{"id":1936,"date":"2021-12-02T19:40:04","date_gmt":"2021-12-03T00:40:04","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-e-answer-key\/"},"modified":"2022-11-02T10:38:32","modified_gmt":"2022-11-02T14:38:32","slug":"midterm-two-version-e-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-e-answer-key\/","title":{"raw":"Midterm 2: Version E Answer Key","rendered":"Midterm 2: Version E Answer Key"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n
    [latex]x-y=-3[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n3<\/td>\n<\/tr>\n
    \u22123<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
    [latex]x+2y=3[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    3<\/td>\n0<\/td>\n<\/tr>\n
    0<\/td>\n[latex]\\dfrac{3}{2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Graph<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(2x&-&5y&=&-2)(-3) \\\\\n&(3x&-&4y&=&\\phantom{-}4)(2) \\\\ \\\\\n&-6x&+&15y&=&6 \\\\\n+&6x&-&8y&=&8 \\\\\n\\hline\n&&&7y&=&14 \\\\\n&&&y&=&2 \\\\ \\\\\n&2x&-&5(2)&=&-2 \\\\\n&2x&-&10&=&-2 \\\\\n&&+&10&&+10 \\\\\n\\hline\n&&&2x&=&8 \\\\\n&&&x&=&4\n\\end{array}[\/latex]\n[latex](4,2)[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(4x&+&3y&=&-29)(-2) \\\\\n&(3x&+&2y&=&-21)(3) \\\\ \\\\\n&-8x&-&6y&=&\\phantom{-}58 \\\\\n+&9x&+&6y&=&-63 \\\\\n\\hline\n&&&x&=&-5 \\\\ \\\\\n&3(-5)&+&2y&=&-21 \\\\\n&-15&+&2y&=&-21 \\\\\n+&15&&&&+15 \\\\\n\\hline\n&&&2y&=&-6 \\\\\n&&&y&=&-3\n\\end{array}[\/latex]\n[latex](-5,-3)[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrrl}\n&(x&+&y&-&3z&=&0)(-2) \\\\ \\\\\n&-2x&-&2y&+&6z&=&0 \\\\\n+&2x&-&3y&&&=&16 \\\\\n\\hline\n&&&-5y&+&6z&=&16 \\\\ \\\\\n&&&(2y&-&2z&=&-12)(3) \\\\ \\\\\n&&&6y&-&6z&=&-36 \\\\\n+&&&-5y&+&6z&=&\\phantom{-}16 \\\\\n\\hline\n&&&&&y&=&-20\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\n2x&-&3y&=&16 \\\\\n2x&-&3(-20)&=&16 \\\\\n2x&+&60&=&16 \\\\\n&&-60&&-60 \\\\\n\\hline\n&&2x&=&-44 \\\\\n&&x&=&-22 \\\\ \\\\\n2y&-&2z&=&-12 \\\\\n2(-20)&-&2z&=&-12 \\\\\n-40&-&2z&=&-12 \\\\\n+40&&&&+40 \\\\\n\\hline\n&&-2z&=&28 \\\\\n&&z&=&-14\n\\end{array}\n\\end{array}[\/latex]\n[latex](-22,-20,-14)[\/latex]<\/li>\n \t
  5. [latex]5-4\\left[2x-2\\cancel{(6x-5)^0}1-(7-2x)\\right][\/latex]\n[latex]5-4\\left[2x-2(1)-7+2x\\right][\/latex]\n[latex]5-4\\left[4x-9\\right][\/latex]\n[latex]5-16x+36[\/latex]\n[latex]-16x+41[\/latex]<\/li>\n \t
  6. [latex]3ab^4(a^2-25)[\/latex]\n[latex]3a^3b^4-75ab^4[\/latex]<\/li>\n \t
  7. [latex]\\begin{array}[t]{rrrrrlrrrr}\n&x^2&+&3x&-&6&&&& \\\\\n\\times &x^2&+&3x&-&6&&&& \\\\\n\\hline\n&x^4&+&3x^3&-&6x^2&&&& \\\\\n&&&3x^3&+&9x^2&-&18x&& \\\\\n+&&&&-&6x^2&-&18x&+&36 \\\\\n\\hline\n&x^4&+&6x^3&-&3x^2&-&36x&+&36\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n\"\"<\/li>\n \t
  9. [latex]x^2-3z+7x-21[\/latex]\n[latex]x(x-3)+7(x-3)[\/latex]\n[latex](x-3)(x+7)[\/latex]<\/li>\n \t
