{"id":1924,"date":"2021-12-02T19:40:01","date_gmt":"2021-12-03T00:40:01","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-b-answer-key\/"},"modified":"2022-11-02T10:38:27","modified_gmt":"2022-11-02T14:38:27","slug":"midterm-two-version-b-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-b-answer-key\/","title":{"raw":"Midterm 2: Version B Answer Key","rendered":"Midterm 2: Version B Answer Key"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n\n
    [latex]x+y=5[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    5<\/td>\n0<\/td>\n<\/tr>\n
    0<\/td>\n5<\/td>\n<\/tr>\n
    3<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
    [latex]2x-y=1[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    1<\/td>\n1<\/td>\n<\/tr>\n
    0<\/td>\n\u22121<\/td>\n<\/tr>\n
    \u22121<\/td>\n\u22123<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Graph<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n4(4y&+&2)&+&3y&=&8 \\\\\n16y&+&8&+&3y&=&8 \\\\\n&-&8&&&&-8 \\\\\n\\hline\n&&&&19y&=&0 \\\\\n&&&&y&=&0\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\nx&=&4y&+&2 \\\\\nx&=&\\cancel{4y}0&+&2 \\\\\nx&=&2&&\n\\end{array}\n\\end{array}[\/latex]\n[latex](2,0)[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&5x&-&3y&=&2 \\\\\n&(3x&+&y&=&4)(3) \\\\ \\\\\n&5x&-&3y&=&\\phantom{1}2 \\\\\n+&9x&+&3y&=&12 \\\\\n\\hline\n&&&14x&=&14 \\\\\n&&&x&=&1 \\\\ \\\\\n&\\therefore 3(1)&+&y&=&4 \\\\\n&3&+&y&=&4 \\\\\n&&&y&=&1\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrrl}\n&&&(x&-&2z&=&-7)(-1) \\\\ \\\\\n&x&+&y&+&z&=&3 \\\\\n+&-x&&&+&2z&=&7 \\\\\n\\hline\n&&&y&+&3z&=&10 \\\\\n&&&(-2y&+&4z&=&20)(\\div 2) \\\\\n&&&&&\\Downarrow&& \\\\\n&&&y&+&3z&=&10 \\\\\n&&+&-y&+&2z&=&10 \\\\\n\\hline\n&&&&&5z&=&20 \\\\\n&&&&&z&=&4 \\\\\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\nx&-&2z&=&-7 \\\\\nx&-&2(4)&=&-7 \\\\\nx&-&8&=&-7 \\\\\n&+&8&&+8 \\\\\n\\hline\n&&x&=&1 \\\\ \\\\\ny&+&3z&=&10 \\\\\ny&+&3(4)&=&10 \\\\\ny&+&12&=&10 \\\\\n&-&12&&-12 \\\\\n\\hline\n&&y&=&-2 \\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex](1,-2,4)[\/latex]<\/li>\n \t
  5. [latex]5-3\\left[4x-2\\cancel{(6x-5)^0}1-(7-2x)\\right][\/latex]\n[latex]5-3\\left[4x-2(1)-(7-2x)\\right][\/latex]\n[latex]5-3\\left[6x-9\\right][\/latex]\n[latex]5-18x+27\\Rightarrow -18x+32[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrlrl}\n&a&+&3&& \\\\\n\\times &a&+&3&& \\\\\n\\hline\n&a^2&+&3a&& \\\\\n+&&&3a&+&9 \\\\\n\\hline\n&a^2&+&6a&+&9 \\\\\n\\times&&&&&3a^2 \\\\\n\\hline\n&3a^4&+&18a^3&+&27a^2\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\begin{array}[t]{rrrlrrrrrr}\n&x^2&+&x&+&5\\phantom{x^2}&&&& \\\\\n\\times&x^2&+&x&-&5\\phantom{x^2}&&&& \\\\\n\\hline\n&x^4&+&x^3&+&5x^2&&&& \\\\\n&&&x^3&+&x^2&+&5x&& \\\\\n+&&&&&-5x^2&-&5x&-&25 \\\\\n\\hline\n&x^4&+&2x^3&+&x^2&-&25&&\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex](x^{4n-3n}x^{-6})^{-1}[\/latex]\n[latex](x^nx^{-6})^{-1}[\/latex]\n[latex]x^{-n}x^6\\text{ or }\\dfrac{x^6}{x^n}[\/latex]<\/li>\n \t
