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, tuendelee na maswali haya. 31. a) i) Tatua: P+8=21. Step 1: Ili kumtafuta P, toa 8 kutoka pande zote mbili za mlinganyo. P + 8 - 8 = 21 - 8 Step 2: Rahisisha. P = 13 Jibu ni P=13. 31. a) ii) Tatua: y+y+4=16. Step 1: Unganisha vigezo vya y. 2y + 4 = 16 Step 2: Toa 4 kutoka pande zote mbili za mlinganyo. 2y + 4 - 4 = 16 - 4 2y = 12 Step 3: Gawanya pande zote mbili kwa 2. (2y)/(2) = (12)/(2) y = 6 Jibu ni y=6. 31. b) Ukipewa g = (1)/(2) na n = 24, p = (2)/(3). Je, pgn ni nini? Step 1: Badilisha thamani za p, g, na n kwenye usemi pgn. pgn = (2)/(3) × (1)/(2) × 24 Step 2: Zidisha nambari hizo. Unaweza kurahisisha kabla ya kuzidisha. pgn = (2 × 1 × 24)/(3 × 2) pgn = (48)/(6) Step 3: Gawanya. pgn = 8 Jibu ni 8. 32. a) Tafuta idadi kubwa zaidi ya mipira inayotolewa kwa wachezaji 30 au 45 kwa usawa bila baki. Hii inahitaji kutafuta Kigezo Kikubwa Zaidi cha Pamoja (HCF) cha 30 na 45. Step 1: Tafuta vigawo vikuu vya 30. 30 = 2 × 3 × 5 Step 2: Tafuta vigawo vikuu vya 45. 45 = 3 × 3 × 5 = 3^2 × 5 Step 3: Tambua vigawo vikuu vya kawaida na uzidishe. Vigawo vikuu vya kawaida ni 3 na 5. HCF(30, 45) = 3 × 5 = 15 Idadi kubwa zaidi ya mipira ni 15. 32. b) Andika 729 kwa vipeo vya 3. Step 1: Gawanya 729 kwa 3 mara kwa mara hadi upate 1. 729 ÷ 3 = 243 243 ÷ 3 = 81 81 ÷ 3 = 27 27 ÷ 3 = 9 9 ÷ 3 = 3 3 ÷ 3 = 1 Step 2: Hesabu idadi ya mara 3 ilivyotumika kama kigawo. 3 ilitumika mara 6. 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3^6 Jibu ni 3^6. That's 2 down. 3 left today — send the next one.