{"id":1819,"date":"2021-12-02T19:39:34","date_gmt":"2021-12-03T00:39:34","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-c-answer-key\/"},"modified":"2023-09-01T13:58:11","modified_gmt":"2023-09-01T17:58:11","slug":"midterm-one-version-c-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/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":"
    \r\n \t
  1. [latex]-(4)-\\sqrt{4^2-4(4)1}\u00a0[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n-4-\\sqrt{16-16} \\\\ \\\\\r\n-4\r\n\\end{array}[\/latex]<\/li>\r\n \t
  2. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrcrrrr}\r\n&2x&-&8&+&8&=&3&-&7x&-&21 \\\\\r\n+&7x&&&&&&&+&7x&& \\\\\r\n\\hline\r\n&&&&&\\dfrac{9x}{9}&=&\\dfrac{-18}{9}&&&& \\\\ \\\\\r\n&&&&&x&=&-2&&&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  3. [latex]\\left(A=\\dfrac{h}{B+b}\\right)(B+b) [\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrr}\r\n\\dfrac{A}{A}(B&+&b)&=&\\dfrac{h}{A}&& \\\\ \\\\\r\nB&+&b&=&\\dfrac{h}{A}&& \\\\\r\n&-&b&&&-&b \\\\\r\n\\hline\r\n&&B&=&\\dfrac{h}{A}&-&b\r\n\\end{array}[\/latex]<\/li>\r\n \t
  4. [latex]\\left(\\dfrac{x}{15}-\\dfrac{x-3}{3}=\\dfrac{1}{5}\\right)(15)[\/latex]\r\n[latex]\\begin{array}{rrcrrrl}\r\nx&-&5(x&-&3)&=&3(1) \\\\\r\nx&-&5x&+&15&=&\\phantom{-1}3 \\\\\r\n&&&-&15&&-15 \\\\\r\n\\hline\r\n&&&&\\dfrac{-4x}{-4}&=&\\dfrac{-12}{-4} \\\\ \\\\\r\n&&&&x&=&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  5. [latex]x=-2[\/latex]\r\n\"Coordinates<\/li>\r\n \t
  6. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\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}[\/latex]<\/li>\r\n \t
  7. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\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}[t]{rrrrrrrlrr}\r\n&&&-2(x&+&1)&=&\\phantom{-}3(y&-&4) \\\\\r\n&&&-2x&-&2&=&\\phantom{-}3y&-&12 \\\\\r\n+&&&-3y&+&12&&-3y&+&12 \\\\\r\n\\hline\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}[\/latex]<\/li>\r\n \t
  8. \r\n\r\n\r\n\r\n\r\n\r\n
    [latex]2x-y=-2[\/latex]<\/caption>\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/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\r\n\"Line<\/li>\r\n \t
  9. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrr}\r\n0&\\le &2x&+&4&<&8 \\\\\r\n-4&&&-4&&&-4 \\\\\r\n\\hline\r\n\\dfrac{-4}{2}&\\le &&\\dfrac{2x}{2}&&<&\\dfrac{4}{2} \\\\ \\\\\r\n-2&\\le &&x&&<&2\r\n\\end{array}[\/latex]\r\n\r\n\"(-2,<\/li>\r\n \t
  10. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\r\ny&-&1&>&3&\\hspace{0.25in} \\text{or}\\hspace{0.25in}&y&-&1&<&-3 \\\\\r\n&+&1&&+1&&&+&1&&+1 \\\\\r\n\\hline\r\n&&y&>&4&\\hspace{0.25in} \\text{or}\\hspace{0.25in}&&&y&<&-2\r\n\\end{array}[\/latex]\r\n\r\n\"(-2,<\/li>\r\n \t
  11. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\r\n2x&-&3&<&-5&\\hspace{0.5in}&2x&-&3&>&5 \\\\\r\n&+&3&&+3&\\hspace{0.5in}&&+&3&&+3 \\\\\r\n\\hline\r\n&&2x&<&-2&\\hspace{0.5in}&&&2x&>&8 \\\\\r\n&&x&<&-1&\\hspace{0.5in}&&&x&>&4\r\n\\end{array}[\/latex]\r\n\"(-1,<\/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
    [latex]y=|x|-3[\/latex]<\/caption>\r\n
    [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/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. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{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}[t]{rrcrrrl}\r\n5L&+&3(2L&-&13)&=&49 \\\\\r\n5L&+&6L&-&39&=&49 \\\\\r\n&&&+&39&&+39 \\\\\r\n\\hline\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}[\/latex]<\/li>\r\n \t
  14. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\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}[\/latex]<\/li>\r\n \t
  15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\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}[t]{rrl}\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}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]-(4)-\\sqrt{4^2-4(4)1}\u00a0[\/latex]
      \n[latex]\\begin{array}[t]{l} -4-\\sqrt{16-16} \\\\ \\\\ -4 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrcrrrr} &2x&-&8&+&8&=&3&-&7x&-&21 \\\\ +&7x&&&&&&&+&7x&& \\\\ \\hline &&&&&\\dfrac{9x}{9}&=&\\dfrac{-18}{9}&&&& \\\\ \\\\ &&&&&x&=&-2&&&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\left(A=\\dfrac{h}{B+b}\\right)(B+b)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} \\dfrac{A}{A}(B&+&b)&=&\\dfrac{h}{A}&& \\\\ \\\\ B&+&b&=&\\dfrac{h}{A}&& \\\\ &-&b&&&-&b \\\\ \\hline &&B&=&\\dfrac{h}{A}&-&b \\end{array}[\/latex]<\/li>\n
