{"id":1932,"date":"2021-12-02T19:40:03","date_gmt":"2021-12-03T00:40:03","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-d-answer-key\/"},"modified":"2022-11-02T10:38:30","modified_gmt":"2022-11-02T14:38:30","slug":"midterm-two-version-d-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-d-answer-key\/","title":{"raw":"Midterm 2: Version D Answer Key","rendered":"Midterm 2: Version D Answer Key"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n
    [latex]x-2y=-6[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n3<\/td>\n<\/tr>\n
    \u22126<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
    [latex]x+y=6[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n6<\/td>\n<\/tr>\n
    6<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Graph<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(3x&-&2y&=&0)(5) \\\\\n&(2x&+&5y&=&0)(2) \\\\ \\\\\n&15x&-&10y&=&0 \\\\\n+&4x&+&10y&=&0 \\\\\n\\hline\n&&&19x&=&0 \\\\\n&&&x&=&0 \\\\ \\\\\n&\\therefore \\cancel{2x}0&+&5y&=&0 \\\\\n&&&5y&=&0 \\\\\n&&&y&=&0\\\\\n\\end{array}\\\\ (0,0)[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&2x&-&3y&=&8 \\\\\n+&-2x&+&3y&=&4 \\\\\n\\hline\n&&&0&=&12 \\\\\n\\end{array}[\/latex]\n[latex]\\phantom{1}[\/latex]\n[latex]\\therefore[\/latex] No solution. Parallel lines.<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrrl}\n&(2x&+&y&-&3z&=&-7)(2) \\\\ \\\\\n&4x&+&2y&-&6z&=&-14 \\\\\n+&&-&2y&+&3z&=&\\phantom{-1}9 \\\\\n\\hline\n&&&4x&-&3z&=&-5 \\\\ \\\\\n&&&(3x&+&z&=&6)(3) \\\\ \\\\\n&&&4x&-&3z&=&-5 \\\\\n+&&&9x&+&3z&=&18 \\\\\n\\hline\n&&&&&13x&=&13 \\\\\n&&&&&x&=&1\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\n3x&+&z&=&6 \\\\\n3(1)&+&z&=&6 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&z&=&3 \\\\ \\\\\n-2y&+&3z&=&9 \\\\\n-2y&+&3(3)&=&9 \\\\\n&&-9&&-9 \\\\\n\\hline\n&&-2y&=&0 \\\\\n&&y&=&0\n\\end{array}\n\\end{array}[\/latex]\n[latex](1,0,3)[\/latex]<\/li>\n \t
  5. [latex]36-\\cancel{\\{-2x-\\left[6x-3(5-2x)\\right]\\}^0}1+3x^2[\/latex]\n[latex]36-1+3x^2[\/latex]\n[latex]35+3x^2[\/latex]<\/li>\n \t
  6. [latex]3a^2(a^2-4a+4)[\/latex]\n[latex]3a^4-12a^3+12a^2[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrlrrrr}\n&x^2&+&2x&-&4&&&& \\\\\n\\times &x^2&+&2x&-&4&&&& \\\\\n\\hline\n&x^4&+&2x^3&-&4x^2&&&& \\\\\n&&&2x^3&+&4x^2&-&8x&& \\\\\n+&&&&-&4x^2&-&8x&+&16 \\\\\n\\hline\n&x^4&+&4x^3&-&4x^2&-&16x&+&16\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n\"\"<\/li>\n \t
  9. [latex]x^2-3x+6x-18[\/latex]\n[latex]x(x-3)+6(x-3)[\/latex]\n[latex](x-3)(x+6)[\/latex]<\/li>\n \t
  10. [latex]3x^2+xy+24xy+8y^2[\/latex]\n[latex]x(3x+y)+8y(3x+y)[\/latex]\n[latex](3x+y)(x+8y)[\/latex]<\/li>\n \t
  11. [latex](5x)^3-y^3[\/latex]\n[latex](5x-y)(25x^2+5xy+y^2)[\/latex]<\/li>\n \t
