Use a pencil and construct and angle of 165° at point X

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Haya, tutasuluhisha maswali haya.

16. In preparation for wedding, a sister was told to buy a roll of carpet of area of $15.0 \text{ m}^2$ which was used to cover a priest's table measuring $22.5 \text{ m}$ by $1.5 \text{ m}$ . The carpet cost shs. 35500 each roll. How much was spent for the carpet?

Hesabu eneo la meza.
Eneo la meza = Urefu $\times$ Upana
$\text{Eneo la meza} = 22.5 \text{ m} \times 1.5 \text{ m} = 33.75 \text{ m}^2$
Hesabu idadi ya roli za zulia zinazohitajika.
Idadi ya roli = Eneo la meza / Eneo la roli moja
$\text{Idadi ya roli} = \frac{33.75 \text{ m}^2}{15.0 \text{ m}^2} = 2.25 \text{ roli}$
Kwa kuwa huwezi kununua sehemu ya roli, tunahitaji kuzungusha juu hadi nambari kamili inayofuata. Hivyo, roli 3 zinahitajika.
Hesabu gharama yote ya zulia.
Gharama yote = Idadi ya roli $\times$ Gharama kwa kila roli
$\text{Gharama yote} = 3 \times \text{shs. } 35500 = \text{shs. } 106500$
Jibu la mwisho ni:
$\boxed{\text{shs. } 106500}$
17. 10 nurses can treat patients in 6 days when working at the same of 3 hours per day. If two nurses leave after 4 days and balance of nurses elevated their working speed to 5 hours per day. Find how many days it will take the remaining nurse to complete the task.
Hesabu jumla ya kazi inayohitajika (kwa "nurse-hours").
Jumla ya kazi = Idadi ya wauguzi $\times$ Siku $\times$ Saa kwa siku
$\text{Jumla ya kazi} = 10 \text{ wauguzi} \times 6 \text{ siku} \times 3 \text{ saa/siku} = 180 \text{ nurse-hours}$
Hesabu kazi iliyofanywa katika siku 4 za kwanza.
Kazi iliyofanywa = Idadi ya wauguzi $\times$ Siku zilizofanya kazi $\times$ Saa kwa siku
$\text{Kazi iliyofanywa} = 10 \text{ wauguzi} \times 4 \text{ siku} \times 3 \text{ saa/siku} = 120 \text{ nurse-hours}$
Hesabu kazi iliyobaki.
Kazi iliyobaki = Jumla ya kazi - Kazi iliyofanywa
$\text{Kazi iliyobaki} = 180 \text{ nurse-hours} - 120 \text{ nurse-hours} = 60 \text{ nurse-hours}$
Tambua idadi mpya ya wauguzi na saa zao mpya za kazi.
Idadi mpya ya wauguzi = $10 - 2 = 8 \text{ wauguzi}$
Saa mpya kwa siku = 5 saa/siku
Hesabu siku zinazohitajika kwa wauguzi waliobaki kukamilisha kazi iliyobaki.
Siku zinazohitajika = Kazi iliyobaki / (Idadi mpya ya wauguzi $\times$ Saa mpya kwa siku)
$\text{Siku zinazohitajika} = \frac{60 \text{ nurse-hours}}{8 \text{ wauguzi} \times 5 \text{ saa/siku}} = \frac{60}{40} \text{ siku} = 1.5 \text{ siku}$
Jibu la mwisho ni:
$\boxed{1.5 \text{ siku}}$
18. Use a pencil and construct and angle of $165^\circ$ at point X.

