Project ID:
6000000065
Accepted:
Typ:
Layout:
Question:
Dopasuj każdą nierówność do rysunku z jej graficznym rozwiązaniem przedstawionym w kolorze czerwonym. Wykorzystaj informację, że wykres odpowiadający lewej stronie nierówności oznaczono kolorem zielonym, a ten odpowiadający prawej stronie nierówności oznaczono kolorem niebieskim.
Questions Title:
Wykresy:
Answers Title:
Nierówności:
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
$x^2+8x-2 \leq 2x+5$
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
$-x^2+8x-2\geq2x+5$
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
$-x^2+8x-2\geq-2x+5$
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
$-x^2+8x-2\leq-2x+5$
Question 5:
{\obrE}
Question 5 Image:
Answer 5:
$-x^2+8x-2\leq2x+5$
Question 6:
{\obrF}
Question 6 Image:
Answer 6:
$x^2+8x-2\geq2x+5$
Tex:
% ticket 32783
\NastavOD{3}
\def\obrA{\obrMsr[x=0.2cm,y=0.15cm]{-12}{8}{-20}{12}
{
\footnotesize
\coordinate (A) at (1,7);
\coordinate (B) at (1,0);
\coordinate (C) at (-7,-9);
\coordinate (D) at (-7,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\draw[red,thick] (-7,0) -- (1,0);
\obrPopisX[below]{-8,-4,4}
\obrPopisY[left]{-16,-12,-8,-4,4,8}
\obrZnackyX{-10,-6,-2,2,6}
\obrZnackyY{-18,-14,-10,-6,-2,2,6,10}
\draw[dashed] (1,0) -- (1,7);
\draw[dashed] (-7,0) -- (-7,-9);
\obrFce[green!60!black]{(\x)^2+8*(\x)-2}
\obrFce[blue]{2*(\x)+5}
\begin{scope}[thick]
\obrKrizek[2pt] {A}{}{}
\obrKrizek[2pt] {B}{}{}
\obrKrizek[2pt] {C}{}{}
\obrKrizek[2pt] {D}{}{}
\end{scope}
}}
\def\obrB{\obrMsr[x=0.2cm,y=0.2cm]{-7}{10}{-8}{16}
{
\footnotesize
\coordinate (A) at (1.585786438,8.17157287);
\coordinate (B) at (1.585786438,0);
\coordinate (C) at (4.414213562,13.82842713);
\coordinate (D) at (4.414213562,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\draw[red,thick] (1.585786438,0) -- (4.414213562,0);
\obrPopisX[below]{-4,4,8}
\obrPopisY[left]{-4,4,8,12}
\obrZnackyX{-6,-2,2,6}
\obrZnackyY{-6,-2,2,6,10,14}
\draw[dashed] (1.585786438,0) -- (1.585786438,8.17157287);
\draw[dashed] (4.414213562,0) -- (4.414213562,13.82842713);
\obrFce[green!60!black]{-(\x)^2+8*(\x)-2}
\obrFce[blue]{2*(\x)+5}
\begin{scope}[thick]
\obrKrizek[2pt] {A}{}{}
\obrKrizek[2pt] {B}{}{}
\obrKrizek[2pt] {C}{}{}
\obrKrizek[2pt] {D}{}{}
\end{scope}
}}
\def\obrC{\obrMsr[x=0.2cm,y=0.15cm]{-6}{12}{-16}{16}
{
\footnotesize
\coordinate (A) at (0.757359314,3.48528138);
\coordinate (B) at (0.757359314,0);
\coordinate (C) at (9.242640686,-13.48528136);
\coordinate (D) at (9.242640686,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\draw[red,thick] (0.757359314,0) -- (9.242640686,0);
\obrPopisX[below]{-4,4,8}
\obrPopisY[left]{-12,-8,-4,4,8,12}