  12. [latex](9y^2-4x^2)(9y^2+4x^2)[\/latex]\n[latex](3y-2x)(3y+2x)(9y^2+4x^2)[\/latex]<\/li>\n \t
  13. [latex]B+G=18\\Rightarrow G=18-B[\/latex]\n[latex]\\begin{array}{rrrcrrrr}\n&G&-&4&=&4(B&-&4) \\\\\n&18-B&-&4&=&4B&-&16 \\\\\n+&16+B&&&&+B&+&16 \\\\\n\\hline\n&&&30&=&5B&& \\\\ \\\\\n&&&B&=&\\dfrac{30}{5}&=&6 \\\\ \\\\\n&&&\\therefore G&=&18&-&B \\\\\n&&&\\phantom{\\therefore}G&=&18&-&6 \\\\\n&&&\\phantom{\\therefore}G&=&12&&\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(D&+&Q&=&20)(-10) \\\\\n&10D&+&25Q&=&350 \\\\ \\\\\n&-10D&-&10Q&=&-200 \\\\\n+&10D&+&25Q&=&\\phantom{-}350 \\\\\n\\hline\n&&&15Q&=&150 \\\\ \\\\\n&&&Q&=&\\dfrac{150}{15}\\text{ or }10 \\\\ \\\\\n\\therefore &D&+&Q&=&\\phantom{-}20 \\\\\n&D&+&10&=&\\phantom{-}20 \\\\\n&&-&10&&-10 \\\\\n\\hline\n&&&D&=&10\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]A+B=60\\Rightarrow B=60-A [\/latex]\n[latex]\\begin{array}[t]{llclrll}\n&&3.80A&+&3.55B&=&\\phantom{-}218.50 \\\\\n3.80A&+&3.55(60&-&A)&=&\\phantom{-}218.50 \\\\\n3.80A&+&213&-&3.55A&=&\\phantom{-}218.50 \\\\\n&-&213&&&=&-213 \\\\\n\\hline\n&&&&0.25A&=&5.50 \\\\ \\\\\n&&&&A&=&\\dfrac{5.50}{0.25}\\text{ or 22 kg} \\\\ \\\\\n&&&&B&=&60-A \\\\\n&&&&B&=&60-22 \\\\\n&&&&B&=&38\\text{ kg}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n
      [latex]x-2y=-6[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n3<\/td>\n<\/tr>\n
      \u22126<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
      [latex]x+y=6[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n6<\/td>\n<\/tr>\n
      6<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(3x&-&2y&=&0)(5) \\\\ &(2x&+&5y&=&0)(2) \\\\ \\\\ &15x&-&10y&=&0 \\\\ +&4x&+&10y&=&0 \\\\ \\hline &&&19x&=&0 \\\\ &&&x&=&0 \\\\ \\\\ &\\therefore \\cancel{2x}0&+&5y&=&0 \\\\ &&&5y&=&0 \\\\ &&&y&=&0\\\\ \\end{array}\\\\ (0,0)[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &2x&-&3y&=&8 \\\\ +&-2x&+&3y&=&4 \\\\ \\hline &&&0&=&12 \\\\ \\end{array}[\/latex]
      \n[latex]\\phantom{1}[\/latex]
      \n[latex]\\therefore[\/latex] No solution. Parallel lines.<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrrl} &(2x&+&y&-&3z&=&-7)(2) \\\\ \\\\ &4x&+&2y&-&6z&=&-14 \\\\ +&&-&2y&+&3z&=&\\phantom{-1}9 \\\\ \\hline &&&4x&-&3z&=&-5 \\\\ \\\\ &&&(3x&+&z&=&6)(3) \\\\ \\\\ &&&4x&-&3z&=&-5 \\\\ +&&&9x&+&3z&=&18 \\\\ \\hline &&&&&13x&=&13 \\\\ &&&&&x&=&1 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} 3x&+&z&=&6 \\\\ 3(1)&+&z&=&6 \\\\ -3&&&&-3 \\\\ \\hline &&z&=&3 \\\\ \\\\ -2y&+&3z&=&9 \\\\ -2y&+&3(3)&=&9 \\\\ &&-9&&-9 \\\\ \\hline &&-2y&=&0 \\\\ &&y&=&0 \\end{array} \\end{array}[\/latex]
      \n[latex](1,0,3)[\/latex]<\/li>\n
    5. [latex]36-\\cancel{\\{-2x-\\left[6x-3(5-2x)\\right]\\}^0}1+3x^2[\/latex]
