This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Judith, katika pembetatu, jumla ya pembe zote ni 180^. Tunapewa pembe tatu: 2x^, 2x^, na (2x^2 - 60)^. Step 1: Andika jumla ya pembe zote za pembetatu. Jumla ya pembe za pembetatu ni 180^. Step 2: Tengeneza mlinganyo kwa kutumia pembe ulizopewa. 2x + 2x + (2x^2 - 60) = 180 Step 3: Rahisisha mlinganyo. 2x^2 + 4x - 60 = 180 Step 4: Panga upya mlinganyo katika mfumo wa quadratic ax^2 + bx + c = 0. 2x^2 + 4x - 60 - 180 = 0 2x^2 + 4x - 240 = 0 Step 5: Gawanya mlinganyo mzima kwa 2 ili kurahisisha. x^2 + 2x - 120 = 0 Step 6: Tatua mlinganyo wa quadratic kwa kutumia njia ya kuzidisha (factoring). Tunatafuta namba mbili ambazo zinazidishana kutoa -120 na kujumlisha kutoa 2. Namba hizo ni 12 na -10. (x + 12)(x - 10) = 0 Hii inatoa suluhisho mbili zinazowezekana kwa x: x + 12 = 0 x = -12 x - 10 = 0 x = 10 Step 7: Angalia suluhisho gani ni halali. Pembe za pembetatu haziwezi kuwa hasi. Kama x = -12: Pembe ya kwanza: 2x = 2(-12) = -24^. Hii haiwezekani. Kama x = 10: Pembe ya kwanza: 2x = 2(10) = 20^. Pembe ya pili: 2x = 2(10) = 20^. Pembe ya tatu: 2x^2 - 60 = 2(10)^2 - 60 = 2(100) - 60 = 200 - 60 = 140^. Jumla ya pembe: 20^ + 20^ + 140^ = 180^. Hii ni sahihi. Kwa hivyo, thamani halali ya x ni 10. The value of x is: 10 3 done, 2 left today. You're making progress.