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
Huu hapa ni ufumbuzi wa swali la 11: Step 1: Tafuta jumla ya pembe za ndani za heksagoni. Jumla ya pembe za ndani za poligoni yenye n pande hutolewa na fomula (n-2) × 180^. Kwa heksagoni, n=6. Jumla ya pembe = (6-2) × 180^ = 4 × 180^ = 720^ Step 2: Tengeneza mlinganyo kwa kujumlisha pembe zote zilizopewa na kuziweka sawa na jumla ya pembe. Pembe zilizopewa ni 2x^, (1)/(2)x^, (x+40)^, 110^, 130^, na 160^. 2x + (1)/(2)x + (x+40) + 110 + 130 + 160 = 720 Step 3: Tatua mlinganyo ili kupata thamani ya x. Kwanza, jumlisha vigezo vya x na namba zisizo na x: (2x + 0.5x + x) + (40 + 110 + 130 + 160) = 720 3.5x + 440 = 720 Toa 440 kutoka pande zote mbili: 3.5x = 720 - 440 3.5x = 280 Gawanya pande zote mbili kwa 3.5: x = (280)/(3.5) x = 80 Step 4: Kokotoa kila pembe kwa kutumia thamani ya x. • Pembe ya kwanza: 2x^ = 2(80)^ = 160^ • Pembe ya pili: (1)/(2)x^ = (1)/(2)(80)^ = 40^ • Pembe ya tatu: (x+40)^ = (80+40)^ = 120^ • Pembe ya nne: 110^ • Pembe ya tano: 130^ • Pembe ya sita: 160^ Step 5: Tambua pembe ndogo zaidi. Kulinganisha pembe zote: 160^, 40^, 120^, 110^, 130^, 160^. Pembe ndogo zaidi ni 40^. Pembe ndogo zaidi ni 40^. Tuma swali linalofuata 📸