Factorize completely: x2 - 16

Ili kuandika 222.2222... katika standard form, tunahamisha desimali mara 2 kushoto.

Tarakimu ya tano ni 2, ambayo ni chini ya 5, kwa hivyo hatubadilishi tarakimu ya nne.

Jibu ni $\boxed{2.222 \times 10^2}$.

8. The temperature in a town was recorded as $18.6^\circ C$ in the morning and $24.2^\circ C$ in the afternoon. Calculate the mean temperature.

Mean temperature (wastani wa joto) hupatikana kwa kujumlisha joto zote na kugawanya kwa idadi ya vipimo.

Jibu ni $\boxed{21.4^\circ C}$.

9. Estimate the height of a classroom wall in kilometres.

Urefu wa ukuta wa darasa kwa kawaida hupimwa kwa mita.

Urefu wa kawaida wa ukuta wa darasa ni takriban mita 3.

Tunajua kuwa kilomita 1 ina mita 1000.

Jibu ni $\boxed{0.003 \text{ km}}$.

10. Express 243 as a power of a prime number.

Nambari prime ni nambari inayoweza kugawanyika na 1 na yenyewe tu.

Anza kugawanya 243 na nambari ndogo zaidi prime.

Kwa kuwa 3 imejirudia mara 5, tunaweza kuandika 243 kama $3^5$.

Jibu ni $\boxed{3^5}$.

11. Simplify using the laws of indices: $(5^2)^{\frac{1}{2}}$

Tunatumia sheria ya indices inayosema $(a^m)^n = a^{m \times n}$.

Jibu ni $\boxed{5}$.

12. Solve for x: $2^{x+1} = 32$

Ili kutatua mlinganyo huu, tunahitaji kufanya besi ziwe sawa.

Kwa kuwa besi ni sawa, vipeo lazima viwe sawa:

Jibu ni $\boxed{x=4}$.

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.

Jibu ni $\boxed{x^2 + 4x}$.

14. Factorize completely: $x^2 - 16$

Huu ni mfumo wa tofauti ya miraba miwili (difference of two squares), ambayo inaweza kuandikwa kama $a^2 - b^2 = (a-b)(a+b)$.

Katika $x^2 - 16$, $a^2 = x^2$, kwa hivyo $a = x$.
Na $b^2 = 16$, kwa hivyo $b = \sqrt{16} = 4$.

Jibu ni $\boxed{(x-4)(x+4)}$.