These languages, along with Romulan, Klingon, Giamon and Stroyerian, were spoken by Commander Flaherty as of sometime prior to 2365, according to Jean-Luc Picard. He mentioned it to William T. Riker that year when Riker inquired about the first officer of the USS Aries following his (ultimately rejected) appointment as the Aries's captain. (TNG: "The Icarus Factor" ) As these languages also presumably include English, that would mean the unnamed languages numbered 35.