{"paper":{"id":"site-3079","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":8,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-3079/zad/3187","paper_id":"site-3079","number":"3187","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"O funkcji liniowej f wiadomo, że f(1)=2 oraz, że do wykresu tej funkcji należy punkt P=(-2,3). Wyznacz wzór funkcji f.","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-3187.svg","solution_image":"img/site/3079/rozw-3187.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/3188","paper_id":"site-3079","number":"3188","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Oblicz miejsce zerowe funkcji f(x)={2x+1 dla x<=0; x+2 dla x>0}","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-3188.svg","solution_image":"img/site/3079/rozw-3188.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/3189","paper_id":"site-3079","number":"3189","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Naszkicuj wykres funkcji o wzorze f(x)={ 2x+1 dla <=0; x+2 dla x>0 }","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-3189.svg","solution_image":"img/site/3079/rozw-3189.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/3190","paper_id":"site-3079","number":"3190","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Napisz równanie prostej równoległej do prostej o równaniu 2x-y-11=0 i przechodzącej przez punkt P=(1,2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-3190.svg","solution_image":"img/site/3079/rozw-3190.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/3250","paper_id":"site-3079","number":"3250","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiąż układ równań {x+3y=5, 2x-y=3}","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-3250.svg","solution_image":"img/site/3079/rozw-3250.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/6869","paper_id":"site-3079","number":"6869","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiąż nierówność. Podaj największą liczbę całkowitą spełniającą tę nierówność. 2x ≥ √5x + 3√5 - 6.","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-6869.svg","solution_image":"img/site/3079/rozw-6869.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/7258","paper_id":"site-3079","number":"7258","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Zbiorem rozwiązań nierówności ax+5 ≥ 0 z niewiadomą x jest przedział (-∞,2>. Wyznacz a.","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-7258.svg","solution_image":"img/site/3079/rozw-7258.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-3079/zad/8148","paper_id":"site-3079","number":"8148","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Funkcja liniowa f jest określona wzorem f(x)=5x+m²+6m, gdzie m jest pewną liczbą rzeczywistą. W kartezjańskim układzie współrzędnych (x,y) wykres funkcji f przecina oś Oy w punkcie o współrzędnych (0,-9). Oblicz m. Zapisz obliczenia.","answer":null,"answer_text":null,"solution":null,"image":"img/site/3079/zad-8148.svg","solution_image":"img/site/3079/rozw-8148.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}