{"id":1339,"date":"2025-12-23T14:00:57","date_gmt":"2025-12-23T13:00:57","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1339"},"modified":"2025-12-23T14:01:01","modified_gmt":"2025-12-23T13:01:01","slug":"zadanie-135","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1339","title":{"rendered":"Zadanie 135"},"content":{"rendered":"\n<p><strong>zadanie 15 \u2013 sierpie\u0144 2024 (1pkt)<\/strong><\/p>\n\n\n\n<p>Trzywyrazowy ci\u0105g (2m\u22125,4,9) jest arytmetyczny. Doko\u0144cz zdanie. Wybierz odpowied\u017a<strong> a)<\/strong> albo<strong> b) <\/strong>oraz odpowied\u017a <strong>1., 2. <\/strong>albo <strong>3.<\/strong> Ten ci\u0105g jest:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>a) rosn\u0105cy<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>b) malej\u0105cy<\/p>\n<\/div>\n<\/div>\n\n\n\n<p>oraz<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>1) m = -1<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>2) m = 2<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>3) m = 3<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22be701c36\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22be701c36\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \nPrawid\u0142owa odpowied\u017a to <p>\na) rosn\u0105cy<br>\n2) m = 2\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22be701c42\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22be701c42\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<p>\nDany jest trzywyrazowy ci\u0105g arytmetyczny: <br>\n(2m \u2212 5, 4, 9)\n<\/p>\n\n<p>\nAby ci\u0105g by\u0142 arytmetyczny, r\u00f3\u017cnica mi\u0119dzy kolejnymi wyrazami musi by\u0107 sta\u0142a. \nOznacza to, \u017ce:\n<\/p>\n\n<p>\n4 \u2212 (2m \u2212 5) = 9 \u2212 4\n<\/p>\n\n<p>\nObliczamy lew\u0105 stron\u0119:\n<br>\n4 \u2212 2m + 5 = 9 \u2212 2m\n<\/p>\n\n<p>\nPrawa strona to:\n<br>\n9 \u2212 4 = 5\n<\/p>\n\n<p>\nZatem:\n<br>\n9 \u2212 2m = 5\n<\/p>\n\n<p>\n9 \u2212 5 = 2m<br>\n4 = 2m<br>\nm = 2\n<\/p>\n\n<p>\nPo podstawieniu m = 2 pierwszy wyraz wynosi:\n<br>\n2m \u2212 5 = 4 \u2212 5 = \u22121\n<\/p>\n\n<p>\nCi\u0105g ma wi\u0119c posta\u0107:\n<br>\n(\u22121, 4, 9)\n<\/p>\n\n<p>\nWyrazy rosn\u0105, poniewa\u017c:<br>\n4 > \u22121 oraz 9 > 4\n<\/p>\n\n<p>\n<strong>Wniosek:<\/strong> ci\u0105g jest rosn\u0105cy, a warto\u015b\u0107 m wynosi 2.\n<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 15 \u2013 sierpie\u0144 2024 (1pkt) Trzywyrazowy ci\u0105g (2m\u22125,4,9) jest arytmetyczny. Doko\u0144cz zdanie. Wybierz odpowied\u017a a) albo b) oraz odpowied\u017a 1., 2. albo 3. Ten ci\u0105g jest: a) rosn\u0105cy b) malej\u0105cy oraz 1) m = -1 2) m = 2 3) m = 3<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"_uag_custom_page_level_css":"","_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[25,204,53,81,83],"tags":[23,205,54],"class_list":["post-1339","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-rozne","category-sierpien-2024","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-rozne","tag-sierpien-2024"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"kubio-fullhd":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"adminmymatma","author_link":"https:\/\/mymatma.pl\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"zadanie 15 \u2013 sierpie\u0144 2024 (1pkt) Trzywyrazowy ci\u0105g (2m\u22125,4,9) jest arytmetyczny. Doko\u0144cz zdanie. Wybierz odpowied\u017a a) albo b) oraz odpowied\u017a 1., 2. albo 3. Ten ci\u0105g jest: a) rosn\u0105cy b) malej\u0105cy oraz 1) m = -1 2) m = 2 3) m = 3","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1339"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1339\/revisions"}],"predecessor-version":[{"id":1340,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1339\/revisions\/1340"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}