which of the following is used by the federal government to support social security and medicare programs

Via Federal Payroll tax.

Explanation:

The social security is being financed through the federal payroll tax, and Employees and Employers contribute with 6.2% of their salaries, whereas the self employed contribute around 12.4%. However, you will need certain monthly premium which is quite small being needed for the non medical coverage. As far as the medicare is concerned, it is a federal program, and you will find it being the same everywhere in the US, and it is being regulated by the centers of Medicare and Medicaid services such as the federal government agencies.