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 kutatua swali hili, tutatumia uhusiano kati ya eneo la kitu, eneo la picha, na kiamua (determinant) cha matriksi ya mabadiliko. Step 1: Tambua uhusiano kati ya eneo na kiamua. Uwiano wa eneo la picha kwa eneo la kitu ni sawa na thamani kamili ya kiamua cha matriksi ya mabadiliko. Eneo la pichaEneo la kitu = |(M)| Tunapewa: Eneo la kitu = 64 cm^2 Eneo la picha = 32 cm^2 Matriksi ya mabadiliko M = x+4 & x \\ 2 & 1 Step 2: Kokotoa kiamua cha matriksi M. Kwa matriksi a & b \\ c & d , kiamua ni ad - bc. Hapa, a = x+4, b = x, c = 2, d = 1. (M) = (x+4)(1) - (x)(2) (M) = x+4 - 2x (M) = 4 - x Step 3: Weka mlinganyo kwa kutumia uwiano wa eneo. (32)/(64) = |4 - x| (1)/(2) = |4 - x| Step 4: Tatua mlinganyo ili kupata thamani ya x. Kuna uwezekano mbili kwa 4 - x: Kesi 1: 4 - x = (1)/(2) x = 4 - (1)/(2) x = (8)/(2) - (1)/(2) x = (7)/(2) Kesi 2: 4 - x = -(1)/(2) x = 4 + (1)/(2) x = (8)/(2) + (1)/(2) x = (9)/(2) Kwa hivyo, kuna thamani mbili zinazowezekana za x. Thamani za x ni (7)/(2) au (9)/(2). Tuma swali linalofuata 📸