  10. [latex]4x^2(x+1)-9(x+1)[\/latex]\n[latex](x+1)(4x^2-9)[\/latex]\n[latex](x+1)(2x-3)(2x+3)[\/latex]<\/li>\n \t
  11. [latex](2x)^3-(3y)^3[\/latex]\n[latex](2x-3y)(4x^2+6xy+9y^2)[\/latex]<\/li>\n \t
  12. [latex]x^4-625x^2+x^2-625[\/latex]\n[latex]x^2(x^2-625)+1(x^2-625)[\/latex]\n[latex](x^2+1)(x^2-625)[\/latex]\n[latex](x^2+1)(x-25)(x+25)[\/latex]<\/li>\n \t
  13. [latex]B+G=20\\Rightarrow B=20-G[\/latex]\n[latex]\\begin{array}{rrrrrrrrrl}\n&G&-&4&=&2(B&-&4)&& \\\\\n&G&-&4&=&2B&-&8&& \\\\ \\\\\n&G&-&4&=&2(20&-&G)&-&8 \\\\\n&G&-&4&=&40&-&2G&-&8 \\\\\n&G&-&4&=&32&-&2G&& \\\\\n+&2G&+&4&&4&+&2G&& \\\\\n\\hline\n&&&3G&=&36&&&& \\\\\n&&&G&=&12&&&& \\\\ \\\\\n&&&B&=&20&-&G&& \\\\\n&&&B&=&20&-&12&=&8 \\\\\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]x=16\\%\\text{ solution} [\/latex]\n[latex]\\begin{array}{rrrrrrrr}\n&16x&+&6(20)&=&12(x&+&20) \\\\\n&16x&+&120&=&12x&+&240 \\\\\n-&12x&-&120&&-12x&-&120 \\\\\n\\hline\n&&&4x&=&120&& \\\\ \\\\\n&&&x&=&\\dfrac{120}{4}&=&30\\text{ ml} \\\\\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(C&+&R&=&60)(-3.40) \\\\ \\\\\n&-3.40C&-&3.40R&=&-204 \\\\\n+&3.40C&+&3.90R&=&\\phantom{-}213\\\\\n\\hline\n&&&0.50R&=&\\phantom{-}9 \\\\ \\\\\n&&&R&=&\\dfrac{9}{0.50}\\text{ or 18 kg} \\\\ \\\\\n&C&+&R&=&\\phantom{-}60 \\\\\n&C&+&18&=&\\phantom{-}60 \\\\\n&&-&18&&-18 \\\\\n\\hline\n&&&C&=&\\phantom{-}42\\text{ kg}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n
      [latex]x-y=-3[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n3<\/td>\n<\/tr>\n
      \u22123<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
      [latex]x+2y=3[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      3<\/td>\n0<\/td>\n<\/tr>\n
      0<\/td>\n[latex]\\dfrac{3}{2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(2x&-&5y&=&-2)(-3) \\\\ &(3x&-&4y&=&\\phantom{-}4)(2) \\\\ \\\\ &-6x&+&15y&=&6 \\\\ +&6x&-&8y&=&8 \\\\ \\hline &&&7y&=&14 \\\\ &&&y&=&2 \\\\ \\\\ &2x&-&5(2)&=&-2 \\\\ &2x&-&10&=&-2 \\\\ &&+&10&&+10 \\\\ \\hline &&&2x&=&8 \\\\ &&&x&=&4 \\end{array}[\/latex]
      \n[latex](4,2)[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(4x&+&3y&=&-29)(-2) \\\\ &(3x&+&2y&=&-21)(3) \\\\ \\\\ &-8x&-&6y&=&\\phantom{-}58 \\\\ +&9x&+&6y&=&-63 \\\\ \\hline &&&x&=&-5 \\\\ \\\\ &3(-5)&+&2y&=&-21 \\\\ &-15&+&2y&=&-21 \\\\ +&15&&&&+15 \\\\ \\hline &&&2y&=&-6 \\\\ &&&y&=&-3 \\end{array}[\/latex]
      \n[latex](-5,-3)[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrrl} &(x&+&y&-&3z&=&0)(-2) \\\\ \\\\ &-2x&-&2y&+&6z&=&0 \\\\ +&2x&-&3y&&&=&16 \\\\ \\hline &&&-5y&+&6z&=&16 \\\\ \\\\ &&&(2y&-&2z&=&-12)(3) \\\\ \\\\ &&&6y&-&6z&=&-36 \\\\ +&&&-5y&+&6z&=&\\phantom{-}16 \\\\ \\hline &&&&&y&=&-20 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} 2x&-&3y&=&16 \\\\ 2x&-&3(-20)&=&16 \\\\ 2x&+&60&=&16 \\\\ &&-60&&-60 \\\\ \\hline &&2x&=&-44 \\\\ &&x&=&-22 \\\\ \\\\ 2y&-&2z&=&-12 \\\\ 2(-20)&-&2z&=&-12 \\\\ -40&-&2z&=&-12 \\\\ +40&&&&+40 \\\\ \\hline &&-2z&=&28 \\\\ &&z&=&-14 \\end{array} \\end{array}[\/latex]