      \n[latex]36-1+3x^2[\/latex]
      \n[latex]35+3x^2[\/latex]<\/li>\n
    6. [latex]3a^2(a^2-4a+4)[\/latex]
      \n[latex]3a^4-12a^3+12a^2[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrlrrrr} &x^2&+&2x&-&4&&&& \\\\ \\times &x^2&+&2x&-&4&&&& \\\\ \\hline &x^4&+&2x^3&-&4x^2&&&& \\\\ &&&2x^3&+&4x^2&-&8x&& \\\\ +&&&&-&4x^2&-&8x&+&16 \\\\ \\hline &x^4&+&4x^3&-&4x^2&-&16x&+&16 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n\"\"<\/li>\n
    9. [latex]x^2-3x+6x-18[\/latex]
      \n[latex]x(x-3)+6(x-3)[\/latex]
      \n[latex](x-3)(x+6)[\/latex]<\/li>\n
    10. [latex]3x^2+xy+24xy+8y^2[\/latex]
      \n[latex]x(3x+y)+8y(3x+y)[\/latex]
      \n[latex](3x+y)(x+8y)[\/latex]<\/li>\n
    11. [latex](5x)^3-y^3[\/latex]
      \n[latex](5x-y)(25x^2+5xy+y^2)[\/latex]<\/li>\n
    12. [latex](9y^2-4x^2)(9y^2+4x^2)[\/latex]
      \n[latex](3y-2x)(3y+2x)(9y^2+4x^2)[\/latex]<\/li>\n
    13. [latex]B+G=18\\Rightarrow G=18-B[\/latex]
      \n[latex]\\begin{array}{rrrcrrrr} &G&-&4&=&4(B&-&4) \\\\ &18-B&-&4&=&4B&-&16 \\\\ +&16+B&&&&+B&+&16 \\\\ \\hline &&&30&=&5B&& \\\\ \\\\ &&&B&=&\\dfrac{30}{5}&=&6 \\\\ \\\\ &&&\\therefore G&=&18&-&B \\\\ &&&\\phantom{\\therefore}G&=&18&-&6 \\\\ &&&\\phantom{\\therefore}G&=&12&& \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(D&+&Q&=&20)(-10) \\\\ &10D&+&25Q&=&350 \\\\ \\\\ &-10D&-&10Q&=&-200 \\\\ +&10D&+&25Q&=&\\phantom{-}350 \\\\ \\hline &&&15Q&=&150 \\\\ \\\\ &&&Q&=&\\dfrac{150}{15}\\text{ or }10 \\\\ \\\\ \\therefore &D&+&Q&=&\\phantom{-}20 \\\\ &D&+&10&=&\\phantom{-}20 \\\\ &&-&10&&-10 \\\\ \\hline &&&D&=&10 \\end{array}[\/latex]<\/li>\n
    15. [latex]A+B=60\\Rightarrow B=60-A[\/latex]
      \n[latex]\\begin{array}[t]{llclrll} &&3.80A&+&3.55B&=&\\phantom{-}218.50 \\\\ 3.80A&+&3.55(60&-&A)&=&\\phantom{-}218.50 \\\\ 3.80A&+&213&-&3.55A&=&\\phantom{-}218.50 \\\\ &-&213&&&=&-213 \\\\ \\hline &&&&0.25A&=&5.50 \\\\ \\\\ &&&&A&=&\\dfrac{5.50}{0.25}\\text{ or 22 kg} \\\\ \\\\ &&&&B&=&60-A \\\\ &&&&B&=&60-22 \\\\ &&&&B&=&38\\text{ kg} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":72,"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-1932","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\/1932","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":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1932\/revisions"}],"predecessor-version":[{"id":1933,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1932\/revisions\/1933"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1932\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1932"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1932"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1932"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}