Huwezi kuonyesha ujenzi halisi hapa, lakini hizi ni hatua za kuunda pembe ya $165^\circ$ kwa kutumia penseli, dira na rula:
Chora mstari ulionyooka (sema AB) na uweke alama X juu yake.
Mstari huu unawakilisha pembe ya $180^\circ$ .
Kwa kutumia dira na X kama kituo, chora upinde mkubwa unaovuka mstari AB (sema kwenye pointi C upande wa kulia wa X).
Kwa kutumia C kama kituo na radius sawa, chora upinde unaovuka upinde wa kwanza (sema kwenye pointi D).
Hii inaunda pembe ya $60^\circ$ (angle DXC).
Kwa kutumia D kama kituo na radius sawa, chora upinde mwingine unaovuka upinde wa kwanza (sema kwenye pointi E).
Hii inaunda pembe ya $120^\circ$ (angle EXC).
Gawanya pembe kati ya $120^\circ$ na $180^\circ$ (yaani, pembe EXB) ili kupata $150^\circ$ .
Weka ncha ya dira kwenye E na kisha kwenye B, chora pinde zinazokutana. Chora mstari kutoka X kupitia makutano haya (sema F). Mstari XF unaunda pembe ya $150^\circ$ na XC.
Gawanya pembe kati ya $150^\circ$ na $180^\circ$ (yaani, pembe FXB).
Weka ncha ya dira kwenye F na kisha kwenye B, chora pinde zinazokutana. Chora mstari kutoka X kupitia makutano haya (sema G). Mstari XG unaunda pembe ya $165^\circ$ na XC.
Jibu la mwisho ni:
$\boxed{\text{Pembe ya } 165^\circ \text{ imejengwa kufuatia hatua zilizotajwa.}}$

Use a pencil and construct and angle of 165° at point X

Answer

Step-by-step solution

Hesabu eneo la meza.

Hesabu idadi ya roli za zulia zinazohitajika.

Hesabu gharama yote ya zulia.

Hesabu jumla ya kazi inayohitajika (kwa "nurse-hours").

Hesabu kazi iliyofanywa katika siku 4 za kwanza.

Hesabu kazi iliyobaki.

Tambua idadi mpya ya wauguzi na saa zao mpya za kazi.

Hesabu siku zinazohitajika kwa wauguzi waliobaki kukamilisha kazi iliyobaki.

Chora mstari ulionyooka (sema AB) na uweke alama X juu yake.

Kwa kutumia dira na X kama kituo, chora upinde mkubwa unaovuka mstari AB (sema kwenye pointi C upande wa kulia wa X).

Kwa kutumia C kama kituo na radius sawa, chora upinde unaovuka upinde wa kwanza (sema kwenye pointi D).

Kwa kutumia D kama kituo na radius sawa, chora upinde mwingine unaovuka upinde wa kwanza (sema kwenye pointi E).

Gawanya pembe kati ya $120^\circ$ na $180^\circ$ (yaani, pembe EXB) ili kupata $150^\circ$ .

Gawanya pembe kati ya $150^\circ$ na $180^\circ$ (yaani, pembe FXB).

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Use a pencil and construct and angle of 165° at point X

Answer

Step-by-step solution

Hesabu eneo la meza.

Hesabu idadi ya roli za zulia zinazohitajika.

Hesabu gharama yote ya zulia.

Hesabu jumla ya kazi inayohitajika (kwa "nurse-hours").

Hesabu kazi iliyofanywa katika siku 4 za kwanza.

Hesabu kazi iliyobaki.

Tambua idadi mpya ya wauguzi na saa zao mpya za kazi.

Hesabu siku zinazohitajika kwa wauguzi waliobaki kukamilisha kazi iliyobaki.

Chora mstari ulionyooka (sema AB) na uweke alama X juu yake.

Kwa kutumia dira na X kama kituo, chora upinde mkubwa unaovuka mstari AB (sema kwenye pointi C upande wa kulia wa X).

Kwa kutumia C kama kituo na radius sawa, chora upinde unaovuka upinde wa kwanza (sema kwenye pointi D).

Kwa kutumia D kama kituo na radius sawa, chora upinde mwingine unaovuka upinde wa kwanza (sema kwenye pointi E).

Gawanya pembe kati ya 120∘120^\circ120∘ na 180∘180^\circ180∘ (yaani, pembe EXB) ili kupata 150∘150^\circ150∘.

Gawanya pembe kati ya 150∘150^\circ150∘ na 180∘180^\circ180∘ (yaani, pembe FXB).

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Gawanya pembe kati ya $120^\circ$ na $180^\circ$ (yaani, pembe EXB) ili kupata $150^\circ$ .

Gawanya pembe kati ya $150^\circ$ na $180^\circ$ (yaani, pembe FXB).