Final answer:
Peter's vision in Acts, which represents the acceptance of Gentile believers by God, is 'unclean animals on a sheet'. This message indicated that non-Jewish people could join the Christian faith without adhering to Jewish customs. Option c) unclean animals on a sheet, is correct answer.
Step-by-step explanation:
In the Acts of the Apostles, the vision of Peter that signifies gentile believers are acceptable to God, who has cleansed them through faith, is c) unclean animals on a sheet. This vision occurs in Acts 10:9-16, where Peter sees a sheet descending from heaven holding all kinds of animals that were considered unclean by Jewish law. In the vision, he is told to kill and eat, to which he initially responds with hesitation because the Jewish law forbade consuming unclean animals. However, a voice speaks to him, indicating that God has made these animals clean. The vision is interpreted as God's message that the Gentiles (non-Jewish people) should not be considered unclean and that they are welcomed into the Christian faith without needing to adhere to the traditional Jewish laws or customs. This pivotal moment in the scripture reflects a significant shift in early Christian theology, broadening the Church's mission to include all humanity.