The term 'vaguely-provided' is a compound adjective formed from 'vaguely' and 'provided'. 'Vaguely' originates from the Latin word 'vagus', meaning 'wandering' or 'indeterminate'. 'Provided' comes from the Latin 'providere', meaning 'to foresee' or 'to supply'.

The word 'vaguely' evolved from the Latin 'vagus' through Old French 'vague', while 'provided' evolved from Latin 'providere' through Old French 'proveer'. The combination of these words into 'vaguely-provided' is a modern English construct.

Initially, 'vaguely' meant 'wandering' or 'indeterminate', and 'provided' meant 'to supply'. Together, they now describe something given in an unclear manner.