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, tuendelee na maswali haya. 15. A triangle XYZ has been enlarged to X'Y'Z' about the centre of enlargement P by a scale factor 2.5. Scale factor (kigezo cha ukuzaji) ni uwiano wa urefu wa upande ulioongezwa kwa urefu wa upande asilia. Urefu mpya = Scale factor × Urefu asilia Urefu asilia = Urefu mpyaScale factor i) Find X'Y' if XY = 4 cm. Step 1: Tumia formula ya ukuzaji. Urefu wa upande ulioongezwa X'Y' ni sawa na scale factor mara urefu wa upande asilia XY. X'Y' = Scale factor × XY X'Y' = 2.5 × 4 cm Step 2: Fanya hesabu. X'Y' = 10 cm Jibu ni 10 cm. ii) Find XZ if X'Z' = 15 cm. Step 1: Tumia formula ya kupata urefu asilia. Urefu wa upande asilia XZ ni sawa na urefu wa upande ulioongezwa X'Z' kugawanya kwa scale factor. XZ = (X'Z')/(Scale factor) XZ = 15 cm2.5 Step 2: Fanya hesabu. XZ = 6 cm Jibu ni 6 cm. iii) Find PX' and XX' if PX = 3 cm. Step 1: Tafuta PX'. PX' ni umbali kutoka kituo cha ukuzaji P hadi kwenye ncha iliyokuzwa X'. PX' = Scale factor × PX PX' = 2.5 × 3 cm PX' = 7.5 cm Step 2: Tafuta XX'. XX' ni umbali kati ya ncha asilia X na ncha iliyokuzwa X'. XX' = PX' - PX XX' = 7.5 cm - 3 cm XX' = 4.5 cm Majibu ni PX' = 7.5 cm na XX' = 4.5 cm. 16. Classify the following numbers as rational or irrational: Nambari rational ni nambari inayoweza kuandikwa kama sehemu (a)/(b) ambapo a na b ni nambari kamili na b ≠ 0. Uwawakilishi wake wa desimali huisha au hurudia. Nambari irrational ni nambari ambayo haiwezi kuandikwa kama sehemu rahisi. Uwawakilishi wake wa desimali hauishi na haurudii. a) 0.666... Step 1: Angalia muundo wa desimali. Nambari hii ni desimali inayorudia (6 inajirudia). Step 2: Ainisha nambari. Kwa sababu inaweza kuandikwa kama sehemu ((2)/(3)), ni nambari rational. Jibu ni Rational. b) sqrt(11) Step 1: Angalia nambari iliyo ndani ya mzizi. 11 si perfect square (nambari kamili ambayo mzizi wake wa pili ni nambari kamili). Step 2: Ainisha nambari. Mzizi wa pili wa nambari isiyo perfect square ni nambari irrational. Jibu ni Irrational. c) 3/8 Step 1: Angalia umbo la nambari. Nambari hii tayari imeandikwa kama sehemu ya nambari kamili ((a)/(b)). Step 2: Ainisha nambari. Kwa sababu imeandikwa kama sehemu, ni nambari rational. Jibu ni Rational. d) Step 1: Kumbuka sifa za . ni uwiano wa mduara wa duara kwa kipenyo chake. Thamani yake ya desimali (3.14159265...) haiishi na haijirudii. Step 2: Ainisha nambari. Kwa sababu haiwezi kuandikwa kama sehemu rahisi na desimali yake haiishi wala haijirudii, ni nambari irrational. Jibu ni Irrational. e) 0.125 Step 1: Angalia muundo wa desimali. Nambari hii ni desimali inayoisha. Step 2: Ainisha nambari. Kwa sababu inaweza kuandikwa kama sehemu ((125)/(1000) = (1)/(8)), ni nambari rational. Jibu ni Rational. 3 done, 2 left today. You're making progress.