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It's a portrait by William Hogarth of Lavinia Fenton, Duchess of Bolton, painted circa 1740-50, and it's in the Tate, London.
Here's the caption:
This is traditionally said to be a portrait of the actress and singer Lavinia Fenton (1708–60), who starred as the heroine Polly Peachum in the original and wildly successful 1728 production of The Beggar's Opera. After it closed, Miss Fenton left the stage to become the mistress of Charles Paulet, 3rd Duke of Bolton (1685–1754). In this role she is said to have been a delightful and accomplished companion, and a model of discretion. She bore the Duke three illegitimate sons, all of whom did well in the army, navy and the church. When the Duke's estranged wife died in 1751, the Duke married Lavinia and she became Duchess of Bolton. This portrait – if correctly identified – shows her in her matronly, riper years.Here also is a link to the Wikipedia article on Beggar's Opera.