{"paper":{"id":"site-4428","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"rozszerzona","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":4,"source_label":"Matematyka · Zbiory zadań · 2015 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-4428/zad/4492","paper_id":"site-4428","number":"4492","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"rozszerzona","text":"Trzy liczby tworzą ciąg arytmetyczny. Jeśli do pierwszej z nich dodamy 5, do drugiej 3, a do trzeciej 4, to otrzymamy rosnący ciąg geometryczny, w którym trzeci wyraz jest cztery razy większy od pierwszego. Znajdź te liczby.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4428/zad-4492.svg","solution_image":"img/site/4428/rozw-4492.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 · 2015 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4428/zad/4494","paper_id":"site-4428","number":"4494","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"rozszerzona","text":"Rozwiąż nierówność z dwoma wartościami bezwzględnymi |2x-6|+|x+7| >= 17.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4428/zad-4494.svg","solution_image":"img/site/4428/rozw-4494.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 · 2015 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4428/zad/4496","paper_id":"site-4428","number":"4496","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"rozszerzona","text":"Na boku AB trójkąta równobocznego ABC wybrano punkt D taki, że |AD|:|DB| = 2:3. Oblicz tangens kąta ACD.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4428/zad-4496.svg","solution_image":"img/site/4428/rozw-4496.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 · 2015 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-4428/zad/4499","paper_id":"site-4428","number":"4499","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2015,"month":null,"level":"rozszerzona","text":"Rozważmy rzut sześcioma kostkami do gry, z których każda ma inny kolor. Oblicz prawdopodobieństwo zdarzenia polegającego na tym, że uzyskany wynik rzutu spełnia równocześnie trzy warunki: Dokładnie na dwóch kostkach otrzymano po jednym oczku; Dokładnie na trzech kostkach otrzymano po sześć oczek; Suma wszystkich otrzymanych liczb oczek jest parzysta.","answer":null,"answer_text":null,"solution":null,"image":"img/site/4428/zad-4499.svg","solution_image":"img/site/4428/rozw-4499.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 · 2015 (rozszerzona)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}