{"id":3216,"date":"2019-11-19T13:52:50","date_gmt":"2019-11-19T18:52:50","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3216"},"modified":"2020-01-04T14:21:40","modified_gmt":"2020-01-04T19:21:40","slug":"midterm-one-version-c-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-one-version-c-answer-key\/","title":{"raw":"Midterm 1: Version C Answer Key","rendered":"Midterm 1: Version C Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\\r\n-(4)-\\sqrt{4^2-4(4)1} \\\\ \\\\\r\n-4-\\sqrt{16-16} \\\\ \\\\\r\n-4\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrrrcrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&2x&-&8&+&8&=&3&-&7x&-&21 \\\\\r\n+&7x&&&&&&&+&7x&& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{9x}{9}&=&\\dfrac{-18}{9}&&&& \\\\ \\\\\r\n&&&&&x&=&-2&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\phantom{1}\\)\r\n\\(\\left(A=\\dfrac{h}{B+b}\\right)(B+b) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{A}{A}(B&+&b)&=&\\dfrac{h}{A}&& \\\\ \\\\\r\nB&+&b&=&\\dfrac{h}{A}&& \\\\\r\n&-&b&&&-&b \\\\\r\n\\midrule\r\n&&B&=&\\dfrac{h}{A}&-&b\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x}{15}-\\dfrac{x-3}{3}=\\dfrac{1}{5}\\right)(15) \\\\ \\)\r\n\\(\\begin{array}{rrcrrrl}\r\nx&-&5(x&-&3)&=&3(1) \\\\\r\nx&-&5x&+&15&=&\\phantom{-1}3 \\\\\r\n&&&-&15&&-15 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-4x}{-4}&=&\\dfrac{-12}{-4} \\\\ \\\\\r\n&&&&x&=&3\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(x=-2\\)\r\n\"Coordinates<\/li>\r\n \t
  6. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\ny&=&mx+6 \\\\\r\n\\therefore y&=&\\dfrac{2}{3}x-3 \\\\ \\\\\r\n\\text{or } 3y&=&2x-9 \\\\\r\n0&=&2x-3y-9 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{ll}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\textbf{1st slope} \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\nm&=&\\dfrac{4--6}{-1-14} \\\\ \\\\\r\nm&=&\\dfrac{10}{-15} \\\\ \\\\\r\nm&=&-\\dfrac{2}{3} \\\\ \\\\\r\n&&\\textbf{Now:} \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n-\\dfrac{2}{3}&=&\\dfrac{y-4}{x--1}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&-2(x&+&1)&=&\\phantom{-}3(y&-&4) \\\\\r\n&&&-2x&-&2&=&\\phantom{-}3y&-&12 \\\\\r\n+&&&-3y&+&12&&-3y&+&12 \\\\\r\n\\midrule\r\n&-2x&-&3y&+&10&=&0&& \\\\\r\n\\text{or}&2x&+&3y&-&10&=&0&& \\\\ \\\\\r\n&&&&&y&=&-\\dfrac{2}{3}x&+&\\dfrac{10}{3}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  8. \r\n\r\n\r\n\r\n\r\n\r\n
    \\(2x-y=-2\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n0&\\le &2x&+&4&<&8 \\\\\r\n-4&&&-4&&&-4 \\\\\r\n\\midrule\r\n\\dfrac{-4}{2}&\\le &&\\dfrac{2x}{2}&&<&\\dfrac{4}{2} \\\\ \\\\\r\n-2&\\le &&x&&<&2\r\n\\end{array}\\)\r\n\"-2<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\\r\ny&-&1&>&3&\\hspace{0.25in} \\text{or}\\hspace{0.25in}&y&-&1&<&-3 \\\\\r\n&+&1&&+1&&&+&1&&+1 \\\\\r\n\\midrule\r\n&&y&>&4&\\hspace{0.25in} \\text{or}\\hspace{0.25in}&&&y&<&-2\r\n\\end{array}\\)\r\n\"y<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\\r\n2x&-&3&<&-5&\\hspace{0.5in}&2x&-&3&>&5 \\\\\r\n&+&3&&+3&\\hspace{0.5in}&&+&3&&+3 \\\\\r\n\\midrule\r\n&&2x&<&-2&\\hspace{0.5in}&&&2x&>&8 \\\\\r\n&&x&<&-1&\\hspace{0.5in}&&&x&>&4\r\n\\end{array}\\)\r\n\"x<\/li>\r\n \t
  12. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(y=|x|-3\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    3<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
    \u22123<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Graph<\/li>\r\n \t
  13. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrl}\r\n5L&+&3S&=&49 \\\\\r\n4L&-&2S&=&26 \\\\ \\\\\r\n\\dfrac{4L}{2}&-&\\dfrac{2S}{2}&=&\\dfrac{26}{2} \\\\ \\\\\r\n2L&-&S&=&13 \\\\ \\\\\r\n&\\text{or}&S&=&2L-13\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrcrrrl}\r\n\\\\ \\\\ \\\\\r\n5L&+&3(2L&-&13)&=&49 \\\\\r\n5L&+&6L&-&39&=&49 \\\\\r\n&&&+&39&&+39 \\\\\r\n\\midrule\r\n&&&&\\dfrac{11L}{11}&=&\\dfrac{88}{11} \\\\ \\\\\r\n&&&&L&=&8 \\\\ \\\\\r\n&&&&\\therefore S&=&2L-13 \\\\\r\n&&&&S&=&2(8)-13 \\\\\r\n&&&&S&=&16-13 \\\\\r\n&&&&S&=&3\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n5x+x&=&42 \\\\\r\n6x&=&42 \\\\\r\nx&=&\\dfrac{42}{6}\\text{ or }7 \\\\ \\\\\r\n\\therefore 5x&=&5(7)\\text{ or }35\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&=&\\dfrac{km}{d^2} \\\\ \\\\\r\n&&\\textbf{1st} \\\\\r\ny&=&3 \\\\\r\nk&=&\\text{find 1st} \\\\\r\nm&=&2 \\\\\r\nd&=&4 \\\\ \\\\\r\ny&=&\\dfrac{km}{d^2} \\\\ \\\\\r\n3&=&\\dfrac{k(2)}{(4)^2} \\\\ \\\\\r\n3&=&\\dfrac{3(4)^2}{2} \\\\ \\\\\r\nk&=&24\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\textbf{2nd} \\\\\r\ny&=&\\text{find} \\\\\r\nk&=&24 \\\\\r\nm&=&25 \\\\\r\nd&=&5 \\\\ \\\\\r\ny&=&\\dfrac{km}{d^2} \\\\ \\\\\r\ny&=&\\dfrac{(24)(25)}{(5)^2} \\\\ \\\\\r\ny&=&24\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

