{"id":"cb_practice_pdf:t11-math-m1-q20","source_id":"cb_practice_pdf","source_item_id":"t11-math-m1-q20","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-11","module_number":1,"position":20,"stem":"20 Circle A in the xy-plane has the equation x + 5 + y - 5 = 25. Circle B has the same ^ h^2 ^ h^2 center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is x + 5 + y - 5 = k, where k ^ h^2 ^ h^2 is a constant. What is the value of k?","stimulus":"","stimulus_html":null,"stem_html":"<p>20 Circle A in the xy-plane has the equation x + 5 + y - 5 = 25. Circle B has the same ^ h^2 ^ h^2 center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is x + 5 + y - 5 = k, where k ^ h^2 ^ h^2 is a constant. What is the value of k?</p>","rationale_html":"<p>100 The correct answer is . An equation of a circle in the xy-plane can be written - 2+ - 2= 2 as ^x th ^y uh r , where the center of the circle is ^t,uh, the radius of the circle is r, and where t, u, and r are constants. It’s given that the equation of +5 2+ -5 2=25 +5 2+ -5 2=52 circle A is ^x h ^y h , which is equivalent to ^x h ^y h . -5,5 Therefore, the center of circle A is ^ h and the radius of circle A is 5. It’s given that circle B has the same center as circle A and that the radius of circle B is two -5,5 times the radius of circle A. Therefore, the center of circle B is ^ h and the 2 5 10 - 10 radius of circle B is ^ h, or . Substituting 5 for t, 5 for u, and for r in the - 2+ - 2= 2 +5 2+ -5 2=102 equation ^x th ^y uh r yields ^x h ^y h , which is equivalent +5 2+ -5 2=100 to ^x h ^y h . It follows that the equation of circle B in the xy-plane is +5 2+ -5 2=100 ^x h ^y h . It’s also given that the equation defining circle B in the +5 2+ -5 2= xy-plane is ^x h ^y h k, where k is a constant. Therefore, the value of k 100 is . 39 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1</p>","correct_answer":["100"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}