      \n[latex](-22,-20,-14)[\/latex]<\/li>\n
    5. [latex]5-4\\left[2x-2\\cancel{(6x-5)^0}1-(7-2x)\\right][\/latex]
      \n[latex]5-4\\left[2x-2(1)-7+2x\\right][\/latex]
      \n[latex]5-4\\left[4x-9\\right][\/latex]
      \n[latex]5-16x+36[\/latex]
      \n[latex]-16x+41[\/latex]<\/li>\n
    6. [latex]3ab^4(a^2-25)[\/latex]
      \n[latex]3a^3b^4-75ab^4[\/latex]<\/li>\n
    7. [latex]\\begin{array}[t]{rrrrrlrrrr} &x^2&+&3x&-&6&&&& \\\\ \\times &x^2&+&3x&-&6&&&& \\\\ \\hline &x^4&+&3x^3&-&6x^2&&&& \\\\ &&&3x^3&+&9x^2&-&18x&& \\\\ +&&&&-&6x^2&-&18x&+&36 \\\\ \\hline &x^4&+&6x^3&-&3x^2&-&36x&+&36 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n\"\"<\/li>\n
    9. [latex]x^2-3z+7x-21[\/latex]
      \n[latex]x(x-3)+7(x-3)[\/latex]
      \n[latex](x-3)(x+7)[\/latex]<\/li>\n
    10. [latex]4x^2(x+1)-9(x+1)[\/latex]
      \n[latex](x+1)(4x^2-9)[\/latex]
      \n[latex](x+1)(2x-3)(2x+3)[\/latex]<\/li>\n
    11. [latex](2x)^3-(3y)^3[\/latex]
      \n[latex](2x-3y)(4x^2+6xy+9y^2)[\/latex]<\/li>\n
    12. [latex]x^4-625x^2+x^2-625[\/latex]
      \n[latex]x^2(x^2-625)+1(x^2-625)[\/latex]
      \n[latex](x^2+1)(x^2-625)[\/latex]
      \n[latex](x^2+1)(x-25)(x+25)[\/latex]<\/li>\n
    13. [latex]B+G=20\\Rightarrow B=20-G[\/latex]
      \n[latex]\\begin{array}{rrrrrrrrrl} &G&-&4&=&2(B&-&4)&& \\\\ &G&-&4&=&2B&-&8&& \\\\ \\\\ &G&-&4&=&2(20&-&G)&-&8 \\\\ &G&-&4&=&40&-&2G&-&8 \\\\ &G&-&4&=&32&-&2G&& \\\\ +&2G&+&4&&4&+&2G&& \\\\ \\hline &&&3G&=&36&&&& \\\\ &&&G&=&12&&&& \\\\ \\\\ &&&B&=&20&-&G&& \\\\ &&&B&=&20&-&12&=&8 \\\\ \\end{array}[\/latex]<\/li>\n
    14. [latex]x=16\\%\\text{ solution}[\/latex]
      \n[latex]\\begin{array}{rrrrrrrr} &16x&+&6(20)&=&12(x&+&20) \\\\ &16x&+&120&=&12x&+&240 \\\\ -&12x&-&120&&-12x&-&120 \\\\ \\hline &&&4x&=&120&& \\\\ \\\\ &&&x&=&\\dfrac{120}{4}&=&30\\text{ ml} \\\\ \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(C&+&R&=&60)(-3.40) \\\\ \\\\ &-3.40C&-&3.40R&=&-204 \\\\ +&3.40C&+&3.90R&=&\\phantom{-}213\\\\ \\hline &&&0.50R&=&\\phantom{-}9 \\\\ \\\\ &&&R&=&\\dfrac{9}{0.50}\\text{ or 18 kg} \\\\ \\\\ &C&+&R&=&\\phantom{-}60 \\\\ &C&+&18&=&\\phantom{-}60 \\\\ &&-&18&&-18 \\\\ \\hline &&&C&=&\\phantom{-}42\\text{ kg} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":73,"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-1936","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\/1936","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\/1936\/revisions"}],"predecessor-version":[{"id":1937,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1936\/revisions\/1937"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1936\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1936"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1936"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1936"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}