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A) find y b) find y

Mathematics

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3 parts
a

60∘60^\circ

b

40∘40^\circ

c
6

Step-by-step solution

11 steps

Haya master, hapa kuna masuluhisho ya maswali yako:

Part a· 3 steps

Find y

Kielelezo kinaonyesha pembetatu yenye pande mbili zilizowekwa alama sawa, ikimaanisha ni pembetatu pacha (isosceles triangle). Katika pembetatu pacha, pembe zinazokabili pande sawa ni sawa. Pembe moja ya msingi ni 60∘60^\circ.

  1. Tambua aina ya pembetatu na sifa zake.

    Pembetatu ni pacha (isosceles) kwa sababu pande mbili ni sawa. Hii inamaanisha pembe za msingi ni sawa.

  2. Tumia sifa ya pembe za msingi.

    Kwa kuwa pembe moja ya msingi ni 60∘60^\circ, pembe nyingine ya msingi (y) pia ni 60∘60^\circ.

  3. Thibitisha kwa kutumia jumla ya pembe za pembetatu.

    Jumla ya pembe za pembetatu ni 180∘180^\circ.

    60∘+60∘+pembe ya juu=180∘60^\circ + 60^\circ + \text{pembe ya juu} = 180^\circ 120∘+pembe ya juu=180∘120^\circ + \text{pembe ya juu} = 180^\circ pembe ya juu=180∘−120∘=60∘\text{pembe ya juu} = 180^\circ - 120^\circ = 60^\circ

    Kwa kuwa pembe zote ni 60∘60^\circ, hii pia ni pembetatu sawa (equilateral triangle).

    Jibu la mwisho:

    60∘\boxed{60^\circ}

Part b

40∘40^\circ

Find y

Kielelezo kinaonyesha pembetatu nyingine pacha (isosceles triangle) kwa sababu pande mbili zimewekwa alama sawa. Pembe moja ya msingi ni 70∘70^\circ. Pembe 'y' ni pembe ya juu (vertex angle).

  1. Tambua aina ya pembetatu na sifa zake.

    Pembetatu ni pacha (isosceles) kwa sababu pande mbili ni sawa. Hii inamaanisha pembe za msingi ni sawa.

  2. Tambua pembe za msingi.

    Kwa kuwa pembe moja ya msingi ni 70∘70^\circ, pembe nyingine ya msingi pia ni 70∘70^\circ.

  3. Tumia jumla ya pembe za pembetatu.

    Jumla ya pembe za pembetatu ni 180∘180^\circ.

    y+70∘+70∘=180∘y + 70^\circ + 70^\circ = 180^\circ y+140∘=180∘y + 140^\circ = 180^\circ

  4. Tatua kwa y.

    y=180∘−140∘y = 180^\circ - 140^\circ y=40∘y = 40^\circ

    Jibu la mwisho:

    40∘\boxed{40^\circ}

Part c6

Solve 12m+7=2m−2\frac{1}{2}m + 7 = 2m - 2

Umeanza vizuri kwa kuzidisha pande zote mbili kwa 2 ili kuondoa sehemu.

  1. Endelea kutoka hatua yako ya mwisho.

    m+14=4m−4m + 14 = 4m - 4

  2. Kusanya vigezo vya mm upande mmoja na nambari upande mwingine.

    Toa mm kutoka pande zote mbili:

    14=4m−m−414 = 4m - m - 4 14=3m−414 = 3m - 4

  3. Ongeza 4 pande zote mbili.

    14+4=3m14 + 4 = 3m 18=3m18 = 3m

  4. Gawanya kwa 3 ili kupata thamani ya mm.

    m=183m = \frac{18}{3} m=6m = 6

    Jibu la mwisho:

    6\boxed{6}
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