They shall levy all needful taxes on the assessable property within the county liable to taxation and provide for collecting the same, and they may make such levy in whole or in part by estimate; they shall provide for the support of the courts, compensate jurors and county or State witnesses, levy for outpensions allowed by themselves or the trustees of the poor, and such sums as may be necessary to pay accounts allowed by them for the funeral expenses of paupers, and pay and discharge all claims on or against the county which have been expressly or impliedly authorized by law.