{"id":"cb_practice_pdf:t8-math-m1-q14","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q14","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-8","module_number":1,"position":14,"stem":"- - - - - -_is_equivalent_to - - - ~ 90y^5 −54y^4 The expression ry^4 15y−9 (), where r is a constant. What is the value of r?","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - - - -_is_equivalent_to - - - ~ 90y^5 −54y^4 The expression ry^4 15y−9 (), where r is a constant. What is the value of r?</p>","rationale_html":"<p>The correct answer is 6. Applying the distributive property to the expression 4 15 -9 15 5-9 4 90 5-54 4 4 15 -9 ry ^ y h yields ry ry . Since y y is equivalent to ry ^ y h, it 90 5-54 4 15 5-9 4 follows that y y is also equivalent to ry ry . Since these expressions are equivalent, it follows that corresponding coefficients are equivalent. 90=15 -54=-9 Therefore, r and r. Solving either of these equations for r will 90=15 15 = yield the value of r. Dividing both sides of r by yields 6 r. Therefore, the value of r is 6.</p>","correct_answer":["6"],"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}}