[tex]Zad. 1\\(a^3-3a^2)^2=(a^3)^2-2*a^3*3a^2+(3a^2)^2=a^6-6a^5+9a^4=a^4(a^2-6a+9)\\Odp. A[/tex]
[tex]Zad. 2\\\frac{\sqrt{245}-\sqrt{45}}{\sqrt2}=\frac{7\sqrt5-3\sqrt5}{\sqrt2}=\frac{(7\sqrt5-3\sqrt5)\sqrt2}2=\frac{7\sqrt{10}-3\sqrt{10}}2=\frac{4\sqrt{10}}2=2\sqrt{10}\\\\Odp. B[/tex]
[tex]Zad. 3\\log_{\frac13}\sqrt{27} \to \frac13^x=\sqrt{27} \to x=-\frac32\\\\Odp. D[/tex]
[tex]Zad. 4\\x - \text{pierwotna cena}\\0.9x - \text{cena po 1 obnizce}\\0.9*0.9x=0.81x - \text{cena po 2 obnizce}\\\\0.9x=100\%\\0.81x=?\\?=\frac{0.81x*100\%}{0.9x}=\frac{81\%}{0.9}=90\%\\Odp. A[/tex]
[tex]Zad. 5\\\text{1 prosta - po lewej:}\\A=(-2, 0)\\B=(0, 4)\\\left \{ {{0=-2a+b} \atop {4=0a+b}} \right. \\\left \{ {{2a=b} \atop {4=b}} \right. \\\left \{ {{2a=4 /:2} \atop {b=4}} \right. \\\left \{ {{a=2} \atop {b=4} \right. \\y=2x+b\\\\\text{2 prosta - po prawej}\\A=(0, -1)\\B=(2, 3)\\\left \{ {{-1=0a+b} \atop {3=2a+b}} \right. \\\left \{ {{-1=b} \atop {3=2a-1 /+1}} \right. \\\left \{ {{b=-1} \atop {4=2a /:2}} \right. \\\left \{ {{b=-1} \atop {a=2}} \right. \\y=2x-1\\\\[/tex]
[tex]\left \{ {{y=2x+4} \atop {y=2x-1}} \right. \\\left \{ {{-2x+y=4} \atop {-2x+y=-1}} \right. \\\left \{ {{x-\frac{y}2=-2} \atop {2x=y+1}} \right. \\\left \{ {{2x-y=-4} \atop {2x-y=1}} \right. \\\\Odp. C[/tex]
