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
Haya master, twende na maswali haya. Swali la 1: Chai ya Maziwa Step 1: Tafuta kiasi cha maziwa. Kiasi cha maji ni lita 12. Kiasi cha maziwa ni 20% zaidi ya maji. Kiasi cha maziwa = Kiasi cha maji + (0.20 × Kiasi cha maji) Kiasi cha maziwa = 12 lita + (0.20 × 12 lita) Kiasi cha maziwa = 12 lita + 2.4 lita Kiasi cha maziwa = 14.4 lita Step 2: Tafuta jumla ya chai iliyoandaliwa. Jumla ya chai ni kiasi cha maji pamoja na kiasi cha maziwa. Jumla ya chai = Kiasi cha maji + Kiasi cha maziwa Jumla ya chai = 12 lita + 14.4 lita Jumla ya chai = 26.4 lita Jumla ya chai iliyoandaliwa ni 26.4 lita. 26.4 lita Swali la 2: Kutatua Mlinganyo Tunapewa mlinganyo: (x+6)/(4) + (x-3-3)/(5) = (5x-4)/(8) Step 1: Rahisisha sehemu ya pili ya mlinganyo. (x-3-3)/(5) = (x-6)/(5) Mlinganyo unakuwa: (x+6)/(4) + (x-6)/(5) = (5x-4)/(8) Step 2: Tafuta Kigawe Kidogo cha Pamoja (LCM) cha madhehebu (4, 5, 8). LCM ya 4, 5, na 8 ni 40. Zidisha pande zote mbili za mlinganyo kwa 40. 40 ( (x+6)/(4) ) + 40 ( (x-6)/(5) ) = 40 ( (5x-4)/(8) ) 10(x+6) + 8(x-6) = 5(5x-4) Step 3: Panua mabano. 10x + 60 + 8x - 48 = 25x - 20 Step 4: Unganisha vigezo na namba zinazofanana. (10x + 8x) + (60 - 48) = 25x - 20 18x + 12 = 25x - 20 Step 5: Kusanya vigezo vya x upande mmoja na namba upande mwingine. Toa 18x kutoka pande zote mbili: 12 = 25x - 18x - 20 12 = 7x - 20 Ongeza 20 pande zote mbili: 12 + 20 = 7x 32 = 7x Step 6: Gawanya kwa 7 ili kupata thamani ya x. x = (32)/(7) Thamani ya x ni (32)/(7). x = (32)/(7) That's 2 down. 3 left today — send the next one.