{"id":"cb_question_bank:a59dc929-cff3-4f45-8098-463dc523f6cb","source_id":"cb_question_bank","source_item_id":"a59dc929-cff3-4f45-8098-463dc523f6cb","external_id":"c99a75dd-0256-4d13-b211-eb05d63ef00d","ibn":null,"question_id":"ef926848","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Square P has a side length of x inches. Square Q has a perimeter that is 176 inches greater than the perimeter of square P. The function f gives the area of square Q, in square inches. Which of the following defines f ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Square P has a side length of <math alttext=\"x\"><mi>x</mi>\n</math> inches. Square Q has a perimeter that is <math alttext=\"176\"><mn>176</mn>\n</math> inches greater than the perimeter of square P. The function <math alttext=\"f\"><mi>f</mi>\n</math> gives the area of square Q, in square inches. Which of the following defines <math alttext=\"f\"><mi>f</mi>\n</math>?</p>","rationale_html":"<p>Choice A is correct. Let <math alttext=\"x\"><mi>x</mi>\n</math> represent the side length, in inches, of square P. It follows that the perimeter of square P is <math alttext=\"4 x\"><mn>4</mn><mi>x</mi></math> inches. It's given that square Q has a perimeter that is <math alttext=\"176\"><mn>176</mn>\n</math> inches greater than the perimeter of square P. Thus, the perimeter of square Q is <math alttext=\"176\"><mn>176</mn>\n</math> inches greater than <math alttext=\"4 x\"><mn>4</mn><mi>x</mi></math> inches, or&nbsp;<math alttext=\"4 x plus 176\"><mn>4</mn><mi>x</mi><mo>+</mo><mn>176</mn></math> inches. Since the perimeter of a square is <math alttext=\"4\"><mn>4</mn>\n</math> times the side length of the square, each side length of Q is <math alttext=\"StartFraction 4 x plus 176 Over 4 EndFraction\"><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>176</mn></mrow><mn>4</mn></mfrac></math>, or&nbsp;<math alttext=\"x plus 44\"><mi>x</mi><mo>+</mo><mn>44</mn></math> inches. Since the area of a square is calculated by multiplying the length of two sides, the area of square Q is <math alttext=\"left parenthesis x plus 44 right parenthesis left parenthesis x plus 44 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>44</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>44</mn></mrow></mfenced></math>, or <math alttext=\"left parenthesis x plus 44 right parenthesis squared\"><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>44</mn></mrow></mfenced><mn>2</mn></msup></math>&nbsp;square inches. It follows that function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals left parenthesis x plus 44 right parenthesis squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>44</mn></mrow></mfenced><mn>2</mn></msup></math>.&nbsp;</p>\n<p>Choice B is incorrect. This function represents a square with side lengths <math alttext=\"left parenthesis x plus 176 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>176</mn></mrow></mfenced></math> inches.</p>\n<p>Choice C is incorrect. This function represents a square with side lengths <math alttext=\"left parenthesis 176 x plus 44 right parenthesis\"><mfenced><mrow><mn>176</mn><mi>x</mi><mo>+</mo><mn>44</mn></mrow></mfenced></math> inches.</p>\n<p>Choice D is incorrect. This function represents a square with side lengths <math alttext=\"left parenthesis 176 x plus 176 right parenthesis\"><mfenced><mrow><mn>176</mn><mi>x</mi><mo>+</mo><mn>176</mn></mrow></mfenced></math> inches.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals left parenthesis x plus 44 right parenthesis squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mrow><mn>44</mn></mrow></mrow></mfenced><mn>2</mn></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals left parenthesis x plus 176 right parenthesis squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mrow><mn>176</mn></mrow></mrow></mfenced><mn>2</mn></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals left parenthesis 176 x plus 44 right parenthesis squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mrow><mrow><mn>176</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>44</mn></mrow></mrow></mfenced><mn>2</mn></msup></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals left parenthesis 176 x plus 176 right parenthesis squared\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mrow><mrow><mn>176</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>176</mn></mrow></mrow></mfenced><mn>2</mn></msup></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}}