(a) The governing authority of each county has original and exclusive jurisdiction over the following subject matters:

(1) The directing and controlling of all the property of the county, according to law, as the governing authority deems expedient;

(2) The levying of a general tax for general county purposes and a special tax for particular county purposes;

(3) The establishing, altering, or abolishing of all roads, bridges, and ferries in conformity to law;

(4) Reserved;

(5) The filling of all vacancies in county offices unless some other body or official is empowered by law to so fill such vacancy;

(6) The examining, settling, and allowing of all claims against the county;

(7) The examining and auditing of the accounts of all officers having the care, management, keeping, collection, or disbursement of money belonging to the county or appropriated for its use and benefit and the settling of the same;

(8) The making of such rules and regulations for the support of the poor of the county, for the county police and patrol, for the promotion of health, and for quarantine as are authorized by law or not inconsistent therewith; and

(9) The regulating of peddling and fixing of the cost of licenses therefor.

(b) Nothing in this Code section shall be construed to prohibit a local law from delegating to a chairman or chief executive officer of a county governing authority jurisdiction over any subject matter provided for in subsection (a) of this Code section.