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Find the value of a in the diagram below.

Mathematics

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Haya, tutasuluhisha maswali haya.

8. Given the venn diagram below, describe the shaded region.

  1. Chunguza mchoro wa Venn.

    Eneo lililotiwa kivuli linajumuisha kila kitu kilicho nje ya duara B, lakini ndani ya mstatili (seti ya ulimwengu).

  2. Eneo hili linaweza kuelezewa kama kikamilisho cha seti B.

    Maelezo ya mwisho ni:

    Kikamilisho cha B (au Bc au B′)\boxed{\text{Kikamilisho cha B (au } B^c \text{ au } B')}

    9. At a certain school, assembly was conducted on Monday at 8:00am. A teacher on duty was 5th from one side and 9th from the other side. How many teachers attended assembly that day?

  3. Ikiwa mwalimu yuko wa 5 kutoka upande mmoja, inamaanisha kuna walimu 4 kabla yake.

  4. Ikiwa mwalimu huyo huyo yuko wa 9 kutoka upande mwingine, inamaanisha kuna walimu 8 baada yake.

  5. Jumla ya walimu ni idadi ya walimu kabla yake, pamoja na mwalimu mwenyewe, pamoja na idadi ya walimu baada yake.

    Jumla ya walimu=4+1+8=13\text{Jumla ya walimu} = 4 + 1 + 8 = 13

    Jibu la mwisho ni:

    13 walimu\boxed{13 \text{ walimu}}

    10. James deposited 20 notes of five thousand shillings. If the first note was serial number DV432370 after consecutive numbering. Find the serial number of the last note.

  6. Tambua nambari ya mfululizo ya noti ya kwanza.

    Nambari ya kwanza ni 370.

  7. Tambua idadi ya noti zilizowekwa.

    Kuna noti 20.

  8. Kwa kuwa nambari zinafuatana, nambari ya mwisho itakuwa nambari ya kwanza pamoja na (idadi ya noti - 1).

    Nambari ya mwisho=370+(20−1)\text{Nambari ya mwisho} = 370 + (20 - 1) Nambari ya mwisho=370+19\text{Nambari ya mwisho} = 370 + 19 Nambari ya mwisho=389\text{Nambari ya mwisho} = 389
  9. Unganisha nambari hii na kiambishi awali cha nambari ya mfululizo.

    Jibu la mwisho ni:

    DV432389\boxed{\text{DV432389}}

    11. Find the value of a in the diagram below.

  10. Chora mstari msaidizi unaopita kwenye kipeo cha pembe 'a' na sambamba na mistari miwili iliyopewa.

    Hii itagawanya pembe 'a' katika sehemu mbili, a1a_1 (juu) na a2a_2 (chini).

  11. Kwa sehemu ya juu (a1a_1)

    Pembe iliyo karibu na 150∘150^\circ kwenye mstari ulionyooka ni 180∘−150∘=30∘180^\circ - 150^\circ = 30^\circ. Pembe hii ya 30∘30^\circ ni alternate interior angle na a1a_1.
    Hivyo, a1=30∘a_1 = 30^\circ.

  12. Kwa sehemu ya chini (a2a_2)

    Pembe ya 75∘75^\circ iliyopewa ni alternate interior angle na a2a_2.
    Hivyo, a2=75∘a_2 = 75^\circ.

  13. Jumla ya pembe 'a' ni jumla ya a1a_1 na a2a_2.

    a=a1+a2a = a_1 + a_2 a=30∘+75∘a = 30^\circ + 75^\circ a=105∘a = 105^\circ

    Jibu la mwisho ni:

    105∘\boxed{105^\circ}
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