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 kubaini kama jozi za mistari ni wima (perpendicular), tunahitaji kulinganisha miteremko yao. Mistari miwili ni wima ikiwa bidhaa ya miteremko yao ni -1. b) 3y = x + 3 na y + 3x = 1 Step 1: Pata mteremko wa mstari wa kwanza. Badilisha 3y = x + 3 kuwa umbo la y = mx + c. y = (1)/(3)x + (3)/(3) y = (1)/(3)x + 1 Mteremko wa mstari wa kwanza ni m_1 = (1)/(3). Step 2: Pata mteremko wa mstari wa pili. Badilisha y + 3x = 1 kuwa umbo la y = mx + c. y = -3x + 1 Mteremko wa mstari wa pili ni m_2 = -3. Step 3: Zidisha miteremko. m_1 · m_2 = (1)/(3) · (-3) = -1 Step 4: Hitimisho. Kwa kuwa bidhaa ya miteremko ni -1, mistari hii ni wima. Mistari ni wima d) y + 4x = 2 na y - 4x = 1 Step 1: Pata mteremko wa mstari wa kwanza. Badilisha y + 4x = 2 kuwa umbo la y = mx + c. y = -4x + 2 Mteremko wa mstari wa kwanza ni m_1 = -4. Step 2: Pata mteremko wa mstari wa pili. Badilisha y - 4x = 1 kuwa umbo la y = mx + c. y = 4x + 1 Mteremko wa mstari wa pili ni m_2 = 4. Step 3: Zidisha miteremko. m_1 · m_2 = (-4) · (4) = -16 Step 4: Hitimisho. Kwa kuwa bidhaa ya miteremko si -1, mistari hii si wima. Mistari si wima f) y = 5x + 3 na y = -5x + 1 Step 1: Pata mteremko wa mstari wa kwanza. Mstari wa kwanza tayari uko katika umbo la y = mx + c. y = 5x + 3 Mteremko wa mstari wa kwanza ni m_1 = 5. Step 2: Pata mteremko wa mstari wa pili. Mstari wa pili tayari uko katika umbo la y = mx + c. y = -5x + 1 Mteremko wa mstari wa pili ni m_2 = -5. Step 3: Zidisha miteremko. m_1 · m_2 = (5) · (-5) = -25 Step 4: Hitimisho. Kwa kuwa bidhaa ya miteremko si -1, mistari hii si wima. Mistari si wima That's 2 down. 3 left today — send the next one.