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
Step 1: Andika mlinganyo uliotolewa. Tunapewa mlinganyo: 4^x + 4^y = 1040 Tunahitaji kutafuta thamani ya x+y. Step 2: Tafuta namba za 4 zinazowezekana. Tutaorodhesha namba za 4 (powers of 4) zilizo karibu na 1040: 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 4^6 = 4096 Step 3: Tambua thamani za x na y. Kutoka kwenye orodha, tunaona kuwa 1024 iko karibu sana na 1040. Tuchukue 4^x = 1024. Hii inamaanisha x=5. Sasa, badilisha 4^x = 1024 kwenye mlinganyo wa awali: 1024 + 4^y = 1040 Step 4: Tatua kwa 4^y. Toa 1024 kutoka pande zote mbili za mlinganyo: 4^y = 1040 - 1024 4^y = 16 Step 5: Tafuta thamani ya y. Tunajua kuwa 4^2 = 16. Hivyo, y=2. Step 6: Kokotoa x+y. Tumepata x=5 na y=2. x+y = 5+2 x+y = 7 Hivyo, thamani ya x+y ni 7. x+y = 7 Tuma swali linalofuata 📸