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Use the figure to find the value of x. Write 2874 in scientific notation.

Mathematics

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2 parts
a

X=50∘X = 50^\circ

b

2.874×1032.874 \times 10^3

Step-by-step solution

7 steps

Hapa kuna suluhisho:

Part a· 4 steps

Tafuta thamani ya xx kutoka kwenye mchoro.

Katika mchoro, mistari miwili ni sambamba (inaonyeshwa na mishale). Pembe ya 80∘80^\circ na pembe iliyo karibu na 2X2X (ambayo ni 180∘−2X180^\circ - 2X) ni pembe za ndani zinazofuatana (consecutive interior angles). Jumla ya pembe hizi ni 180∘180^\circ.

  1. Tambua uhusiano kati ya pembe.

    Pembe ya 80∘80^\circ na pembe inayolingana nayo kwenye mstari wa juu (pembe ya ndani upande wa kushoto) ni sawa. Tuiite pembe hiyo yy. Hivyo y=80∘y = 80^\circ.
    Pembe 2X2X na pembe yy zinaunda jozi ya mstari (linear pair), ambayo jumla yake ni 180∘180^\circ.

    2X+y=180∘2X + y = 180^\circ

  2. Badilisha thamani ya yy kwenye mlinganyo.

    2X+80∘=180∘2X + 80^\circ = 180^\circ

  3. Tatua mlinganyo kwa XX.

    Toa 80∘80^\circ kutoka pande zote mbili:

    2X=180∘−80∘2X = 180^\circ - 80^\circ 2X=100∘2X = 100^\circ

  4. Gawanya pande zote mbili kwa 2.

    X=100∘2X = \frac{100^\circ}{2} X=50∘X = 50^\circ

    Thamani ya XX ni:

    X=50∘\boxed{X = 50^\circ}

Part b

2.874×1032.874 \times 10^3

Andika 2874 katika nukuu ya kisayansi (scientific notation).

Nukuu ya kisayansi huandikwa kama a×10ba \times 10^b, ambapo 1≤∣a∣<101 \le |a| < 10 na bb ni namba kamili.

  1. Sogeza desimali ili iwe baada ya namba ya kwanza isiyo sifuri.

    Kwa namba 2874, desimali iko mwishoni (2874.). Tunaisogeza kushoto hadi iwe kati ya 2 na 8.

    2.8742.874

  2. Hesabu idadi ya nafasi ambazo desimali imesogezwa.

    Desimali imesogezwa nafasi 3 kushoto.

  3. Andika namba katika nukuu ya kisayansi.

    Kwa kuwa desimali imesogezwa nafasi 3 kushoto, nguvu ya 10 itakuwa chanya 3.

    2874=2.874×1032874 = 2.874 \times 10^3

    Namba 2874 katika nukuu ya kisayansi ni:

    2.874×103\boxed{2.874 \times 10^3}
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