  9. [latex]2a(7xy-3z)-1(7xy-3z)[\/latex]\n[latex](7xy-3z)(2a-1)[\/latex]<\/li>\n \t
  10. [latex]a^2-3ab+5ab-15b^2[\/latex]\n[latex]a(a-3b)+5b(a-3b)[\/latex]\n[latex](a-3b)(a+5b)[\/latex]<\/li>\n \t
  11. [latex]2x^2(x+4)-1(x+4)[\/latex]\n[latex](x+4)(2x^2-1)[\/latex]<\/li>\n \t
  12. [latex](3x)^3+(2y)^3[\/latex]\n[latex](3x+2y)(9x^2-6xy+4y^2)[\/latex]<\/li>\n \t
  13. [latex]F+D=38\\Rightarrow F=38-D[\/latex]\n[latex]\\begin{array}{rrrrrrr}\n(F&+&6)&=&4(D&+&6) \\\\\n38-D&+&6\\phantom{)}&=&4D&+&24 \\\\\n-24+D&&&&+D&-&24 \\\\\n\\hline\n&&20&=&5D&& \\\\ \\\\\n&&D&=&\\dfrac{20}{5}&=&4 \\\\ \\\\\n&&\\therefore F&=&38&-&D \\\\\n&&F&=&38&-&4 \\\\\n&&F&=&34&&\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]A+B=90\\Rightarrow B=90-A[\/latex]\n[latex]\\begin{array}{rrrrrrl}\n3A&+&5(90&-&A)&=&\\phantom{-}370 \\\\\n3A&+&450&-&5A&=&\\phantom{-}370 \\\\\n&-&450&&&&-450 \\\\\n\\hline\n&&&&-2A&=&-80 \\\\ \\\\\n&&&&A&=&\\dfrac{-80}{-2}\\text{ or }40\\text{ kg} \\\\ \\\\\n&&&&\\therefore B&=&90-A \\\\\n&&&&B&=&90-40 \\\\\n&&&&B&=&50\\text{ kg}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n10x&+&25(40)&=&15(x&+&40) \\\\ \\\\\n10x&+&1000&=&15x&+&600 \\\\\n-10x&-&600&&-10x&-&600 \\\\\n\\hline\n&&400&=&5x&& \\\\ \\\\\n&&x&=&\\dfrac{400}{5}&=&80\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n\n
      [latex]x+y=5[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      5<\/td>\n0<\/td>\n<\/tr>\n
      0<\/td>\n5<\/td>\n<\/tr>\n
      3<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
      [latex]2x-y=1[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      1<\/td>\n1<\/td>\n<\/tr>\n
      0<\/td>\n\u22121<\/td>\n<\/tr>\n
      \u22121<\/td>\n\u22123<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 4(4y&+&2)&+&3y&=&8 \\\\ 16y&+&8&+&3y&=&8 \\\\ &-&8&&&&-8 \\\\ \\hline &&&&19y&=&0 \\\\ &&&&y&=&0 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} x&=&4y&+&2 \\\\ x&=&\\cancel{4y}0&+&2 \\\\ x&=&2&& \\end{array} \\end{array}[\/latex]
      \n[latex](2,0)[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &5x&-&3y&=&2 \\\\ &(3x&+&y&=&4)(3) \\\\ \\\\ &5x&-&3y&=&\\phantom{1}2 \\\\ +&9x&+&3y&=&12 \\\\ \\hline &&&14x&=&14 \\\\ &&&x&=&1 \\\\ \\\\ &\\therefore 3(1)&+&y&=&4 \\\\ &3&+&y&=&4 \\\\ &&&y&=&1 \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrrl} &&&(x&-&2z&=&-7)(-1) \\\\ \\\\ &x&+&y&+&z&=&3 \\\\ +&-x&&&+&2z&=&7 \\\\ \\hline &&&y&+&3z&=&10 \\\\ &&&(-2y&+&4z&=&20)(\\div 2) \\\\ &&&&&\\Downarrow&& \\\\ &&&y&+&3z&=&10 \\\\ &&+&-y&+&2z&=&10 \\\\ \\hline &&&&&5z&=&20 \\\\ &&&&&z&=&4 \\\\ \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} x&-&2z&=&-7 \\\\ x&-&2(4)&=&-7 \\\\ x&-&8&=&-7 \\\\ &+&8&&+8 \\\\ \\hline &&x&=&1 \\\\ \\\\ y&+&3z&=&10 \\\\ y&+&3(4)&=&10 \\\\ y&+&12&=&10 \\\\ &-&12&&-12 \\\\ \\hline &&y&=&-2 \\\\ \\end{array} \\end{array}[\/latex]
