Identify the names of the triangles drawn below.

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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 $132 \text{ cm}$ .

Kokotoa umbali wote uliopitiwa.
Umbali wote = Mzingo wa gurudumu $\times$ Idadi ya mizunguko.
$\text{Umbali} = 132 \text{ cm} \times 100$ $\text{Umbali} = 13200 \text{ cm}$
Umbali uliopitiwa na gurudumu ni:
$\boxed{\text{13200 cm}}$
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 $V = \pi r^2 h$ .
Tunapewa:
Radiasi $r = 7 \text{ cm}$
Ujazo $V = 770 \text{ cm}^3$
Tunatumia $\pi = \frac{22}{7}$ .
Badilisha maadili kwenye fomula ya ujazo.
$770 \text{ cm}^3 = \frac{22}{7} \times (7 \text{ cm})^2 \times h$ $770 \text{ cm}^3 = \frac{22}{7} \times 49 \text{ cm}^2 \times h$
Rahisisha na tafuta urefu $h$ .
$770 \text{ cm}^3 = 22 \times 7 \text{ cm}^2 \times h$ $770 \text{ cm}^3 = 154 \text{ cm}^2 \times h$ $h = \frac{770 \text{ cm}^3}{154 \text{ cm}^2}$ $h = 5 \text{ cm}$
Urefu wa mshumaa ni:
$\boxed{\text{5 cm}}$
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 $T_C = 39.50^{\circ}\text{C}$ .
Badilisha halijoto ya Selsiasi kuwa Kelvin.
$T_K = 39.50 + 273.15$ $T_K = 312.65 \text{ K}$
Halijoto ya Medrine katika Kelvin ilikuwa:
$\boxed{\text{312.65 K}}$
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 $30^{\circ}, 110^{\circ}, 40^{\circ}$ ): 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%.
Kokotoa kiasi cha hasara.
$\text{Hasara} = 30\% \text{ ya Sh. } 24000$ $\text{Hasara} = \frac{30}{100} \times 24000$ $\text{Hasara} = \text{Sh. } 7200$
Kokotoa bei ya kuuza.
Bei ya kuuza = Bei ya kununua - Hasara.
$\text{Bei ya kuuza} = \text{Sh. } 24000 - \text{Sh. } 7200$ $\text{Bei ya kuuza} = \text{Sh. } 16800$
Philip aliuza friji kwa:
$\boxed{\text{Sh. 16800}}$
26. (b) Find the value of the angles marked with letters.

Katika mchoro, mistari miwili ya juu ni sambamba.
Tafuta thamani ya $x$ .
Pembe $x$ na pembe ya $40^{\circ}$ ni pembe mbadala za ndani (alternate interior angles).
Kwa hiyo, $x = 40^{\circ}$ .
Tafuta thamani ya $z$ .
Pembe $z$ na pembe ya $70^{\circ}$ ni pembe mbadala za ndani (alternate interior angles).
Kwa hiyo, $z = 70^{\circ}$ .
Tafuta thamani ya $k$ .
Pembe $x$ , $z$ , na $k$ ni pembe za ndani za pembetatu. Jumla ya pembe za ndani za pembetatu ni $180^{\circ}$ .
$x + z + k = 180^{\circ}$ $40^{\circ} + 70^{\circ} + k = 180^{\circ}$ $110^{\circ} + k = 180^{\circ}$ $k = 180^{\circ} - 110^{\circ}$ $k = 70^{\circ}$
Thamani za pembe ni:
$\boxed{x = 40^{\circ}, z = 70^{\circ}, k = 70^{\circ}}$
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.
Kokotoa mauzo yanayostahiki tume.
$\text{Mauzo yanayostahiki tume} = \text{Mauzo yote} - \text{Kiasi kisichostahiki tume}$ $\text{Mauzo yanayostahiki tume} = \text{Sh. } 25000 - \text{Sh. } 10000$ $\text{Mauzo yanayostahiki tume} = \text{Sh. } 15000$
Kokotoa kiasi cha tume.
$\text{Tume} = 10\% \text{ ya Sh. } 15000$ $\text{Tume} = \frac{10}{100} \times 15000$ $\text{Tume} = \text{Sh. } 1500$
Kokotoa jumla ya mapato.
$\text{Jumla ya mapato} = \text{Mshahara wa kila mwezi} + \text{Tume}$ $\text{Jumla ya mapato} = \text{Sh. } 9000 + \text{Sh. } 1500$ $\text{Jumla ya mapato} = \text{Sh. } 10500$
Mwanamke huyo aliingiza jumla ya:
$\boxed{\text{Sh. 10500}}$
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.
Tafuta thamani ya sehemu moja ya uwiano.
Sehemu ya wanawake katika uwiano ni 3.
Ikiwa sehemu 3 zinawakilisha wanawake 60, basi sehemu 1 inawakilisha:
$\text{Sehemu 1} = \frac{60}{3} = 20 \text{ watu}$
28. (i) how many children attended the wedding?

Sehemu ya watoto katika uwiano ni 5.
$\text{Idadi ya watoto} = 5 \times \text{Sehemu 1}$ $\text{Idadi ya watoto} = 5 \times 20 = 100 \text{ watoto}$
Idadi ya watoto waliohudhuria harusi ni:
$\boxed{\text{100 watoto}}$
28. (ii) how many men attended the wedding?

Sehemu ya wanaume katika uwiano ni 2.
$\text{Idadi ya wanaume} = 2 \times \text{Sehemu 1}$ $\text{Idadi ya wanaume} = 2 \times 20 = 40 \text{ wanaume}$
Idadi ya wanaume waliohudhuria harusi ni:
$\boxed{\text{40 wanaume}}$
28. (iii) how many more children than men attended the wedding?

Tofauti kati ya idadi ya watoto na wanaume.
$\text{Tofauti} = \text{Idadi ya watoto} - \text{Idadi ya wanaume}$ $\text{Tofauti} = 100 - 40 = 60$
Watoto walikuwa wengi kuliko wanaume kwa:
$\boxed{\text{60}}$

Identify the names of the triangles drawn below.

Step-by-step solution

Kokotoa umbali wote uliopitiwa.

Badilisha maadili kwenye fomula ya ujazo.

Rahisisha na tafuta urefu $h$ .

Badilisha halijoto ya Selsiasi kuwa Kelvin.

Kokotoa kiasi cha hasara.

Kokotoa bei ya kuuza.

Tafuta thamani ya $x$ .

Tafuta thamani ya $z$ .

Tafuta thamani ya $k$ .

Kokotoa mauzo yanayostahiki tume.

Kokotoa kiasi cha tume.

Kokotoa jumla ya mapato.

Tafuta thamani ya sehemu moja ya uwiano.

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More Mathematics Questions

Identify the names of the triangles drawn below.

Step-by-step solution

Kokotoa umbali wote uliopitiwa.

Badilisha maadili kwenye fomula ya ujazo.

Rahisisha na tafuta urefu hhh.

Badilisha halijoto ya Selsiasi kuwa Kelvin.

Kokotoa kiasi cha hasara.

Kokotoa bei ya kuuza.

Tafuta thamani ya xxx.

Tafuta thamani ya zzz.

Tafuta thamani ya kkk.

Kokotoa mauzo yanayostahiki tume.

Kokotoa kiasi cha tume.

Kokotoa jumla ya mapato.

Tafuta thamani ya sehemu moja ya uwiano.

Still stuck on this one?

More Mathematics Questions

Rahisisha na tafuta urefu $h$ .

Tafuta thamani ya $x$ .

Tafuta thamani ya $z$ .

Tafuta thamani ya $k$ .