    <\/h1>","rendered":"
      \n
    1. \"\begin{array}{l}<\/li>\n
    2. \"\begin{array}{rrrrrrrcrrrr}<\/li>\n
    3. \"\phantom{1}\"
      \n\"\left(A=\dfrac{h}{B+b}\right)(B+b) \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    4. \"\phantom{1}\"
      \n\"\left(\dfrac{x}{15}-\dfrac{x-3}{3}=\dfrac{1}{5}\right)(15) \\\"
      \n\"\begin{array}{rrcrrrl}<\/li>\n
    5. \"x=-2\"
      \n\"Coordinates<\/li>\n
    6. \"\begin{array}{rrl}<\/li>\n
    7. \"\begin{array}{ll}<\/li>\n
    8. \n\n\n\n\n\n\n
      \"2x-y=-2\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n2<\/td>\n<\/tr>\n
      \u22121<\/td>\n0<\/td>\n<\/tr>\n
      \u22122<\/td>\n\u22122<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n

    9. \"\begin{array}{rrrrrrr}
      \n\"-2<\/li>\n
    10. \"\begin{array}{rrrrrrrrrrr}
      \n\"y<\/li>\n
    11. \"\begin{array}{rrrrrrrrrrr}
      \n\"x<\/li>\n
    12. \n\n\n\n\n\n\n\n\n\n\n
      \"y=|x|-3\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      3<\/td>\n0<\/td>\n<\/tr>\n
      2<\/td>\n\u22121<\/td>\n<\/tr>\n
      1<\/td>\n\u22122<\/td>\n<\/tr>\n
      0<\/td>\n\u22123<\/td>\n<\/tr>\n
      \u22121<\/td>\n\u22122<\/td>\n<\/tr>\n
      \u22122<\/td>\n\u22121<\/td>\n<\/tr>\n
      \u22123<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    13. \"\begin{array}{ll}<\/li>\n
    14. \"\begin{array}{rrl}<\/li>\n
    15. \"\begin{array}{ll}<\/li>\n<\/ol>\n

      <\/h1>\n","protected":false},"author":14,"menu_order":34,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3216","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3216\/revisions"}],"predecessor-version":[{"id":3763,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3216\/revisions\/3763"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3216\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3216"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3216"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3216"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}