IPA: /rɪˈzɒl.juːt.li/
KK: /rɪˈzɑːlətli/
In a way that shows determination and firmness in purpose or action.
She resolutely refused to give up on her dreams.
Resolutely → It is formed from "re-" (meaning again) and "solutus" (from Latin, meaning loosened or freed) and the suffix "-ly" (meaning in a manner of). The word "resolutely" means in a manner that is determined or firmly decided, as if one has freed oneself from doubt.
Think of someone who is 'freed' ('solutus') from uncertainty and is acting 'again' ('re-') with determination — that's what it means to act resolutely.