{"id":"cb_question_bank:98d97d6b-1089-46c9-928d-be179d749424","source_id":"cb_question_bank","source_item_id":"98d97d6b-1089-46c9-928d-be179d749424","external_id":"acd27116-7079-469e-b599-5c238ac3e563","ibn":null,"question_id":"c01f4a95","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"j left parenthesis x right parenthesis equals m x plus 144 For the linear function j , m is a constant and j left parenthesis 12 right parenthesis equals 18 . What is the value of j left parenthesis 10 right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"j left parenthesis x right parenthesis equals m x plus 144\"><mi>j</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mrow><mn>144</mn></mrow></math></p>\n<p style=\"text-align: left;\">For the linear function <math alttext=\"j\"><mi>j</mi>\n</math>, <math alttext=\"m\"><mi>m</mi>\n</math> is a constant and <math alttext=\"j left parenthesis 12 right parenthesis equals 18\"><mi>j</mi><mo>(</mo><mrow><mn>12</mn></mrow><mo>)</mo><mo>=</mo><mrow><mn>18</mn></mrow></math>. What is the value of&nbsp;<math alttext=\"j left parenthesis 10 right parenthesis\"><mi>j</mi><mo>(</mo><mrow><mn>10</mn></mrow><mo>)</mo></math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"39\"><mn>39</mn>\n</math>. It’s given that for the linear function <math alttext=\"j\"><mi>j</mi>\n</math>, <math alttext=\"m\"><mi>m</mi>\n</math> is a constant and&nbsp;<math alttext=\"j left parenthesis 12 right parenthesis equals 18\"><mi>j</mi><mfenced><mn>12</mn></mfenced><mo>=</mo><mn>18</mn></math>. Substituting <math alttext=\"12\"><mn>12</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> and <math alttext=\"18\"><mn>18</mn>\n</math> for&nbsp;<math alttext=\"j left parenthesis x right parenthesis\"><mi>j</mi><mfenced><mi>x</mi></mfenced></math> in the given equation&nbsp;yields <math alttext=\"18 equals m left parenthesis 12 right parenthesis plus 144\"><mn>18</mn><mo>=</mo><mi>m</mi><mfenced><mn>12</mn></mfenced><mo>+</mo><mn>144</mn></math>. Subtracting <math alttext=\"144\"><mn>144</mn>\n</math> from both sides of this equation yields <math alttext=\"negative 126 equals m left parenthesis 12 right parenthesis\"><mo>-</mo><mn>126</mn><mo>=</mo><mi>m</mi><mfenced><mn>12</mn></mfenced></math>. Dividing both sides of this equation by <math alttext=\"12\"><mn>12</mn>\n</math> yields&nbsp;<math alttext=\"negative 10.5 equals m\"><mo>-</mo><mn>10.5</mn><mo>=</mo><mi>m</mi></math>. Substituting&nbsp;<math alttext=\"negative 10.5\"><mo>-</mo><mn>10.5</mn></math> for <math alttext=\"m\"><mi>m</mi>\n</math> in the given equation,&nbsp;<math alttext=\"j left parenthesis x right parenthesis equals m x plus 144\"><mi>j</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mn>144</mn></math>, yields <math alttext=\"j left parenthesis x right parenthesis equals minus 10.5 x plus 144\"><mi>j</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>10.5</mn><mi>x</mi><mo>+</mo><mn>144</mn></math>. Substituting <math alttext=\"10\"><mn>10</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields&nbsp;<math alttext=\"j left parenthesis 10 right parenthesis equals left parenthesis negative 10.5 right parenthesis left parenthesis 10 right parenthesis plus 144\"><mi>j</mi><mfenced><mn>10</mn></mfenced><mo>=</mo><mfenced><mrow><mo>-</mo><mn>10.5</mn></mrow></mfenced><mfenced><mn>10</mn></mfenced><mo>+</mo><mn>144</mn></math>, or <math alttext=\"j left parenthesis 10 right parenthesis equals 39\"><mi>j</mi><mfenced><mn>10</mn></mfenced><mo>=</mo><mn>39</mn></math>. Therefore, the value of <math alttext=\"j left parenthesis 10 right parenthesis\"><mi>j</mi><mfenced><mn>10</mn></mfenced></math> is <math alttext=\"39\"><mn>39</mn>\n</math>.</p>","correct_answer":["39"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.812000+00:00","source_updated_at":"2023-08-02T20:25:59.812000+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}}