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
Hapa kuna hatua za kutafuta usawa tatu zinazokidhi eneo R: Swali la 16: Unda usawa tatu zinazokidhi eneo R lililopewa. Tutapata mlinganyo wa kila mstari (L_1, L_2, L_3) kisha tutabainisha ishara sahihi ya usawa kulingana na eneo R. Hatua ya 1: Tafuta usawa kwa mstari L_1. Mstari L_1 unapita kwenye pointi (0, 3) na (3, 4). • Mteremko m_1 = (4-3)/(3-0) = (1)/(3). • Y-intercept ni c_1 = 3. • Mlinganyo wa mstari ni y = (1)/(3)x + 3. • Eneo R liko juu ya mstari L_1. Ili kuthibitisha, chagua sehemu ndani ya R, kwa mfano (0, 4): 4 (1)/(3)(0) + 3 4 3, ambayo ni kweli. • Kwa hivyo, usawa ni y (1)/(3)x + 3. • Kuzidisha kwa 3 ili kuondoa sehemu: 3y x + 9. • Kupanga upya: x - 3y -9. Hatua ya 2: Tafuta usawa kwa mstari L_2. Mstari L_2 unapita kwenye pointi (0, -1) na (2, 1). • Mteremko m_2 = (1 - (-1))/(2 - 0) = (2)/(2) = 1. • Y-intercept ni c_2 = -1. • Mlinganyo wa mstari ni y = x - 1. • Eneo R liko juu ya mstari L_2. Ili kuthibitisha, chagua sehemu ndani ya R, kwa mfano (0, 4): 4 0 - 1 4 -1, ambayo ni kweli. • Kwa hivyo, usawa ni y x - 1. • Kupanga upya: x - y 1. Hatua ya 3: Tafuta usawa kwa mstari L_3. Mstari L_3 unapita kwenye pointi (0, 5) na (5, 3). • Mteremko m_3 = (3-5)/(5-0) = (-2)/(5). • Y-intercept ni c_3 = 5. • Mlinganyo wa mstari ni y = -(2)/(5)x + 5. • Eneo R liko chini ya mstari L_3. Ili kuthibitisha, chagua sehemu ndani ya R, kwa mfano (0, 4): 4 -(2)/(5)(0) + 5 4 5, ambayo ni kweli. • Kwa hivyo, usawa ni y -(2)/(5)x + 5. • Kuzidisha kwa 5 ili kuondoa sehemu: 5y -2x + 25. • Kupanga upya: 2x + 5y 25. Usawa tatu zinazokidhi eneo R ni: x - 3y -9 x - y 1 2x + 5y 25 3 done, 2 left today. You're making progress.