" inch olympus subs and i need to hook another battery up to power the beasts lol. the guy gave me his yellow top optima with the system but i dont know if it will charge right with my car battery.
PLEASE HELP ME!!!
Update: i have a 08 mustang gt500
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