{"paper":{"id":"site-2405","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":34,"source_label":"Matematyka · Zbiory zadań · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2405/zad/2406","paper_id":"site-2405","number":"2406","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Wskaż nierówność, która opisuje sumę przedziałów zaznaczonych na osi liczbowej.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2406.svg","solution_image":"img/site/2405/rozw-2406.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2407","paper_id":"site-2405","number":"2407","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Na seans filmowy sprzedano 280 biletów, w tym 126 ulgowych. Jaki procent sprzedanych biletów stanowiły bilety ulgowe?","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2407.svg","solution_image":"img/site/2405/rozw-2407.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2408","paper_id":"site-2405","number":"2408","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"6% liczby x jest równe 9. Wtedy x=?","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2408.svg","solution_image":"img/site/2405/rozw-2408.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2409","paper_id":"site-2405","number":"2409","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Iloraz 32^{-3}:(1/8)^4 jest równy a) 2^{-27} b) 2^{-3} c) 2^3 d) 2^{27}","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2409.svg","solution_image":"img/site/2405/rozw-2409.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2410","paper_id":"site-2405","number":"2410","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"O liczbie x wiadomo, że log_3 x = 9. Zatem a) x = 2 b) x=1/2 c) x=3^9 d) x=9^3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2410.svg","solution_image":"img/site/2405/rozw-2410.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2411","paper_id":"site-2405","number":"2411","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Wyrażenie 27x^3+y^3 jest równe iloczynowi a) (3x+y)(9x^2-3xy+y^2) b) (3x+y)(9x^2+3xy+y^2) c) (3x-y)(9x^2+3xy+y^2) d) (3x-y)(9x^2+3xy+y^2)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2411.svg","solution_image":"img/site/2405/rozw-2411.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2412","paper_id":"site-2405","number":"2412","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Dane są wielomiany: W(x)=x^3-3x+1 oraz V(x)=2x^3. Wielomian W(x)*V(x) jest równy a) 2x^5-6x^4+2x^3 b) 2x^6-6x^4+2x^3 c) 2x^5+3x+1 d) 2x^5+6x^4+2x^3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2412.svg","solution_image":"img/site/2405/rozw-2412.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2413","paper_id":"site-2405","number":"2413","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Wierzchołek paraboli o równaniu y=-3(x+1)^2 ma współrzędne A. (-1,0) B. (0,-1) C.(1,0) D.(0,1)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2413.svg","solution_image":"img/site/2405/rozw-2413.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2414","paper_id":"site-2405","number":"2414","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Do wykresu funkcji f(x)=x^2+x-2 należy punkt A.(-1,-4), B.(-1,1), C.(-1,-1), D.(-1,-2).","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2414.svg","solution_image":"img/site/2405/rozw-2414.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2415","paper_id":"site-2405","number":"2415","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Rozwiązaniem równania x-5 / x+3 = 2/3 jest 21, 7, 7/3 czy 0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2415.svg","solution_image":"img/site/2405/rozw-2415.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2416","paper_id":"site-2405","number":"2416","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Zbiór rozwiązań nierówności (x+1)(x-3)>0 przedstawiony jest na rysunku A. B. C. czy D.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2416.svg","solution_image":"img/site/2405/rozw-2416.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2417","paper_id":"site-2405","number":"2417","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Dla n=1,2,3,... ciąg (a_n) jest określony wzorem: a_n=(-1)^n\\c(3-n). Wtedy A. a_3<0 B. a_3=0 C. a_3=1 D. a_3>1","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2417.svg","solution_image":"img/site/2405/rozw-2417.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2418","paper_id":"site-2405","number":"2418","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"W ciągu arytmetycznym trzeci wyraz jest równy 14, a jedenasty jest równy 34. Różnica tego ciągu jest równa A. 9 B. 5/2 C. 2 D. 2/5","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2418.svg","solution_image":"img/site/2405/rozw-2418.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2419","paper_id":"site-2405","number":"2419","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"W ciągu geometrycznym (a_n) dane są: a_1=32 i a_4=-4. Iloraz tego ciągu jest równy: A. 12 B. 1/2 C. -1/2 D. -12","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2419.svg","solution_image":"img/site/2405/rozw-2419.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2420","paper_id":"site-2405","number":"2420","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Kąt alfa jest ostry i sin(alfa)=8/9. Wtedy cos(alfa) jest równy A. 1/9 B. 8/9 C. pierwiastek z 17 / 9 D. pierwiastek z 65 / 9","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2420.svg","solution_image":"img/site/2405/rozw-2420.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2421","paper_id":"site-2405","number":"2421","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Dany jest trójkąt prostokątny (patrz rysunek). Wtedy tg alfa jest równy A. pierwiastek z 2 B. pierwiastek z 2 przez pierwiastek 3 C. pierwiastek z 3 przez pierwiastek z 2 D. 1 przez pierwiastek z 2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2421.svg","solution_image":"img/site/2405/rozw-2421.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2422","paper_id":"site-2405","number":"2422","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"W trójkącie równoramiennym ABC dane są |AC|=|BC|=7 oraz |AB|=12. Wysokość opuszczona z wierzchołka C jest równa A. pierwiastek z 13 B. pierwiastek z 5 C. pierwiastek z 1 D. pierwiastek z 5","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2422.svg","solution_image":"img/site/2405/rozw-2422.