{"id":"cb_question_bank:626ee2c3-58aa-4e0d-b54c-d9290b91c0e5","source_id":"cb_question_bank","source_item_id":"626ee2c3-58aa-4e0d-b54c-d9290b91c0e5","external_id":"46dc5769-2263-4a0c-adbe-bfe4c54562bc","ibn":null,"question_id":"717a1964","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":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"z squared plus 10 z minus 24 equals 0 What is one of the solutions to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"z squared plus 10 z minus 24 equals 0\"><mrow>\n\t<mrow>\n\t\t<msup>\n\t\t\t<mi>z</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>10</mn>\n\t\t\t<mi>z</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mn>24</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">What is one of the solutions to the given equation?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is either <math alttext=\"2\"><mn>2</mn>\n</math> or <math alttext=\"negative 12\"><mo>-</mo><mn>12</mn>\n</math>. The left-hand side of the given equation can be rewritten by factoring. The two values that multiply to <math alttext=\"negative 24\"><mo>-</mo><mn>24</mn>\n</math> and add to <math alttext=\"10\"><mn>10</mn>\n</math> are <math alttext=\"12\"><mn>12</mn>\n</math> and <math alttext=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math>. It follows that the given equation can be rewritten as <math alttext=\"left parenthesis z plus 12 right parenthesis left parenthesis z minus 2 right parenthesis equals 0\"><mfenced><mrow><mi>z</mi><mo>+</mo><mn>12</mn></mrow></mfenced><mfenced><mrow><mi>z</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>. Setting each factor equal to <math alttext=\"0\"><mn>0</mn>\n</math> yields two equations: <math alttext=\"z plus 12 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>z</mi>\n\t\t<mo>+</mo>\n\t\t<mn>12</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> and <math alttext=\"z minus 2 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>z</mi>\n\t\t<mo>-</mo>\n\t\t<mn>2</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Subtracting <math alttext=\"12\"><mn>12</mn>\n</math> from both sides of the equation <math alttext=\"z plus 12 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>z</mi>\n\t\t<mo>+</mo>\n\t\t<mn>12</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> results in <math alttext=\"z equals negative 12\"><mrow>\n\t<mi>z</mi>\n\t<mo>=</mo>\n\t<mo>-</mo><mn>12</mn>\n</mrow>\n</math>. Adding <math alttext=\"2\"><mn>2</mn>\n</math> to both sides of the equation <math alttext=\"z minus 2 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>z</mi>\n\t\t<mo>-</mo>\n\t\t<mn>2</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> results in <math alttext=\"z equals 2\"><mrow>\n\t<mi>z</mi>\n\t<mo>=</mo>\n\t<mn>2</mn>\n</mrow>\n</math>. Note that 2 and -12 are examples of ways to enter a correct answer.</p>","correct_answer":["2","-12"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.822000+00:00","source_updated_at":"2023-08-02T20:25:59.822000+00:00","options":[],"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}}