How does faith relate to the heart according to the Bible?

In Romans 10:9-10, it is stated that 'If thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.' This signifies that true belief stems from a transformed heart, one that has been made new by the grace of God. The heart, in this context, is not merely a seat of emotions but signifies the core of one's spiritual being where authentic faith resides, enabling individuals to accept and trust in Jesus Christ for their salvation.