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.
ScanSolve AI Answer
Ili kutatua t katika mlinganyo uliotolewa, tutatumia njia ya kuweka makundi (factoring by grouping). Step 1: Andika mlinganyo uliotolewa. Mlinganyo ni: 5t^2 - 30t + 40 = 0 Step 2: Gawanya neno la kati ( -30t ) katika maneno mawili ambayo jumla yao ni -30t na bidhaa yao ni (5)(40) = 200 . Nambari hizo ni -20t na -10t . 5t^2 - 20t - 10t + 40 = 0 Step 3: Weka makundi ya maneno na utoe vipengele vya kawaida. Kutoka kundi la kwanza ( 5t^2 - 20t ), toa 5t . Kutoka kundi la pili ( -10t + 40 ), toa -10 . 5t(t - 4) - 10(t - 4) = 0 Step 4: Toa kipengele cha kawaida (t - 4) . (5t - 10)(t - 4) = 0 Step 5: Weka kila kipengele sawa na sifuri na utatue kwa t. 5t - 10 = 0 au t - 4 = 0 Kutatua kipengele cha kwanza: 5t = 10 t = (10)/(5) t = 2 Kutatua kipengele cha pili: t = 4 Hivyo, thamani za t ni: t = 2 au t = 4 Tuma swali linalofuata 📸