    4. [latex]\\left(\\dfrac{x}{15}-\\dfrac{x-3}{3}=\\dfrac{1}{5}\\right)(15)[\/latex]
      \n[latex]\\begin{array}{rrcrrrl} x&-&5(x&-&3)&=&3(1) \\\\ x&-&5x&+&15&=&\\phantom{-1}3 \\\\ &&&-&15&&-15 \\\\ \\hline &&&&\\dfrac{-4x}{-4}&=&\\dfrac{-12}{-4} \\\\ \\\\ &&&&x&=&3 \\end{array}[\/latex]<\/li>\n
    5. [latex]x=-2[\/latex]
      \n\"Coordinates<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} y&=&mx+6 \\\\ \\therefore y&=&\\dfrac{2}{3}x-3 \\\\ \\\\ \\text{or } 3y&=&2x-9 \\\\ 0&=&2x-3y-9 \\\\ \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st slope} \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ m&=&\\dfrac{4--6}{-1-14} \\\\ \\\\ m&=&\\dfrac{10}{-15} \\\\ \\\\ m&=&-\\dfrac{2}{3} \\\\ \\\\ &&\\textbf{Now:} \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ -\\dfrac{2}{3}&=&\\dfrac{y-4}{x--1} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrrlrr} &&&-2(x&+&1)&=&\\phantom{-}3(y&-&4) \\\\ &&&-2x&-&2&=&\\phantom{-}3y&-&12 \\\\ +&&&-3y&+&12&&-3y&+&12 \\\\ \\hline &-2x&-&3y&+&10&=&0&& \\\\ \\text{or}&2x&+&3y&-&10&=&0&& \\\\ \\\\ &&&&&y&=&-\\dfrac{2}{3}x&+&\\dfrac{10}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
    8. \n\n\n\n\n\n\n
      [latex]2x-y=-2[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/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. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 0&\\le &2x&+&4&<&8 \\\\ -4&&&-4&&&-4 \\\\ \\hline \\dfrac{-4}{2}&\\le &&\\dfrac{2x}{2}&&<&\\dfrac{4}{2} \\\\ \\\\ -2&\\le &&x&&<&2 \\end{array}[\/latex]\n\n\"(-2,<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrr} y&-&1&>&3&\\hspace{0.25in} \\text{or}\\hspace{0.25in}&y&-&1&<&-3 \\\\ &+&1&&+1&&&+&1&&+1 \\\\ \\hline &&y&>&4&\\hspace{0.25in} \\text{or}\\hspace{0.25in}&&&y&<&-2 \\end{array}[\/latex]\n\n\"(-2,<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrr} 2x&-&3&<&-5&\\hspace{0.5in}&2x&-&3&>&5 \\\\ &+&3&&+3&\\hspace{0.5in}&&+&3&&+3 \\\\ \\hline &&2x&<&-2&\\hspace{0.5in}&&&2x&>&8 \\\\ &&x&<&-1&\\hspace{0.5in}&&&x&>&4 \\end{array}[\/latex]
      \n\"(-1,<\/li>\n
    12. \n\n\n\n\n\n\n\n\n\n\n
      [latex]y=|x|-3[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/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. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrl} 5L&+&3S&=&49 \\\\ 4L&-&2S&=&26 \\\\ \\\\ \\dfrac{4L}{2}&-&\\dfrac{2S}{2}&=&\\dfrac{26}{2} \\\\ \\\\ 2L&-&S&=&13 \\\\ \\\\ &\\text{or}&S&=&2L-13 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrcrrrl} 5L&+&3(2L&-&13)&=&49 \\\\ 5L&+&6L&-&39&=&49 \\\\ &&&+&39&&+39 \\\\ \\hline &&&&\\dfrac{11L}{11}&=&\\dfrac{88}{11} \\\\ \\\\ &&&&L&=&8 \\\\ \\\\ &&&&\\therefore S&=&2L-13 \\\\ &&&&S&=&2(8)-13 \\\\ &&&&S&=&16-13 \\\\ &&&&S&=&3 \\end{array} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 5x+x&=&42 \\\\ 6x&=&42 \\\\ x&=&\\dfrac{42}{6}\\text{ or }7 \\\\ \\\\ \\therefore 5x&=&5(7)\\text{ or }35 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} y&=&\\dfrac{km}{d^2} \\\\ \\\\ &&\\textbf{1st} \\\\ y&=&3 \\\\ k&=&\\text{find 1st} \\\\ m&=&2 \\\\ d&=&4 \\\\ \\\\ y&=&\\dfrac{km}{d^2} \\\\ \\\\ 3&=&\\dfrac{k(2)}{(4)^2} \\\\ \\\\ 3&=&\\dfrac{3(4)^2}{2} \\\\ \\\\ k&=&24 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} &&\\textbf{2nd} \\\\ y&=&\\text{find} \\\\ k&=&24 \\\\ m&=&25 \\\\ d&=&5 \\\\ \\\\ y&=&\\dfrac{km}{d^2} \\\\ \\\\ y&=&\\dfrac{(24)(25)}{(5)^2} \\\\ \\\\ y&=&24 \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":39,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1819","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1819","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":3,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1819\/revisions"}],"predecessor-version":[{"id":2215,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1819\/revisions\/2215"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1819\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1819"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1819"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1819"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}