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2423","paper_id":"site-2405","number":"2423","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Oblicz długość odcinak AE wiedząc, że AB||CD i |AB|=6, |AC|=4, |CD|=8.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2423.svg","solution_image":"img/site/2405/rozw-2423.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2424","paper_id":"site-2405","number":"2424","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Dane są punkty A=(-2,3) oraz B=(4,6). Długość odcinka AB jest równa ...","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2424.svg","solution_image":"img/site/2405/rozw-2424.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2425","paper_id":"site-2405","number":"2425","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Promień okręgu o równaniu (x-1)^2+y^2=16 jest równy ...","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2425.svg","solution_image":"img/site/2405/rozw-2425.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2426","paper_id":"site-2405","number":"2426","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Wykres funkcji liniowej określonej wzorem f(x)=3x+2 jest prostą prostopadłą do prostej o równaniu ...","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2426.svg","solution_image":"img/site/2405/rozw-2426.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2427","paper_id":"site-2405","number":"2427","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Prosta o równaniu y=-4x+(2m-7) przechodzi przez punkt A=(2,-1). Wtedy ...","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2427.svg","solution_image":"img/site/2405/rozw-2427.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2428","paper_id":"site-2405","number":"2428","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Pole powierzchni całkowitej sześcianu jest równe 150cm. Długość krawędzi tego sześcianu A. 5cm B. 4cm C. 4/5cm D. 5cm","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2428.svg","solution_image":"img/site/2405/rozw-2428.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2429","paper_id":"site-2405","number":"2429","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Średnia arytmetyczna pięciu liczb 5, x, 1, 3, 1 jest równa 3. Wtedy A. x=2 B. x=3 C. x=4 D. x=5","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2429.svg","solution_image":"img/site/2405/rozw-2429.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2430","paper_id":"site-2405","number":"2430","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Wybieramy liczbę a ze zbioru A={2, 3, 4, 5} oraz liczbę b ze zbioru B={1,4}. Ile jest takich par (a,b), że iloczyn a * b jest liczbą nieparzystą?","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2430.svg","solution_image":"img/site/2405/rozw-2430.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2431","paper_id":"site-2405","number":"2431","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Rozwiązywanie nierówności kwadratowej x^2-3x+2 mniejsze lub równe 0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2431.svg","solution_image":"img/site/2405/rozw-2431.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2432","paper_id":"site-2405","number":"2432","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Przekształcanie wielomianu x^3-7x^2+2x-14=0 do postaci iloczynowej w celu odczytania jego pierwiastków.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2432.svg","solution_image":"img/site/2405/rozw-2432.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2433","paper_id":"site-2405","number":"2433","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"W układzie współrzędnych na płaszczyźnie punkty A=(2,5) i C=(6,7) są przeciwległymi wierzchołkami kwadratu ABCD. Wyznacz równanie prostej BD.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2433.svg","solution_image":"img/site/2405/rozw-2433.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2434","paper_id":"site-2405","number":"2434","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Kąt alfa jest ostry i tg(alfa)={4/3}. Oblicz sin(alfa)+cos(alfa)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2434.svg","solution_image":"img/site/2405/rozw-2434.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2435","paper_id":"site-2405","number":"2435","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Wykaż, że dla każdego m ciąg m+1/4, m+3/6, m+9/12 jest arytmetyczny.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2435.svg","solution_image":"img/site/2405/rozw-2435.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2436","paper_id":"site-2405","number":"2436","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Uczeń przeczytał książkę liczącą 480 stron, przy czym każdego dnia czytał jednakową liczbę stron. Gdyby czytał każdego dnia o 8 stron więcej, to przeczytałby tę książkę o 3 dni wcześniej. Oblicz, ile dni uczeń czytał tę książkę.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2436.svg","solution_image":"img/site/2405/rozw-2436.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2438","paper_id":"site-2405","number":"2438","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Trójkąty ABC i CDE są równoboczne. Punkty A, C i E leżą na jednej prostej. Punkty K, L i M są środkami odcinków AC, CE i BD (zobacz rysunek). Wykaż, że punkty K, L, M są wierzchołkami trójkąta równobocznego.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2438.svg","solution_image":"img/site/2405/rozw-2438.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2439","paper_id":"site-2405","number":"2439","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Pole trójkąta prostokątnego jest równe 60cm^2. Jedna przyprostokątna jest o 7cm dłuższa od drugiej. Oblicz długość przeciwprostokątnej tego trójkąta.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2439.svg","solution_image":"img/site/2405/rozw-2439.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2405/zad/2440","paper_id":"site-2405","number":"2440","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":2009,"month":null,"level":"podstawowa","text":"Punkty A=(2,0) i B=(12,0) są wierzchołkami trójkąta prostokątnego ABC o przeciwprostokątnej AB. Wierzchołek C leży na prostej o równaniu y=x. Oblicz współrzędne punktu C.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2405/zad-2440.svg","solution_image":"img/site/2405/rozw-2440.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 · 2009 (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}