At the time appointed for hearing such petition, or at the time to which such hearing may be adjourned by the mayor and city council, the mayor and city council shall consider the said petition, and all objections filed thereto, and shall hear the said parties; provided it shall then appear to the satisfaction of the mayor and city council that notice of said hearing has been given as herein provided, and in the event that such body shall determine to grant the prayer of said petition, the mayor and city council shall thereupon, by ordinance, vacate such street, avenue, public way or portion thereof. (1983 Code § 12.08.030)