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
1. Chora ndege ya Cartesian na uweke lebo: Ili kuchora ndege ya Cartesian, chora mistari miwili inayopishana (x-axis na y-axis). Kwenye x-axis*, weka lebo kutoka -10 hadi +10. Kwenye y-axis*, weka lebo kutoka -8 hadi +16. Hakikisha umeweka alama za vitengo sawa kwenye kila mhimili. 2. Soma na uandike kuratibu za pointi P, Q, R, S, T na U: Kutoka kwenye ndege ya Cartesian uliyopewa, kuratibu za pointi ni: P: (-6, -3) Q: (-2, 7) R: (0, -5) S: (1, -2) T: (4, 3) U: (8, 0) 3. Tafuta na uweke pointi zifuatazo kwenye ndege ya Cartesian: Hizi ni kuratibu za pointi unazopaswa kuziweka kwenye ndege ya Cartesian: (i) A(0, -3) (ii) B(4, 6) (iii) C(-3, 2) (iv) D(-6, -3) (v) E(5, -4) (vi) F(-2, 10) (vii) G(1, 0) (viii) H(0, +5) 4. Unda jedwali la thamani kwa kila mlinganyo wa mstari uliotolewa: a) y - 2x + 4 = 0 Kwanza, tengeneza y iwe mada ya fomula: y = 2x - 4 Chagua thamani za x na uhesabu y: | x | y = 2x - 4 | | :-- | :----------- | | -2 | 2(-2) - 4 = -4 - 4 = -8 | | -1 | 2(-1) - 4 = -2 - 4 = -6 | | 0 | 2(0) - 4 = 0 - 4 = -4 | | 1 | 2(1) - 4 = 2 - 4 = -2 | | 2 | 2(2) - 4 = 4 - 4 = 0 | Jedwali la thamani: | x | -2 | -1 | 0 | 1 | 2 | | :-- | :- | :- | :- | :- | :- | | y | -8 | -6 | -4 | -2 | 0 | b) y + x = 3 Kwanza, tengeneza y iwe mada ya fomula: y = -x + 3 Chagua thamani za x na uhesabu y: | x | y = -x + 3 | | :-- | :----------- | | -2 | -(-2) + 3 = 2 + 3 = 5 | | -1 | -(-1) + 3 = 1 + 3 = 4 | | 0 | -(0) + 3 = 0 + 3 = 3 | | 1 | -(1) + 3 = -1 + 3 = 2 | | 2 | -(2) + 3 = -2 + 3 = 1 | Jedwali la thamani: | x | -2 | -1 | 0 | 1 | 2 | | :-- | :- | :- | :- | :- | :- | | y | 5 | 4 | 3 | 2 | 1 | 5. Jaza jedwali kwa kutumia mlinganyo y = (1)/(2)x - 4 na uamue kipimo kinachofaa: Step 1: Jaza jedwali. Tumia mlinganyo y = (1)/(2)x - 4 kwa kila thamani ya x: Kwa x = 10: y = (1)/(2)(10) - 4 = 5 - 4 = 1 Kwa x = 20: y = (1)/(2)(20) - 4 = 10 - 4 = 6 Kwa x = 30: y = (1)/(2)(30) - 4 = 15 - 4 = 11 Kwa x = 40: y = (1)/(2)(40) - 4 = 20 - 4 = 16 Kwa x = 50: y = (1)/(2)(50) - 4 = 25 - 4 = 21 Kwa x = 60: y = (1)/(2)(60) - 4 = 30 - 4 = 26 Jedwali lililojazwa: | x | 10 | 20 | 30 | 40 | 50 | 60 | | :-- | :-- | :-- | :-- | :-- | :-- | :-- | | y | 1 | 6 | 11 | 16 | 21 | 26 | Step 2: Amua kipimo kinachofaa. Thamani za x zinaanzia 10 hadi 60, na thamani za y zinaanzia 1 hadi 26. Kwa x-axis*: Kipimo kinachofaa kinaweza kuwa 1 kitengo = 10 vitengo. Kwa y-axis*: Kipimo kinachofaa kinaweza kuwa 1 kitengo = 5 vitengo. Tuma swali linalofuata 📸