Zadanie 1. Kąt BAC 40 stopni. Kąt CBA 25 stopni. Kąt ACB 115 stopni. Zadanie 2. x-pierwszy z kątów x + 38 - drugi kąt x+x+38=180 2x=142 x=71 x+38=109 Zadanie 3. [latex]x^{2} + 100 = (x+2)^{2} \ x^{2} + 100 = x^{2} + 4x + 4 \ 4x = 96 \ x = 24 [/latex] a) Obw. = 24 + 10 + 26 = 60 b) 26 = 2R R = 13 c) [latex]r = frac{24+10-26}{2}[/latex] r = 4 Zadanie 4. [latex]sin^{2}alpha + cos^{2}alpha = 1 \ sin^{2}alpha = 1 - cos^{2}alpha \ sinalpha = sqrt{1 - cos^{2}alpha} \ sinalpha = sqrt{1-frac{9}{25}} \ sinalpha = sqrt{frac{16}{25}} \ sinalpha = frac{4}{5} \ tgalpha = frac{sinalpha}{cosalpha} \ tgalpha = frac{frac{4}{5}}{frac{3}{5}} \ tgalpha = frac{4}{3}[/latex] Zadanie 5. [latex] P = frac{6^{2}cdot sqrt{3}}{4} \ P = frac{36sqrt{3}}{4} \ P = 9sqrt{3}[/latex] Zadanie 6. a) x należy do < - 5,8 > b) [latex] Zw_{f} = < -3,3 >[/latex] c) [latex]( -5,2 )cup ( 1,7 )[/latex] d) < -5,1 > < 6,8 > e) f(-4) = -2 f(6) = -3 f(-1) = 1 [latex] -2cdot (-3) - 1 = 6 - 1 = 5[/latex] Zadanie 7. f(x) = 3x - 1 A(-3,1) a) y = 3x - b [latex]1 = 3cdot (-3) - b \ 1 = -9 - b \ b = -10[/latex] y = 3x - 10 b) y = ax + b [latex] acdot 3 = -1 \ a = -frac{1}{3} \ y = -frac{1}{3}x + b \ 1 = -frac{1}{3}cdot (-3) + b \ 1 = 1 + b \ b = 0 \ y = -frac{1}{3}x[/latex]
