The council shall hold regular public meetings weekly, day or night, at a regular hour to be fixed by said council from time to time and publicly announced; it may hold such special or other meetings as the business of the city may require. The presence of five council members will constitute a quorum for the conduct of official council business. The affirmative vote of at least five members of the council shall be sufficient for the passage of any resolution, bylaw ordinance, or the transaction of any business of any sort by the said council or the exercise of any of the powers conferred upon it by the terms of this chapter or bylaw, or which may hereafter be conferred upon it. No resolution, bylaw or ordinance granting any franchise, appropriating any money for any purpose, providing for any public improvements, any regulation concerning the public health, or of any other general or permanent nature, shall be enacted except at a regular or special public meeting of said council. Every ordinance introduced at any and every meeting shall be in writing and shall be read before any vote thereon shall be taken, and the yeas and nays thereon shall be recorded; provided that if the vote of all council members present be unanimous, it may be so stated in the journal without recording the yeas and nays. A record of the proceedings of every meeting of the council shall be kept, and every resolution or ordinance passed by the council must be recorded, and the record of the proceedings of the meeting shall, when approved by the council, be signed by the president of the council and the city clerk. Such records shall be kept available for inspection by all citizens of such city during regular business hours. No ordinance of permanent operation shall be considered at the meeting at which it was introduced except by unanimous consent of all members of the council present, and such unanimous consent shall be entered upon the minutes of said meeting; provided, however, that if all members of the council present vote for the passage of the ordinance and their names are so entered of record as voting in favor thereof, it shall be construed as giving unanimous consent to the action upon such ordinance at the meeting at which it is introduced. All ordinances or resolutions of a permanent nature, after having been passed by the council, shall be transmitted by the clerk within 48 hours after their passage to the mayor for his consideration, who, if he shall approve thereof, shall sign and return the same to the clerk, who shall publish them, if publication thereof is required, and such ordinances and resolutions shall thereupon become effective and have the force of law. Delivery to the office of the mayor shall constitute delivery to the mayor. An ordinance or resolution may be recalled from the mayor at any time before it has become law, or has been acted on by him, by a resolution adopted by a majority of the members elected to the council in regular or special session. If the mayor shall disapprove of any ordinance or resolution transmitted to him as aforesaid, he shall, within 10 days of the time of its passage by the council, return the same to the clerk with his objections in writing, and the clerk shall make a report thereof to the next regular meeting of the city council; and if five members elected to the said council shall at said meeting adhere to said ordinance or resolution, notwithstanding said objections, said vote being taken by yeas and nays and spread upon the minutes, then, and not otherwise, said ordinance or resolution shall after publication thereof, if publication is required, have the force of law. If publication of said ordinance or resolution is not required, it shall take effect upon its passage over such veto. The failure of the mayor to return to the city clerk an ordinance or resolution with his veto within 10 days after its passage by the council shall operate and have the same effect as an approval of the same, and the city clerk, if publication is required, shall publish the same as is herein provided for publication of laws and ordinances of said city. If no publication is required, the ordinance or resolution shall become effective upon the expiration of said 10 days. These provisions are subject to the publication of ordinances as set out in section 11-45-8. Anything in this section to the contrary notwithstanding, the mayor shall not have the power of veto over any action of the council relating to an investigation as provided herein.