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 kazi! Swali la 31: Takwimu hapa chini inaonyesha pembetatu AEB. Itumie kujibu maswali yanayofuata. a) Tafuta thamani ya x. Step 1: Andika jumla ya pembe za pembetatu. Tunajua kuwa jumla ya pembe za ndani za pembetatu ni 180^. Hivyo, A + E + B = 180^. (x - 10)^ + (3x - 10)^ + (2x + 40)^ = 180^ Step 2: Unganisha vigezo vya x na nambari zisizobadilika. x + 3x + 2x - 10 - 10 + 40 = 180 6x + 20 = 180 Step 3: Tatua mlinganyo ili kupata thamani ya x. Toa 20 kutoka pande zote mbili: 6x = 180 - 20 6x = 160 Gawanya kwa 6: x = (160)/(6) x = (80)/(3) Jibu la Swali la 31 (a): Thamani ya x ni: (80)/(3) b) Taja pembetatu AEB. Step 1: Kokotoa ukubwa wa kila pembe kwa kutumia thamani ya x = (80)/(3). A = x - 10 = (80)/(3) - 10 = (80 - 30)/(3) = (50)/(3)^ ≈ 16.67^ E = 3x - 10 = 3((80)/(3)) - 10 = 80 - 10 = 70^ B = 2x + 40 = 2((80)/(3)) + 40 = (160)/(3) + 40 = (160 + 120)/(3) = (280)/(3)^ ≈ 93.33^ Step 2: Bainisha aina ya pembetatu kulingana na pembe zake. Kwa kuwa pembe moja ( B ≈ 93.33^) ni kubwa kuliko 90^, pembetatu hii ni pembetatu butu (obtuse-angled triangle). Pia, kwa kuwa pembe zote tatu zina ukubwa tofauti, pembetatu hii pia ni pembetatu ya skelini (scalene triangle). Jibu la Swali la 31 (b): Pembetatu AEB ni: Pembetatu Butu (Obtuse-angled triangle) That's 2 down. 3 left today — send the next one.