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.
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Haya, tutasuluhisha maswali haya. 19. St. Paul Junior school organized a tour for candidate class to Jinja which is 240km away. After covering (2)/(5) of the journey, candidates were taken for breakfast. Work out the distance which was remaining to reach Jinja. Step 1: Tambua umbali wote wa safari. Umbali wote ni 240 km. Step 2: Hesabu sehemu ya safari iliyobaki. Ikiwa (2)/(5) ya safari imefunikwa, basi sehemu iliyobaki ni 1 - (2)/(5). 1 - (2)/(5) = (5)/(5) - (2)/(5) = (3)/(5) Step 3: Hesabu umbali uliosalia kufika Jinja. Umbali uliosalia = Sehemu iliyobaki × Umbali wote Umbali uliosalia = (3)/(5) × 240 km Umbali uliosalia = 3 × (240)/(5) km Umbali uliosalia = 3 × 48 km Umbali uliosalia = 144 km Jibu la mwisho ni: 144 km 20. Simplify: (1)/(2)(4x + 4) - (1)/(5)(x + 5) Step 1: Panua (distribute) nambari za nje kwenye mabano. (1)/(2)(4x + 4) = (1)/(2) × 4x + (1)/(2) × 4 = 2x + 2 (1)/(5)(x + 5) = (1)/(5) × x + (1)/(5) × 5 = (1)/(5)x + 1 Step 2: Andika upya mlinganyo kwa kutumia matokeo ya upanuzi. Kumbuka kutoa nambari zote za pili. (2x + 2) - ((1)/(5)x + 1) 2x + 2 - (1)/(5)x - 1 Step 3: Panga upya maneno yanayofanana pamoja. 2x - (1)/(5)x + 2 - 1 Step 4: Unganisha maneno yanayofanana. Kwa maneno ya x: 2x - (1)/(5)x = (10)/(5)x - (1)/(5)x = (9)/(5)x Kwa maneno ya nambari: 2 - 1 = 1 Step 5: Andika jibu lililorahisishwa. (9)/(5)x + 1 Jibu la mwisho ni: (9)/(5)x + 1 3 done, 2 left today. You're making progress.