      \n[latex](1,-2,4)[\/latex]<\/li>\n
    5. [latex]5-3\\left[4x-2\\cancel{(6x-5)^0}1-(7-2x)\\right][\/latex]
      \n[latex]5-3\\left[4x-2(1)-(7-2x)\\right][\/latex]
      \n[latex]5-3\\left[6x-9\\right][\/latex]
      \n[latex]5-18x+27\\Rightarrow -18x+32[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrlrl} &a&+&3&& \\\\ \\times &a&+&3&& \\\\ \\hline &a^2&+&3a&& \\\\ +&&&3a&+&9 \\\\ \\hline &a^2&+&6a&+&9 \\\\ \\times&&&&&3a^2 \\\\ \\hline &3a^4&+&18a^3&+&27a^2 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\begin{array}[t]{rrrlrrrrrr} &x^2&+&x&+&5\\phantom{x^2}&&&& \\\\ \\times&x^2&+&x&-&5\\phantom{x^2}&&&& \\\\ \\hline &x^4&+&x^3&+&5x^2&&&& \\\\ &&&x^3&+&x^2&+&5x&& \\\\ +&&&&&-5x^2&-&5x&-&25 \\\\ \\hline &x^4&+&2x^3&+&x^2&-&25&& \\end{array}[\/latex]<\/li>\n
    8. [latex](x^{4n-3n}x^{-6})^{-1}[\/latex]
      \n[latex](x^nx^{-6})^{-1}[\/latex]
      \n[latex]x^{-n}x^6\\text{ or }\\dfrac{x^6}{x^n}[\/latex]<\/li>\n
    9. [latex]2a(7xy-3z)-1(7xy-3z)[\/latex]
      \n[latex](7xy-3z)(2a-1)[\/latex]<\/li>\n
    10. [latex]a^2-3ab+5ab-15b^2[\/latex]
      \n[latex]a(a-3b)+5b(a-3b)[\/latex]
      \n[latex](a-3b)(a+5b)[\/latex]<\/li>\n
    11. [latex]2x^2(x+4)-1(x+4)[\/latex]
      \n[latex](x+4)(2x^2-1)[\/latex]<\/li>\n
    12. [latex](3x)^3+(2y)^3[\/latex]
      \n[latex](3x+2y)(9x^2-6xy+4y^2)[\/latex]<\/li>\n
    13. [latex]F+D=38\\Rightarrow F=38-D[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} (F&+&6)&=&4(D&+&6) \\\\ 38-D&+&6\\phantom{)}&=&4D&+&24 \\\\ -24+D&&&&+D&-&24 \\\\ \\hline &&20&=&5D&& \\\\ \\\\ &&D&=&\\dfrac{20}{5}&=&4 \\\\ \\\\ &&\\therefore F&=&38&-&D \\\\ &&F&=&38&-&4 \\\\ &&F&=&34&& \\end{array}[\/latex]<\/li>\n
    14. [latex]A+B=90\\Rightarrow B=90-A[\/latex]
      \n[latex]\\begin{array}{rrrrrrl} 3A&+&5(90&-&A)&=&\\phantom{-}370 \\\\ 3A&+&450&-&5A&=&\\phantom{-}370 \\\\ &-&450&&&&-450 \\\\ \\hline &&&&-2A&=&-80 \\\\ \\\\ &&&&A&=&\\dfrac{-80}{-2}\\text{ or }40\\text{ kg} \\\\ \\\\ &&&&\\therefore B&=&90-A \\\\ &&&&B&=&90-40 \\\\ &&&&B&=&50\\text{ kg} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 10x&+&25(40)&=&15(x&+&40) \\\\ \\\\ 10x&+&1000&=&15x&+&600 \\\\ -10x&-&600&&-10x&-&600 \\\\ \\hline &&400&=&5x&& \\\\ \\\\ &&x&=&\\dfrac{400}{5}&=&80 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":70,"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-1924","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\/1924","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\/1924\/revisions"}],"predecessor-version":[{"id":1925,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1924\/revisions\/1925"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1924\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1924"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1924"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1924"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}