Chemical energetics: compare question

The standard enthalpy change of formation of carbon dioxide, $\ce{CO2(g)}$, is represented by $\Delta H_f^\circ$. The standard enthalpy change of combustion of carbon (graphite), $\ce{C(s)}$, is represented by $\Delta H_c^\circ$.

Compare the two enthalpy changes, $\Delta H_f^\circ$ of $\ce{CO2(g)}$ and $\Delta H_c^\circ$ of $\ce{C(s)}$. In your answer, include the definitions of each enthalpy change, standard conditions, and an explanation of why the numerical values are related.