{"id":"cb_question_bank:cc0caf17-2997-4cb5-88ea-9794a4958b68","source_id":"cb_question_bank","source_item_id":"cc0caf17-2997-4cb5-88ea-9794a4958b68","external_id":null,"ibn":"027107-DC","question_id":"928498f3","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"What are the solutions to the given equation?","stimulus":"6 x squared, plus 5 x, minus 7, equals 0","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/263346e377e3aed293d84e09ec0af6c56a6c41c46900f20623c5d54c4907d0e0\" alt=\"6 x squared, plus 5 x, minus 7, equals 0\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">What are the solutions to the given equation?</p>\n","rationale_html":"<p>Choice A is correct. The quadratic formula, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2688dfc6adcebb064be581b68d3b5ce487f95792ae10472a925b67bbc0ed70c3\" alt=\"x equals, the fraction with numerator negative b plus or minus, the square root of, b squared, minus 4 a, c, end root, and denominator 2 a, end fraction\"></span>, can be used to find the solutions to an equation in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2c869bdc70b1a9ecef53fb3c6051020877ac5c401e6cc5aaf10e36e3b7478c63\" alt=\"a, x squared, plus b x, plus c, equals 0\"></span>. In the given equation, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c15d3bafbba571689680a93dce223db12d346366b1b8590509e090a22341331d\" alt=\"a, equals 6\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/70bcc5029fa8429202856178a8f15b635fd9bd8c2d07442b86f0932b9655d401\" alt=\"b equals 5\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d2a5b7c417eeafcad9e9ee60a877894650a835d412e31b6b5a0c3846b138f044\" alt=\"c equals negative 7\"></span>. Substituting these values into the quadratic formula gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bf6683e87cb5ddb5b7213e6a4bdee49b17db319a6a3d7cf8668eac9793b03c\" alt=\"the fraction with numerator negative 5 plus or minus, the square root of, 5 squared minus 4, times 6, times 7, end root, and denominator 2 times 6, end fraction\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/79a65b7bbd25842a472743748cec2a4d4e8ae5c381dd94f29db0fa772079947f\" alt=\"the fraction with numerator negative 5 plus or minus, the square root of, 25 minus 168, end root, and denominator 12, end fraction\"></span>.</p><p>Choice B is incorrect and may result from using <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a70ae983336186015ea68e04a919ef207f4b44a7cc588ea704f4bd640f573638\" alt=\"the fraction with numerator negative a, plus or minus, the square root of, b squared, minus 4 a, c, end root, and denominator 2 a, end fraction\"></span> as the quadratic formula. Choice C is incorrect and may result from using<span class=\"tcp-5e6dadaf-4ab1-4124-bf80-526178eb0f36\"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/486a6da7ddd0315f9176a9a9688b94c305a88354519456a351e13c2f8f69c375\" alt=\"the fraction with numerator negative b plus or minus, the square root of, a, squared, plus 4 a, c, end root, and denominator 2 a, end fraction \"></span> as the quadratic formula. Choice D is incorrect and may result from using <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/180310442cd692ce5819715b754a565b0e9b8254a99e9e2c7379731bcb33d0a7\" alt=\"the fraction with numerator negative a, plus or minus, the square root of, a, squared, plus 4 a, c, end root, and denominator 2 a, end fraction \"></span> as the quadratic formula.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/79a65b7bbd25842a472743748cec2a4d4e8ae5c381dd94f29db0fa772079947f\" alt=\"the fraction with numerator negative 5, plus or minus the square root of 25 plus 168, end root, and denominator 12\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3f5c33f686e357b902ecdd351413a6c9789d1063c4cf2a3f19ca548e594dda58\" alt=\"the fraction with numerator negative 6, plus or minus the square root of 25 plus 168, end root, and denominator 12\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1ff365194ecf8dc9fa209742603ec1e3160fbddbba63f5bbfc41dc3f5b9f8845\" alt=\"the fraction with numerator negative 5, plus or minus the square root of 36 minus 168, end root, and denominator 12\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3c580ba6e7fe5e0bbf29a8e281ca36b68d897b656825df266e42c775a3fd4cb\" alt=\"the fraction with numerator negative 6, plus or minus the square root of 36 minus 168, end root, and denominator 12\"></span></span>\n          </p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}