Hệ bất phương trình bậc nhất hai ẩn

Home Lớp 10 Toán lớp 10 - Sách Kết nối tri thức Bài 4: Hệ bất phương trình bậc nhất hai ẩnBài tập nâng cao

{"common":{"save":0,"post_id":"6079","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5308","mon_id":"1158767","chapter_id":"1158774","post_id":"6079","question":"M\u1ed9t x\u01b0\u1edfng l\u1eafp ráp máy tính d\u1ef1 \u0111\u1ecbnh ráp x chi\u1ebfc máy tính cá nhân<\/span> và y chi\u1ebfc máy tính b\u1ea3ng<\/span> trong m\u1ed9t ngày. Do h\u1ea1n ch\u1ebf v\u1ec1 nhân công nên m\u1ed7i ngày ch\u1ec9 có th\u1ec3 xu\u1ea5t x\u01b0\u1edfng t\u1ed5ng hai lo\u1ea1i máy tính trên không quá 160 chi\u1ebfc. H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình nào d\u01b0\u1edbi \u0111ây mô t\u1ea3 \u0111i\u1ec1u ki\u1ec7n ràng bu\u1ed9c \u0111\u1ed1i v\u1edbi x, y<\/span>?<\/p>","options":["A.<\/strong> $\\begin{cases} x \\geq 0 \\\\ y \\geq 0\\\\ x + y \\geq 160 \\end{cases}$<\/span>","B.<\/strong> $\\begin{cases} x \\leq 0 \\\\ y \\leq 0\\\\ x + y \\leq 160 \\end{cases}$<\/span>","C.<\/strong> $\\begin{cases} x \\geq 0 \\\\ y \\geq 0\\\\ x + y \\leq 160 \\end{cases}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"Vì x\u01b0\u1edfng l\u1eafp ráp máy tính d\u1ef1 \u0111\u1ecbnh ráp x chi\u1ebfc máy tính cá nhân<\/span> và y chi\u1ebfc máy tính b\u1ea3ng<\/span> trong m\u1ed9t ngày nên <\/p> $x \\geq 0, \\space y \\geq 0$<\/span>.<\/p>Vì m\u1ed7i ngày ch\u1ec9 có th\u1ec3 xu\u1ea5t x\u01b0\u1edfng t\u1ed5ng hai lo\u1ea1i máy tính trên không quá 160 chi\u1ebfc nên $x +y \\leq 160$<\/span><\/p>T\u1eeb \u0111ó ta thu \u0111\u01b0\u1ee3c h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình là $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\leq160\\end{cases}$<\/span><\/p>\u0110áp án là C.<\/strong> $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\leq160\\end{cases}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2022-09-02 02:43:45","option_type":"math","len":0},{"id":"5309","mon_id":"1158767","chapter_id":"1158774","post_id":"6079","question":"Bác Ba d\u1ef1 \u0111\u1ecbnh tr\u1ed3ng x (ha) \u0111\u1eadu \u0111en<\/span> và y (ha) ngô <\/span>trên m\u1ed9t m\u1ea3nh \u0111\u1ea5t có di\u1ec7n tích 10 ha. N\u1ebfu tr\u1ed3ng 1 ha \u0111\u1eadu \u0111en thì c\u1ea7n 30 ngày công và thu \u0111\u01b0\u1ee3c 45 tri\u1ec7u \u0111\u1ed3ng. N\u1ebfu tr\u1ed3ng 1 ha ngô thì c\u1ea7n 20 ngày công và thu \u0111\u01b0\u1ee3c 40 tri\u1ec7u \u0111\u1ed3ng. Bi\u1ebft bác Ba ch\u1ec9 có th\u1ec3 s\u1eed d\u1ee5ng không quá 210 ngày công cho vi\u1ec7c tr\u1ed3ng \u0111\u1eadu \u0111en và ngô, h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình nào d\u01b0\u1edbi \u0111ây mô t\u1ea3 \u0111i\u1ec1u ki\u1ec7n ràng bu\u1ed9c \u0111\u1ed1i v\u1edbi x, y<\/span>?<\/p>","options":["A.<\/strong> $\\begin{cases}x\\leq0\\\\y\\leq0\\\\x+y\\leq10\\\\30x+20y\\leq210\\end{cases}$<\/span>","B.<\/strong> $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\geq10\\\\30x+20y\\geq210\\end{cases}$<\/span>","C.<\/strong> $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\leq10\\\\20x+30y\\leq210\\end{cases}$<\/span>","D.<\/strong> $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\leq10\\\\30x+20y\\leq210\\end{cases}$<\/span>"],"correct":"4","level":"3","hint":"","answer":"Vì bác Ba d\u1ef1 \u0111\u1ecbnh tr\u1ed3ng x (ha) \u0111\u1eadu \u0111en và y (ha) ngô <\/span>nên $x\\geq0,\\space y\\geq0$<\/span><\/span>.<\/p>Vì m\u1ea3nh \u0111\u1ea5t có di\u1ec7n tích 10 ha nên $x+y\\leq10$<\/span><\/span>.<\/p>Vì tr\u1ed3ng 1 ha \u0111\u1eadu \u0111en thì c\u1ea7n 30 ngày công, tr\u1ed3ng 1 ha ngô thì c\u1ea7n 20 ngày công và không quá 210 ngày công nên<\/p>$30x+20y\\leq210$<\/span><\/span>.<\/p>Ta có h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\leq10\\\\30x+20y\\leq210\\end{cases}$<\/span><\/p>\u0110áp án \u0111úng là D.<\/strong> $\\begin{cases}x\\geq0\\\\y\\geq0\\\\x+y\\leq10\\\\30x+20y\\leq210\\end{cases}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2022-09-02 03:19:04","option_type":"math","len":0},{"id":"5312","mon_id":"1158767","chapter_id":"1158774","post_id":"6079","question":"Giá tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $F(x; y)=2x+5y\\space$<\/span> v\u1edbi $(x;y)$<\/span> thu\u1ed9c mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình $\\begin{cases}x\\geq-1\\\\x\\leq3\\\\y\\geq-3\\\\y\\leq0\\end{cases}$<\/span> là bao nhiêu?