{"id":"cb_question_bank:0a1b6fd4-dd0a-4c8b-a035-b159da5cefa7","source_id":"cb_question_bank","source_item_id":"0a1b6fd4-dd0a-4c8b-a035-b159da5cefa7","external_id":"a87d4ca6-6608-46d3-9f6b-60f4ad868594","ibn":null,"question_id":"1e003284","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":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x equals 49 y equals StartRoot x EndRoot plus 9 The graphs of the given equations intersect at the point left parenthesis x comma y right parenthesis in the xy -plane. What is the value of y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x equals 49\"><mi>x</mi><mo>=</mo><mrow><mn>49</mn></mrow></math></p>\n<p style=\"text-align: center;\"><math alttext=\"y equals StartRoot x EndRoot plus 9\"><mi>y</mi><mo>=</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mrow><mn>9</mn></mrow></math></p>\n<p style=\"text-align: left;\">The graphs of the given equations intersect at the point&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> in the <em>xy</em>-plane.&nbsp;What is the value of <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that the graphs of the given equations intersect at the point <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> in the <em>xy</em>-plane. It follows that&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> represents a solution to the system consisting of the given equations. The first equation given is <math alttext=\"x equals 49\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>49</mn>\n</mrow>\n</math>. Substituting <math alttext=\"49\"><mn>49</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the second equation given, <math alttext=\"y equals StartRoot x EndRoot plus 9\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<msqrt>\n\t\t\t<mi>x</mi>\n\t\t</msqrt>\n\t\t<mo>+</mo>\n\t\t<mn>9</mn>\n\t</mrow>\n</mrow>\n</math>, yields&nbsp;<math alttext=\"y equals StartRoot 49 EndRoot plus 9\"><mi>y</mi><mo>=</mo><msqrt><mn>49</mn></msqrt><mo>+</mo><mn>9</mn></math>, which is equivalent to&nbsp;<math alttext=\"y equals 7 plus 9\"><mi>y</mi><mo>=</mo><mn>7</mn><mo>+</mo><mn>9</mn></math>, or&nbsp;<math alttext=\"y equals 16\"><mi>y</mi><mo>=</mo><mn>16</mn></math>. It follows that the graphs of the given equations intersect at the point <math alttext=\"left parenthesis 49 comma 16 right parenthesis\"><mfenced><mrow><mn>49</mn><mo>,</mo><mn>16</mn></mrow></mfenced></math>. Therefore, the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"16\"><mn>16</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.824000+00:00","source_updated_at":"2023-08-02T20:25:59.824000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"16\"><mn>16</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"40\"><mn>40</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"81\"><mn>81</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"130\"><mn>130</mn>\n</math></p>","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}}