{"id":1980,"date":"2021-12-02T19:40:18","date_gmt":"2021-12-03T00:40:18","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-3\/"},"modified":"2022-11-02T10:38:53","modified_gmt":"2022-11-02T14:38:53","slug":"answer-key-10-3","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-3\/","title":{"raw":"Answer Key 10.3","rendered":"Answer Key 10.3"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{30}{2}&=&15 \\\\ \\\\\n15^2&=&225 \\\\\n\\therefore x^2&-&30x+225\\text{ or }(x-15)^2\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{24}{2}&=&12 \\\\ \\\\\n12^2&=&144 \\\\\n\\therefore a^2&-&24a+144\\text{ or }(a-12)^2\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{36}{2}&=&18 \\\\ \\\\\n18^2&=&324 \\\\\n\\therefore m^2&-&36m+324\\text{ or }(m-18)^2\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{34}{2}&=&17 \\\\ \\\\\n17^2&=&289 \\\\\n\\therefore x^2&-&34x+289\\text{ or }(x-17)^2\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{15}{2}&=&7.5 \\\\ \\\\\n7.5^2&=&56.25 \\\\\n\\therefore x^2&-&15x+56.25\\text{ or }\\left(x-\\dfrac{15}{2}\\right)^2\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{19}{2}&=&\\dfrac{19}{2} \\\\ \\\\\n\\left(\\dfrac{19}{2}\\right)^2&=&\\dfrac{361}{4} \\\\\n\\therefore r^2&-&19r+\\dfrac{361}{4}\\text{ or } \\left(r-\\dfrac{19}{2}\\right)^2\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\dfrac{1}{2}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\left(\\dfrac{1}{2}\\right)^2&=&\\dfrac{1}{4} \\\\\n\\therefore y^2&-&y+\\dfrac{1}{4}\\text{ or } \\left(y-\\dfrac{1}{2}\\right)^2\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\dfrac{17}{2}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\left(\\dfrac{17}{2}\\right)^2&=&\\dfrac{289}{4} \\\\\n\\therefore p^2&-&17p+\\dfrac{289}{4}\\text{ or }\\left(p-\\dfrac{17}{2}\\right)^2\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrlrrr}\nx^2&-&16x&+&55&=&0&& \\\\\n&&&-&55&&-55&& \\\\\n\\hline\n&&x^2&-&16x&=&-55&& \\\\ \\\\\nx^2&-&16x&+&64&=&64&-&55 \\\\\n&&(x&-&8)^2&=&9&&\n\\end{array}\\\\ \\sqrt{(x-8)^2}=\\sqrt{9}\\\\ \\begin{array}{rrrrrrr}x&-&8&=&\\pm &3& \\\\\n&+&8&&+ &8& \\\\\n\\hline\n&&x&=&8&\\pm &3 \\\\\n&&x&=&5,&11 &\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nn^2&-&4n&-&12&=&0&& \\\\\n&&&+&12&&+12&& \\\\\n\\hline\n&&n^2&-&4n&=&12&& \\\\ \\\\\nn^2&-&4n&+&4&=&12&+&4 \\\\\n&&(n&-&2)^2&=&16&&\n\\end{array}\\\\ \\sqrt{(n-2)^2}=\\pm \\sqrt{16}\\\\ \\begin{array}{rrrrrrr}\nn&-&2&=&\\pm &4& \\\\\n&+&2&&+&2& \\\\\n\\hline\n&&n&=&2&\\pm &4 \\\\\n&&n&=&6,&-2&\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nv^2&-&4v&-&21&=&0&& \\\\\n&&&+&21&&+21&& \\\\\n\\hline\n&&v^2&-&4v&=&21&& \\\\ \\\\\nv^2&-&4v&+&4&=&21&+&4 \\\\\n&&(v&-&2)^2&=&25&&\n\\end{array}\\\\ \\sqrt{(v-2)^2}=\\sqrt{25}\\\\ \\begin{array}{rrrrrrr}\nv&-&2&=&\\pm &5& \\\\\n&+&2&&+&2& \\\\\n\\hline\n&&v&=&2&\\pm &5 \\\\\n&&v&=&7,&-3&\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nb^2&+&8b&+&7&=&0&& \\\\\n&&&-&7&&-7&& \\\\\n\\hline\n&&b^2&+&8b&=&-7&& \\\\ \\\\\nb^2&+&8b&+&16&=&-7&+&16 \\\\\n&&(b&+&4)^2&=&9&&\n\\end{array}\\\\ \\sqrt{(b+4)^2}=\\sqrt{9}\\\\ \\begin{array}{rrrrrrr}\nb&+&4&=&\\pm&3& \\\\\n&-&4&&-&4& \\\\\n\\hline\n&&b&=&-4&\\pm &3 \\\\\n&&b&=&-7,&-1&\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nx^2&-&8x&+&16&=&-6&+&16 \\\\\n&&(x&-&4)^2&=&10&&\n\\end{array}\\\\ \\sqrt{(x-4)^2}=\\sqrt{10}\\\\ \\begin{array}{rrrrrrr}\nx&-&4&=&\\pm&\\sqrt{10}& \\\\\n&+&4&&+&4& \\\\\n\\hline\n&&x&=&4&\\pm&\\sqrt{10}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nx^2&&&-&13&=&4x&& \\\\\n&-&4x&+&13&&-4x&+&13 \\\\\n\\hline\nx^2&-&4x&+&4&=&13&+&4 \\\\\n&&(x&-&2)^2&=&17&&\n\\end{array}\\\\ \\sqrt{(x-2)^2}=\\sqrt{17}\\\\ \\begin{array}{rrrrrrr}\nx&-&2&=&\\pm&\\sqrt{17}& \\\\\n&+&2&&+&2& \\\\\n\\hline\n&&x&=&2&\\pm&\\sqrt{17}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&\\dfrac{3}{3}(k^2&+&8k)&=&\\dfrac{-1}{3}&& \\\\ \\\\\n&&k^2&+&8k&=&-\\dfrac{1}{3}&& \\\\ \\\\\nk^2&+&8k&+&16&=&-\\dfrac{1}{3}&+&16 \\\\ \\\\\n&&(k&+&4)^2&=&15\\dfrac{2}{3}&&\n\\end{array}\\\\ \\sqrt{(k+4)^2}=\\sqrt{15\\dfrac{2}{3}}\\\\ \\begin{array}{rrrrrrr}\nk&+&4&=&\\pm &\\sqrt{\\dfrac{47}{3}}& \\\\\n&-&4&&-&4& \\\\\n\\hline\n&&k&=&-4&\\pm &\\sqrt{\\dfrac{47}{3}}\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&\\dfrac{4}{4}(a^2&+&9a)&=&\\dfrac{-2}{4}&& \\\\ \\\\\na^2&+&9a&+&20.25&=&-\\dfrac{1}{2}&+&20.25 \\\\ \\\\\n&&(a&+&4.5)^2&=&19.75&&\n\\end{array}\\\\ \\sqrt{(a+4.5)^2}=\\pm \\sqrt{19.75}\\\\ \\begin{array}{rrrrrcl}\na&+&4.5&=&\\pm&\\sqrt{19.75}& \\\\\n&-&4.5&&-&4.5& \\\\\n\\hline\n&&a&=&-4.5&\\pm&\\sqrt{19.75}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{30}{2}&=&15 \\\\ \\\\ 15^2&=&225 \\\\ \\therefore x^2&-&30x+225\\text{ or }(x-15)^2 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{24}{2}&=&12 \\\\ \\\\ 12^2&=&144 \\\\ \\therefore a^2&-&24a+144\\text{ or }(a-12)^2 \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{36}{2}&=&18 \\\\ \\\\ 18^2&=&324 \\\\ \\therefore m^2&-&36m+324\\text{ or }(m-18)^2 \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{34}{2}&=&17 \\\\ \\\\ 17^2&=&289 \\\\ \\therefore x^2&-&34x+289\\text{ or }(x-17)^2 \\end{array}[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{15}{2}&=&7.5 \\\\ \\\\ 7.5^2&=&56.25 \\\\ \\therefore x^2&-&15x+56.25\\text{ or }\\left(x-\\dfrac{15}{2}\\right)^2 \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{19}{2}&=&\\dfrac{19}{2} \\\\ \\\\ \\left(\\dfrac{19}{2}\\right)^2&=&\\dfrac{361}{4} \\\\ \\therefore r^2&-&19r+\\dfrac{361}{4}\\text{ or } \\left(r-\\dfrac{19}{2}\\right)^2 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\dfrac{1}{2}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\left(\\dfrac{1}{2}\\right)^2&=&\\dfrac{1}{4} \\\\ \\therefore y^2&-&y+\\dfrac{1}{4}\\text{ or } \\left(y-\\dfrac{1}{2}\\right)^2 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\dfrac{17}{2}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\left(\\dfrac{17}{2}\\right)^2&=&\\dfrac{289}{4} \\\\ \\therefore p^2&-&17p+\\dfrac{289}{4}\\text{ or }\\left(p-\\dfrac{17}{2}\\right)^2 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrlrrr} x^2&-&16x&+&55&=&0&& \\\\ &&&-&55&&-55&& \\\\ \\hline &&x^2&-&16x&=&-55&& \\\\ \\\\ x^2&-&16x&+&64&=&64&-&55 \\\\ &&(x&-&8)^2&=&9&& \\end{array}\\\\ \\sqrt{(x-8)^2}=\\sqrt{9}\\\\ \\begin{array}{rrrrrrr}x&-&8&=&\\pm &3& \\\\ &+&8&&+ &8& \\\\ \\hline &&x&=&8&\\pm &3 \\\\ &&x&=&5,&11 & \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} n^2&-&4n&-&12&=&0&& \\\\ &&&+&12&&+12&& \\\\ \\hline &&n^2&-&4n&=&12&& \\\\ \\\\ n^2&-&4n&+&4&=&12&+&4 \\\\ &&(n&-&2)^2&=&16&& \\end{array}\\\\ \\sqrt{(n-2)^2}=\\pm \\sqrt{16}\\\\ \\begin{array}{rrrrrrr} n&-&2&=&\\pm &4& \\\\ &+&2&&+&2& \\\\ \\hline &&n&=&2&\\pm &4 \\\\ &&n&=&6,&-2& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} v^2&-&4v&-&21&=&0&& \\\\ &&&+&21&&+21&& \\\\ \\hline &&v^2&-&4v&=&21&& \\\\ \\\\ v^2&-&4v&+&4&=&21&+&4 \\\\ &&(v&-&2)^2&=&25&& \\end{array}\\\\ \\sqrt{(v-2)^2}=\\sqrt{25}\\\\ \\begin{array}{rrrrrrr} v&-&2&=&\\pm &5& \\\\ &+&2&&+&2& \\\\ \\hline &&v&=&2&\\pm &5 \\\\ &&v&=&7,&-3& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} b^2&+&8b&+&7&=&0&& \\\\ &&&-&7&&-7&& \\\\ \\hline &&b^2&+&8b&=&-7&& \\\\ \\\\ b^2&+&8b&+&16&=&-7&+&16 \\\\ &&(b&+&4)^2&=&9&& \\end{array}\\\\ \\sqrt{(b+4)^2}=\\sqrt{9}\\\\ \\begin{array}{rrrrrrr} b&+&4&=&\\pm&3& \\\\ &-&4&&-&4& \\\\ \\hline &&b&=&-4&\\pm &3 \\\\ &&b&=&-7,&-1& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} x^2&-&8x&+&16&=&-6&+&16 \\\\ &&(x&-&4)^2&=&10&& \\end{array}\\\\ \\sqrt{(x-4)^2}=\\sqrt{10}\\\\ \\begin{array}{rrrrrrr} x&-&4&=&\\pm&\\sqrt{10}& \\\\ &+&4&&+&4& \\\\ \\hline &&x&=&4&\\pm&\\sqrt{10} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} x^2&&&-&13&=&4x&& \\\\ &-&4x&+&13&&-4x&+&13 \\\\ \\hline x^2&-&4x&+&4&=&13&+&4 \\\\ &&(x&-&2)^2&=&17&& \\end{array}\\\\ \\sqrt{(x-2)^2}=\\sqrt{17}\\\\ \\begin{array}{rrrrrrr} x&-&2&=&\\pm&\\sqrt{17}& \\\\ &+&2&&+&2& \\\\ \\hline &&x&=&2&\\pm&\\sqrt{17} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} &&\\dfrac{3}{3}(k^2&+&8k)&=&\\dfrac{-1}{3}&& \\\\ \\\\ &&k^2&+&8k&=&-\\dfrac{1}{3}&& \\\\ \\\\ k^2&+&8k&+&16&=&-\\dfrac{1}{3}&+&16 \\\\ \\\\ &&(k&+&4)^2&=&15\\dfrac{2}{3}&& \\end{array}\\\\ \\sqrt{(k+4)^2}=\\sqrt{15\\dfrac{2}{3}}\\\\ \\begin{array}{rrrrrrr} k&+&4&=&\\pm &\\sqrt{\\dfrac{47}{3}}& \\\\ &-&4&&-&4& \\\\ \\hline &&k&=&-4&\\pm &\\sqrt{\\dfrac{47}{3}} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} &&\\dfrac{4}{4}(a^2&+&9a)&=&\\dfrac{-2}{4}&& \\\\ \\\\ a^2&+&9a&+&20.25&=&-\\dfrac{1}{2}&+&20.25 \\\\ \\\\ &&(a&+&4.5)^2&=&19.75&& \\end{array}\\\\ \\sqrt{(a+4.5)^2}=\\pm \\sqrt{19.75}\\\\ \\begin{array}{rrrrrcl} a&+&4.5&=&\\pm&\\sqrt{19.75}& \\\\ &-&4.5&&-&4.5& \\\\ \\hline &&a&=&-4.5&\\pm&\\sqrt{19.75} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":95,"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-1980","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\/1980","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\/1980\/revisions"}],"predecessor-version":[{"id":1981,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1980\/revisions\/1981"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1980\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1980"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1980"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1980"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}