<\/p>","options":["6","–2","–17","–9"],"correct":"1","level":"3","hint":"","answer":"Mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình \u0111ã cho là hình ch\u1eef nh\u1eadt ABCD v\u1edbi A(–1; 0), B(3; 0), C(3; –3) và D(–1; –3)<\/p><svg height=\"170\" width=\"270\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"172\" id=\"canvas_background\" width=\"272\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_3\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <rect fill=\"#ffff56\" height=\"110\" id=\"svg_24\" stroke=\"#ffff00\" stroke-width=\"1.5\" transform=\"rotate(90 216.5124969482422,80.33750152587893) \" width=\"183.99999\" x=\"124.51251\" y=\"25.3375\"><\/rect> <rect fill=\"#ffff56\" height=\"62\" id=\"svg_23\" stroke=\"#ffff00\" stroke-width=\"1.5\" transform=\"rotate(90 29.512500762939442,84.33750915527345) \" width=\"183.99999\" x=\"-62.4875\" y=\"53.33751\"><\/rect> <rect fill=\"#ffff56\" height=\"30\" id=\"svg_22\" stroke=\"#ffff00\" stroke-width=\"1.5\" width=\"317\" x=\"-18.9875\" y=\"138.8375\"><\/rect> <rect fill=\"#ffff56\" height=\"62\" id=\"svg_21\" stroke=\"#ffff00\" stroke-width=\"1.5\" width=\"317\" x=\"-38.9875\" y=\"0.8375\"><\/rect> <g id=\"svg_4\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"-69.9875\" x2=\"271.0125\" y1=\"65.8375\" y2=\"66\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1,0,0,1.334422945976257,1,-27.52564511669061) \" x=\"258.0125\" xml:space=\"preserve\" y=\"78.35831\">><\/text> <\/g> <g id=\"svg_7\" stroke=\"null\"> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" transform=\"rotate(-90 86.27069091796876,100.26028442382812) \" x1=\"-12.15478\" x2=\"184.69616\" y1=\"100.17904\" y2=\"100.34154\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 85.70800018310548,4.7138805389404235) matrix(0.5772754769719199,0,0,1.3344229459762569,91.61252447060849,-82.04525266063592) \" x=\"-17.24109\" xml:space=\"preserve\" y=\"73.77044\">><\/text> <\/g> <line fill=\"none\" id=\"svg_8\" stroke=\"#0000ff\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"2.0125\" x2=\"300\" y1=\"136.8375\" y2=\"136.8375\"><\/line> <line fill=\"none\" id=\"svg_9\" stroke=\"#ff0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" transform=\"rotate(90 62.50624847412109,86.83750152587892) \" x1=\"-48.9875\" x2=\"174\" y1=\"86.8375\" y2=\"86.8375\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_10\" stroke=\"#00ff00\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"94.0125\" xml:space=\"preserve\" y=\"20.8375\">y<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#00ff00\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"250.0125\" xml:space=\"preserve\" y=\"90.8375\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_13\" stroke=\"#00ff00\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"15.0125\" xml:space=\"preserve\" y=\"19.8375\">x = -1<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_15\" stroke=\"#00ff00\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"164.0125\" xml:space=\"preserve\" y=\"20.8375\">x = 3<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_16\" stroke=\"#00ff00\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"220.0125\" xml:space=\"preserve\" y=\"151.8375\">y = -3<\/text> <line fill=\"none\" id=\"svg_17\" stroke=\"#ff0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" transform=\"rotate(90 160.50625610351565,91.83750152587892) \" x1=\"49.0125\" x2=\"272\" y1=\"91.8375\" y2=\"91.8375\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"88.0125\" xml:space=\"preserve\" y=\"58.8375\">O<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"39.0125\" xml:space=\"preserve\" y=\"57.8375\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"163.0125\" xml:space=\"preserve\" y=\"58.8375\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_19\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"163.0125\" xml:space=\"preserve\" y=\"154.8375\">C<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"39.0125\" xml:space=\"preserve\" y=\"156.8375\">D<\/text> <\/g> <\/svg><\/span><\/p>Tính giá tr\u1ecb c\u1ee7a F t\u1ea1i các \u0111\u1ec9nh ta \u0111\u01b0\u1ee3c:<\/p>F(–1; 0) = 2 . (–1) + 5 . 0 = –2<\/p>F(3; 0) = 2 . 3 + 5 . 0 = 6<\/p>F(3; –3) = 2 . 3 + 5 . (–3) = –9<\/p>F(–1; –3) = 2 . (–1) + 5 . (–3) = –17<\/p>Suy ra giá tr\u1ecb l\u1edbn nh\u1ea5t là F(3; 0) = 6<\/span><\/p>\u0110áp án \u0111úng là 6<\/span><\/strong><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2022-09-02 04:19:27","option_type":"txt","len":0}]}