\obrZnackyX{-2,2,6,10}
\obrZnackyY{-14,-10,-6,-2,2,6,10,14}
\draw[dashed] (0.757359314,0) -- (0.757359314,3.48528138);
\draw[dashed] (9.242640686,0) -- (9.242640686,-13.48528136);
\obrFce[green!60!black]{-(\x)^2+8*(\x)-2}
\obrFce[blue]{-2*(\x)+5}
\begin{scope}[thick]
\obrKrizek[2pt] {A}{}{}
\obrKrizek[2pt] {B}{}{}
\obrKrizek[2pt] {C}{}{}
\obrKrizek[2pt] {D}{}{}
\end{scope}
}}
\def\obrD{\obrMsr[x=0.2cm,y=0.15cm]{-6}{12}{-16}{16}
{
\footnotesize
\coordinate (A) at (0.757359314,3.48528138);
\coordinate (B) at (0.757359314,0);
\coordinate (C) at (9.242640686,-13.48528136);
\coordinate (D) at (9.242640686,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\draw[red,thick] (-6,0) -- (0.757359314,0);
\draw[red,thick] (9.242640686,0) -- (12,0);
\obrPopisX[below]{-4,4,8}
\obrPopisY[left]{-12,-8,-4,4,8,12}
\obrZnackyX{-2,2,6,10}
\obrZnackyY{-14,-10,-6,-2,2,6,10,14}
\draw[dashed] (0.757359314,0) -- (0.757359314,3.48528138);
\draw[dashed] (9.242640686,0) -- (9.242640686,-13.48528136);
\obrFce[green!60!black]{-(\x)^2+8*(\x)-2}
\obrFce[blue]{-2*(\x)+5}
\begin{scope}[thick]
\obrKrizek[2pt] {A}{}{}
\obrKrizek[2pt] {B}{}{}
\obrKrizek[2pt] {C}{}{}
\obrKrizek[2pt] {D}{}{}
\end{scope}
}}
\def\obrE{\obrMsr[x=0.2cm,y=0.2cm]{-7}{10}{-8}{16}
{
\footnotesize
\coordinate (A) at (1.585786438,8.17157287);
\coordinate (B) at (1.585786438,0);
\coordinate (C) at (4.414213562,13.82842713);
\coordinate (D) at (4.414213562,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\draw[red,thick] (-7,0) -- (1.585786438,0);
\draw[red,thick] (4.414213562,0) -- (10,0);
\obrPopisX[below]{-4,4,8}
\obrPopisY[left]{-4,4,8,12}
\obrZnackyX{-6,-2,2,6}
\obrZnackyY{-6,-2,2,6,10,14}
\draw[dashed] (1.585786438,0) -- (1.585786438,8.17157287);
\draw[dashed] (4.414213562,0) -- (4.414213562,13.82842713);
\obrFce[green!60!black]{-(\x)^2+8*(\x)-2}
\obrFce[blue]{2*(\x)+5}
\begin{scope}[thick]
\obrKrizek[2pt] {A}{}{}
\obrKrizek[2pt] {B}{}{}
\obrKrizek[2pt] {C}{}{}
\obrKrizek[2pt] {D}{}{}
\end{scope}
}}
\def\obrF{\obrMsr[x=0.2cm,y=0.15cm]{-12}{8}{-20}{12}
{
\footnotesize
\coordinate (A) at (1,7);
\coordinate (B) at (1,0);
\coordinate (C) at (-7,-9);
\coordinate (D) at (-7,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\draw[red,thick] (-12,0) -- (-7,0);
\draw[red,thick] (1,0) -- (8,0);
\obrPopisX[below]{-8,-4,4}
\obrPopisY[left]{-16,-12,-8,-4,4,8}
\obrZnackyX{-10,-6,-2,2,6}
\obrZnackyY{-18,-14,-10,-6,-2,2,6,10}
\draw[dashed] (1,0) -- (1,7);
\draw[dashed] (-7,0) -- (-7,-9);
\obrFce[green!60!black]{(\x)^2+8*(\x)-2}
\obrFce[blue]{2*(\x)+5}
\begin{scope}[thick]
\obrKrizek[2pt] {A}{}{}
\obrKrizek[2pt] {B}{}{}
\obrKrizek[2pt] {C}{}{}
\obrKrizek[2pt] {D}{}{}
\end{scope}
}}