This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hapa kuna masuluhisho ya maswali yako: 1. Express 0.04024 in standard form. Ili kuandika nambari katika standard form (a × 10^n), tunahitaji kusogeza desimali ili a iwe nambari kati ya 1 na 10. Step 1: Sogeza desimali hadi baada ya nambari ya kwanza isiyo sifuri. Nambari ni 0.04024. Tukisogeza desimali sehemu mbili kwenda kulia, tunapata 4.024. Step 2: Tambua exponent ya 10. Kwa sababu tulisogeza desimali sehemu mbili kwenda kulia, exponent itakuwa hasi 2. 0.04024 = 4.024 × 10^-2 Jibu la mwisho: 4.024 × 10^-2 2. Find the total surface area of the figure. Kielelezo ni cuboid (mchemraba) chenye urefu (l), upana (w), na kimo (h). Kutoka kwenye picha, vipimo ni l = 10 cm, w = 8 cm, na h = 5 cm. Step 1: Andika formula ya total surface area (TSA) ya cuboid. TSA = 2(lw + lh + wh) Step 2: Badilisha vipimo kwenye formula. TSA = 2((10 cm × 8 cm) + (10 cm × 5 cm) + (8 cm × 5 cm)) Step 3: Fanya hesabu ndani ya mabano. TSA = 2(80 cm^2 + 50 cm^2 + 40 cm^2) Step 4: Jumlisha maeneo na kuzidisha kwa 2. TSA = 2(170 cm^2) TSA = 340 cm^2 Jibu la mwisho: 340 cm^2 3. Given the figure below. Find angle x. Kielelezo ni pembetatu yenye pembe x, 2x-60^, na x+20^. Jumla ya pembe za ndani za pembetatu ni 180^. Step 1: Tengeneza mlinganyo kwa kujumlisha pembe zote na kuziweka sawa na 180^. x + (2x - 60^) + (x + 20^) = 180^ Step 2: Unganisha vigezo vya x na nambari. (x + 2x + x) + (-60^ + 20^) = 180^ 4x - 40^ = 180^ Step 3: Ongeza 40^ pande zote mbili za mlinganyo. 4x = 180^ + 40^ 4x = 220^ Step 4: Gawanya kwa 4 ili kupata thamani ya x. x = (220^)/(4) x = 55^ Jibu la mwisho: 55^ Tuma swali linalofuata 📸