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Hapa kuna masuluhisho ya maswali yako: 1. I think of a number, add 7 to it and double the result is 40. Find the number. Huu ni mlinganyo wa aljebra. Wacha tuseme nambari hiyo ni x. Step 1: Andika mlinganyo kulingana na maelezo. • Nambari, x. • Ongeza 7: x + 7. • Fanya matokeo mara mbili: 2(x + 7). • Matokeo ni 40: 2(x + 7) = 40. Step 2: Tatua mlinganyo kwa x. Gawanya pande zote mbili kwa 2: (2(x+7))/(2) = (40)/(2) x+7 = 20 Step 3: Toa 7 kutoka pande zote mbili. x = 20 - 7 x = 13 Jibu la mwisho: 13 2. Change 124_six to binary base. Kwanza, tutabadilisha nambari kutoka base 6 kwenda base 10, kisha kutoka base 10 kwenda binary (base 2). Step 1: Badilisha 124_six kwenda base 10. 124_six = (1 × 6^2) + (2 × 6^1) + (4 × 6^0) 124_six = (1 × 36) + (2 × 6) + (4 × 1) 124_six = 36 + 12 + 4 124_six = 52_ten Step 2: Badilisha 52_ten kwenda binary (base 2). Tutagawanya 52 kwa 2 mara kwa mara na kurekodi salio. • 52 ÷ 2 = 26 salio 0 • 26 ÷ 2 = 13 salio 0 • 13 ÷ 2 = 6 salio 1 • 6 ÷ 2 = 3 salio 0 • 3 ÷ 2 = 1 salio 1 • 1 ÷ 2 = 0 salio 1 Soma salio kutoka chini kwenda juu. Jibu la mwisho: 110100_two 3. Find the Area of the shaded part. Kielelezo kinaonyesha mraba na duara ndani yake. Sehemu iliyotiwa kivuli ni eneo la mraba ukitoa eneo la duara. Kutoka kwenye mchoro, upande wa mraba ni 21 cm, na hii pia ni kipenyo cha duara. Step 1: Tambua vipimo. Upande wa mraba (s) = 21 cm. Kipenyo cha duara (d) = 21 cm. Radiasi ya duara (r) = (d)/(2) = (21)/(2) cm. Step 2: Kokotoa eneo la mraba. Eneo_mraba = s^2 Eneo_mraba = (21 cm)^2 Eneo_mraba = 441 cm^2 Step 3: Kokotoa eneo la duara. Tumia ≈ (22)/(7). Eneo_duara = r^2 Eneo_duara = (22)/(7) × ((21)/(2) cm)^2 Eneo_duara = (22)/(7) × (21)/(2) × (21)/(2) cm^2 Eneo_duara = 11 × (3)/(1) × (21)/(2) cm^2 Eneo_duara = (693)/(2) cm^2 Eneo_duara = 346.5 cm^2 Step 4: Kokotoa eneo la sehemu iliyotiwa kivuli. Eneo_kivuli = Eneo_mraba - Eneo_duara Eneo_kivuli = 441 cm^2 - 346.5 cm^2 Eneo_kivuli = 94.5 cm^2 Jibu la mwisho: 94.5 cm^2 4. Simplify: 4x - 3q + 6x + 5q Ili kurahisisha usemi huu, unganisha vigezo vinavyofanana. Step 1: Panga upya vigezo vinavyofanana pamoja. 4x + 6x - 3q + 5q Step 2: Jumlisha au toa vigezo vinavyofanana. (4x + 6x) + (-3q + 5q) 10x + 2q Jibu la mwisho: 10x + 2q 5. IF Set R has 127 proper subsets. Find the Number in set R. Idadi ya proper subsets (vijisehemu halisi) ya seti yenye n vipengele hutolewa na formula 2^n - 1. Step 1: Weka formula sawa na idadi ya proper subsets iliyopewa. 2^n - 1 = 127 Step 2: Ongeza 1 pande zote mbili za mlinganyo. 2^n = 127 + 1 2^n = 128 Step 3: Tafuta thamani ya n kwa kuandika 128 kama nguvu ya 2. Tunajua kuwa 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32, 2^6 = 64, 2^7 = 128. Hivyo, 2^n = 2^7. Step 4: Linganisha exponents. n = 7 Jibu la mwisho: 7 Got more? Send 'em.