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Find the value of angle W in the figure below. 2. Solve the equation: 5t − 2(t+1) = 1. 3. Solve m+2 / 2 = 4m−4 / 11

Mathematics

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3 parts
1

65∘\text{}65^\circ\text{}

2

1\text{}1\text{}

3

−10\text{} -10\text{}

Step-by-step solution

11 steps

Haya, tutasuluhisha maswali uliyotuma.

Part 1· 3 steps

Tafuta thamani ya pembe W

  1. Tambua pembe mbadala za ndani (alternate interior angles).

    Kwa kuwa mistari miwili ni sambamba, pembe ya 35∘35^\circ ni pembe mbadala ya ndani na pembe iliyo ndani ya pembetatu upande wa kushoto. Hivyo, pembe hiyo ni 35∘35^\circ. Vile vile, pembe ya 80∘80^\circ ni pembe mbadala ya ndani na pembe iliyo ndani ya pembetatu upande wa kulia. Hivyo, pembe hiyo ni 80∘80^\circ.

  2. Tumia jumla ya pembe za ndani za pembetatu.

    Jumla ya pembe za ndani za pembetatu ni 180∘180^\circ. Kwa hiyo, tunaweza kuandika mlinganyo:

    W+35∘+80∘=180∘W + 35^\circ + 80^\circ = 180^\circ
  3. Tatua kwa W.

    W+115∘=180∘W + 115^\circ = 180^\circ W=180∘−115∘W = 180^\circ - 115^\circ W=65∘W = 65^\circ

    Thamani ya pembe W ni 65∘\boxed{\text{}65^\circ\text{}}

Part 2

1\text{}1\text{}

Tatua mlinganyo 5t−2(t+1)=15t - 2(t+1) = 1

  1. Panua mabano.

    Gawanya −2-2 kwa kila neno ndani ya mabano.

    5t−2(t)−2(1)=15t - 2(t) - 2(1) = 1 5t−2t−2=15t - 2t - 2 = 1
  2. Unganisha vigezo vinavyofanana.

    3t−2=13t - 2 = 1
  3. Tenga tt.

    Ongeza 2 pande zote mbili za mlinganyo.

    3t=1+23t = 1 + 2 3t=33t = 3
  4. Gawanya kwa 3.

    3t3=33\frac{3t}{3} = \frac{3}{3} t=1t = 1

    Thamani ya tt ni 1\boxed{\text{}1\text{}}

Part 3

−10\text{} -10\text{}

Tatua mlinganyo m+22=4m−411\frac{m+2}{2} = \frac{4m-4}{11}

  1. Fanya "cross-multiplication".

    Zidisha namba ya juu ya upande mmoja na namba ya chini ya upande mwingine.

    11(m+2)=2(4m−4)11(m+2) = 2(4m-4)
  2. Panua mabano.

    11m+11(2)=2(4m)−2(4)11m + 11(2) = 2(4m) - 2(4) 11m+22=8m−811m + 22 = 8m - 8
  3. Kusanya vigezo vya mm upande mmoja na namba upande mwingine.

    Toa 8m8m kutoka pande zote mbili.

    11m−8m+22=−811m - 8m + 22 = -8 3m+22=−83m + 22 = -8

    Toa 22 kutoka pande zote mbili.

    3m=−8−223m = -8 - 22 3m=−303m = -30
  4. Gawanya kwa 3.

    3m3=−303\frac{3m}{3} = \frac{-30}{3} m=−10m = -10

    Thamani ya mm ni −10\boxed{\text{} -10\text{}}

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