{"id":"act_quizme:math:q2:04","source_id":"act_quizme","source_item_id":"math-q2-04","external_id":"6bab852893e11bc0","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":4,"scored":true,"layout_warning":null,"stem":"An object is launched vertically at 30 meters per second from a 55-meter-tall platform. The height, h of t h ( t ) meters, of the object t seconds after launch is modeled by h of t = negative 4.9t squared +30t+55 h ( t ) = - 4 . 9 t 2 + 30 t + 55 . What will be the height, in meters, of the object 3 seconds after launch?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"><div class=\"item-content\" id=\"p40\"> \t\t\t\t\t \t\t\t\t\t<div>An object is launched vertically at 30 meters per second from a 55-meter-tall platform. The height, <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\">h of t</span><math class=\"srTransform\"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>&nbsp;meters,</span> of the object t seconds after launch is modeled by <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\">h of t = negative 4.9t squared +30t+55</span><math class=\"srTransform\"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>-</mo><mn>4</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>9</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>30</mn><mi>t</mi><mo>+</mo><mn>55</mn></math>.</span> What will be the height, in meters, of the object 3 seconds after launch?</div>   \t\t\t\t</div> \t\t\t\t</div>\n<div><div class=\"math-answer-select-wrap\"></div></div>","rationale_html":"<p><strong>F.</strong> <strong>Incorrect.</strong> Substitute&nbsp;<math><mi>t</mi><mo>=</mo><mn>3</mn></math>&nbsp;into all terms of the given equation. Make sure to keep track of the signs on the terms.&nbsp;</p><p><strong>G.</strong> <strong>Correct.</strong> Substitute&nbsp;<math><mi>t</mi><mo>=</mo><mn>3</mn></math>&nbsp;into all terms of the given equation: <span style=\"white-space: nowrap;\"><math><mi>h</mi><mfenced><mn>3</mn></mfenced><mo>=</mo><mo>-</mo><mn>4</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>9</mn><mfenced><msup><mn>3</mn><mn>2</mn></msup></mfenced><mo>+</mo><mn>30</mn><mfenced><mn>3</mn></mfenced><mo>+</mo><mn>55</mn><mo>=</mo><mn>100</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>9</mn></math>.</span></p><p><strong>H.</strong> <strong>Incorrect.</strong> Substitute&nbsp;<math><mi>t</mi><mo>=</mo><mn>3</mn></math>&nbsp;into all terms of the given equation. You may have calculated and added only the middle and last terms of the equation, <span style=\"white-space: nowrap;\"><math><mn>30</mn><mfenced><mn>3</mn></mfenced><mo>+</mo><mn>55</mn><mo>=</mo><mn>145</mn></math>.</span></p><p><strong>J.</strong> <strong>Incorrect.</strong> Substitute&nbsp;<math><mi>t</mi><mo>=</mo><mn>3</mn></math>&nbsp;into all terms of the given equation. You may have calculated the terms correctly, but missed the negative sign on the first term: <span style=\"white-space: nowrap;\"><math><mn>4</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>9</mn><mfenced><msup><mn>3</mn><mn>2</mn></msup></mfenced><mo>+</mo><mn>30</mn><mfenced><mn>3</mn></mfenced><mo>+</mo><mn>55</mn><mo>=</mo><mn>189</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>1</mn></math>.</span></p>","correct_answer":["G"],"equiv_key":"39247ed0bbbb8d53972c9900","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"<p>44.1</p>","ord":0},{"label":"G","content_html":"<p>100.9</p>","ord":1},{"label":"H","content_html":"<p>145</p>","ord":2},{"label":"J","content_html":"<p>189.1</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free on the public web; not licensed for redistribution.","redistributable":false,"item_count":78},"equivalents":[]}