Factorize completely: x2 - 16

Haya, tuendelee na maswali mengine. 7. Find the reciprocal of 0.0045 and express your answer in standard form to 4 significant figures. Reciprocal ya nambari ni 1 kugawanya nambari hiyo. Step 1: Tafuta reciprocal ya 0.0045. (1)/(0.0045) = 222.2222... Step 2: Andika jibu katika standard form (mfumo sanifu). Ili kuandika 222.2222... katika standard form, tunahamisha desimali mara 2 kushoto. 2.2222... × 10^2 Step 3: Punguza jibu kwa tarakimu muhimu 4 (4 significant figures). Tarakimu ya tano ni 2, ambayo ni chini ya 5, kwa hivyo hatubadilishi tarakimu ya nne. 2.222 × 10^2 Jibu ni 2.222 × 10^2. 8. The temperature in a town was recorded as 18.6^ C in the morning and 24.2^ C in the afternoon. Calculate the mean temperature. Mean temperature (wastani wa joto) hupatikana kwa kujumlisha joto zote na kugawanya kwa idadi ya vipimo. Step 1: Jumuisha joto zote mbili. 18.6^ C + 24.2^ C = 42.8^ C Step 2: Gawanya jumla kwa idadi ya vipimo (2). (42.8^ C)/(2) = 21.4^ C Jibu ni 21.4^ C. 9. Estimate the height of a classroom wall in kilometres. Urefu wa ukuta wa darasa kwa kawaida hupimwa kwa mita. Step 1: Kadiria urefu wa ukuta wa darasa kwa mita. Urefu wa kawaida wa ukuta wa darasa ni takriban mita 3. Step 2: Badilisha mita kuwa kilomita. Tunajua kuwa kilomita 1 ina mita 1000. 3 m1000 m/km = 0.003 km Jibu ni 0.003 km. 10. Express 243 as a power of a prime number. Nambari prime ni nambari inayoweza kugawanyika na 1 na yenyewe tu. Step 1: Tafuta vigawo prime vya 243. Anza kugawanya 243 na nambari ndogo zaidi prime. 243 ÷ 3 = 81 81 ÷ 3 = 27 27 ÷ 3 = 9 9 ÷ 3 = 3 3 ÷ 3 = 1 Step 2: Andika 243 kama nguvu ya nambari prime. Kwa kuwa 3 imejirudia mara 5, tunaweza kuandika 243 kama 3^5. 243 = 3 × 3 × 3 × 3 × 3 = 3^5 Jibu ni 3^5. 11. Simplify using the laws of indices: (5^2)^(1)/(2) Tunatumia sheria ya indices inayosema (a^m)^n = a^m × n. Step 1: Tumia sheria ya indices. (5^2)^(1)/(2) = 5^2 × (1)/(2) Step 2: Rahisisha kipeo. 5^2 × (1)/(2) = 5^1 5^1 = 5 Jibu ni 5. 12. Solve for x: 2^x+1 = 32 Ili kutatua mlinganyo huu, tunahitaji kufanya besi ziwe sawa. Step 1: Andika 32 kama nguvu ya 2. 32 = 2 × 2 × 2 × 2 × 2 = 2^5 Step 2: Linganisha besi na kisha linganisha vipeo. 2^x+1 = 2^5 Kwa kuwa besi ni sawa, vipeo lazima viwe sawa: x+1 = 5 Step 3: Tatua kwa x. x = 5 - 1 x = 4 Jibu ni x=4. 13. The width of a rectangle is x cm and its length is (x+4) cm. Form an algebraic expression for its area. Eneo la mstatili (rectangle) hupatikana kwa kuzidisha urefu na upana. Step 1: Andika formula ya eneo la mstatili. Area = length × width Step 2: Badilisha urefu na upana uliopewa kwenye formula. Area = (x+4) cm × x cm Step 3: Rahisisha usemi. Area = x(x+4) cm^2 Area = (x^2 + 4x) cm^2 Jibu ni x^2 + 4x. 14. Factorize completely: x^2 - 16 Huu ni mfumo wa tofauti ya miraba miwili (difference of two squares), ambayo inaweza kuandikwa kama a^2 - b^2 = (a-b)(a+b). Step 1: Tambua a na b. Katika x^2 - 16, a^2 = x^2, kwa hivyo a = x. Na b^2 = 16, kwa hivyo b = sqrt(16) = 4. Step 2: Tumia formula ya tofauti ya miraba miwili. x^2 - 4^2 = (x-4)(x+4) Jibu ni (x-4)(x+4). That's 2 down. 3 left today — send the next one.