Identify the names of the triangles drawn below.

Hapa kuna masuluhisho ya maswali uliyotuma: 25. (a) (ii) the distance covered by the wheel after it makes 100 revolutions on a flat surface. Kutoka jibu lililopita, mzingo wa gurudumu (umbali unaofunikwa kwa mzunguko mmoja) ni 132 cm. Step 1: Kokotoa umbali wote uliopitiwa. Umbali wote = Mzingo wa gurudumu × Idadi ya mizunguko. Umbali = 132 cm × 100 Umbali = 13200 cm Umbali uliopitiwa na gurudumu ni: 13200 cm 25. (b) Calculate the height of a cylindrical candle whose radius is 7cm and has a volume of 770cm³. Fomula ya ujazo wa silinda ni V = r^2 h. Tunapewa: Radiasi r = 7 cm Ujazo V = 770 cm^3 Tunatumia = (22)/(7). Step 1: Badilisha maadili kwenye fomula ya ujazo. 770 cm^3 = (22)/(7) × (7 cm)^2 × h 770 cm^3 = (22)/(7) × 49 cm^2 × h Step 2: Rahisisha na tafuta urefu h. 770 cm^3 = 22 × 7 cm^2 × h 770 cm^3 = 154 cm^2 × h h = 770 cm^3154 cm^2 h = 5 cm Urefu wa mshumaa ni: 5 cm 25. (c) When Medrine fell sick, her temperature rose to 39.50c. What was her temperature in Kelvin? Ili kubadilisha halijoto kutoka Selsiasi kwenda Kelvin, tunatumia fomula T_K = T_C + 273.15. Halijoto katika Selsiasi T_C = 39.50^C. Step 1: Badilisha halijoto ya Selsiasi kuwa Kelvin. T_K = 39.50 + 273.15 T_K = 312.65 K Halijoto ya Medrine katika Kelvin ilikuwa: 312.65 K 25. (c) Identify the names of the triangles drawn below. Hapa kuna majina sahihi ya pembetatu: • Pembetatu ya kwanza (yenye alama tatu za mistari sawa): Pembetatu pacha (Equilateral triangle) • Pembetatu ya pili (yenye alama ya pembe mraba): Pembetatu mraba (Right-angled triangle) • Pembetatu ya tatu (yenye pembe 30^, 110^, 40^): Pembetatu tofauti (Scalene triangle) • Pembetatu ya nne (yenye alama mbili za mistari sawa): Pembetatu pacha miguu miwili (Isosceles triangle) 26. (a) Philip bought a refrigerator for Sh.24000. He later sold it at a loss of 30%. How much did he sell the refrigerator? Bei ya kununua = Sh. 24000. Hasara = 30%. Step 1: Kokotoa kiasi cha hasara. Hasara = 30\% ya Sh. 24000 Hasara = (30)/(100) × 24000 Hasara = Sh. 7200 Step 2: Kokotoa bei ya kuuza. Bei ya kuuza = Bei ya kununua - Hasara. Bei ya kuuza = Sh. 24000 - Sh. 7200 Bei ya kuuza = Sh. 16800 Philip aliuza friji kwa: Sh. 16800 26. (b) Find the value of the angles marked with letters. Katika mchoro, mistari miwili ya juu ni sambamba. Step 1: Tafuta thamani ya x. Pembe x na pembe ya 40^ ni pembe mbadala za ndani (alternate interior angles). Kwa hiyo, x = 40^. Step 2: Tafuta thamani ya z. Pembe z na pembe ya 70^ ni pembe mbadala za ndani (alternate interior angles). Kwa hiyo, z = 70^. Step 3: Tafuta thamani ya k. Pembe x, z, na k ni pembe za ndani za pembetatu. Jumla ya pembe za ndani za pembetatu ni 180^. x + z + k = 180^ 40^ + 70^ + k = 180^ 110^ + k = 180^ k = 180^ - 110^ k = 70^ Thamani za pembe ni: x = 40^, z = 70^, k = 70^ 27. A saleswoman was paid a monthly salary of Sh.9000. She was also paid a commission of 10% for all the goods she sold above Sh.10000. In one month, she sold goods worth Sh.25000. What did she earn at the end of that month? Mshahara wa kila mwezi = Sh. 9000. Mauzo yote = Sh. 25000. Tume = 10% kwa mauzo yanayozidi Sh. 10000. Step 1: Kokotoa mauzo yanayostahiki tume. Mauzo yanayostahiki tume = Mauzo yote - Kiasi kisichostahiki tume Mauzo yanayostahiki tume = Sh. 25000 - Sh. 10000 Mauzo yanayostahiki tume = Sh. 15000 Step 2: Kokotoa kiasi cha tume. Tume = 10\% ya Sh. 15000 Tume = (10)/(100) × 15000 Tume = Sh. 1500 Step 3: Kokotoa jumla ya mapato. Jumla ya mapato = Mshahara wa kila mwezi + Tume Jumla ya mapato = Sh. 9000 + Sh. 1500 Jumla ya mapato = Sh. 10500 Mwanamke huyo aliingiza jumla ya: Sh. 10500 28. In a wedding party, the number of men, women and children were in the ratio 2:3:5 respectively. If 60 women attended the wedding, Uwiano wa wanaume : wanawake : watoto = 2 : 3 : 5. Idadi ya wanawake = 60. Step 1: Tafuta thamani ya sehemu moja ya uwiano. Sehemu ya wanawake katika uwiano ni 3. Ikiwa sehemu 3 zinawakilisha wanawake 60, basi sehemu 1 inawakilisha: Sehemu 1 = (60)/(3) = 20 watu 28. (i) how many children attended the wedding? Sehemu ya watoto katika uwiano ni 5. Idadi ya watoto = 5 × Sehemu 1 Idadi ya watoto = 5 × 20 = 100 watoto Idadi ya watoto waliohudhuria harusi ni: 100 watoto 28. (ii) how many men attended the wedding? Sehemu ya wanaume katika uwiano ni 2. Idadi ya wanaume = 2 × Sehemu 1 Idadi ya wanaume = 2 × 20 = 40 wanaume Idadi ya wanaume waliohudhuria harusi ni: 40 wanaume 28. (iii) how many more children than men attended the wedding? Tofauti kati ya idadi ya watoto na wanaume. Tofauti = Idadi ya watoto - Idadi ya wanaume Tofauti = 100 - 40 = 60 Watoto walikuwa wengi kuliko wanaume kwa: 60 3 done, 2 left today. You're making progress.