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
Haya master, twende na maswali haya. Swali la 1: Tatua kwa x katika mlinganyo (2x-3)/(5) + (x+1)/(2) = (3x+7)/(10) Step 1: Tafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha madhehebu. Madhehebu ni 5, 2, na 10. LCM ya 5, 2, na 10 ni 10. Step 2: Zidisha kila neno kwa LCM. Zidisha pande zote mbili za mlinganyo kwa 10 ili kuondoa madhehebu. 10 ((2x-3)/(5)) + 10 ((x+1)/(2)) = 10 ((3x+7)/(10)) 2(2x-3) + 5(x+1) = 1(3x+7) Step 3: Panua mabano. 4x - 6 + 5x + 5 = 3x + 7 Step 4: Unganisha vigezo vinavyofanana. 9x - 1 = 3x + 7 Step 5: Kusanya vigezo vya x upande mmoja na namba upande mwingine. Toa 3x kutoka pande zote mbili. 9x - 3x - 1 = 7 6x - 1 = 7 Ongeza 1 pande zote mbili. 6x = 7 + 1 6x = 8 Step 6: Gawanya kwa 6. (6x)/(6) = (8)/(6) x = (4)/(3) Thamani ya x ni (4)/(3) Swali la 2: Tafuta thamani ya X katika mchoro Step 1: Tambua jumla ya pembe kwenye mstari ulionyooka. Pembe kwenye mstari ulionyooka hujumlisha hadi 180^. Katika mchoro, tuna pembe tatu: 28^, 90^ (iliyowakilishwa na mraba mdogo), na 2X^. Step 2: Andika mlinganyo. 28^ + 90^ + 2X^ = 180^ Step 3: Unganisha namba zinazofanana. 118^ + 2X^ = 180^ Step 4: Tenga 2X^. Toa 118^ kutoka pande zote mbili. 2X^ = 180^ - 118^ 2X^ = 62^ Step 5: Tatua kwa X. Gawanya kwa 2. X = (62^)/(2) X = 31^ Thamani ya X ni 31^ Swali la 3: Tatua usawa 1 + (1)/(2)x > 2 Step 1: Tenga neno lenye x. Toa 1 kutoka pande zote mbili za usawa. (1)/(2)x > 2 - 1 (1)/(2)x > 1 Step 2: Tatua kwa x. Zidisha pande zote mbili kwa 2. 2 ((1)/(2)x) > 2(1) x > 2 Suluhisho la usawa ni x > 2 Swali la 4: Tafuta mshahara wa Peter Step 1: Andika taarifa kama mlinganyo. Acha mshahara wa Peter uwe P na mshahara wa Mary uwe M. Tunapewa: "(2)/(3) ya mshahara wa Peter ni sawa na (3)/(4) ya mshahara wa Mary." Hii inaweza kuandikwa kama: (2)/(3)P = (3)/(4)M Step 2: Badilisha mshahara wa Mary kwenye mlinganyo. Tunapewa kuwa mshahara wa Mary ni Sh120,000. Hivyo, M = 120,000. (2)/(3)P = (3)/(4)(120,000) Step 3: Rahisisha upande wa kulia. (2)/(3)P = 3 × 30,000 (2)/(3)P = 90,000 Step 4: Tatua kwa P. Ili kupata P, zidisha pande zote mbili kwa (3)/(2). P = 90,000 × (3)/(2) P = 45,000 × 3 P = 135,000 Mshahara wa Peter ni Sh135,000 That's 2 down. 3 left today — send the next one.