{"id":1966,"date":"2019-08-29T14:35:20","date_gmt":"2019-08-29T18:35:20","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1966"},"modified":"2019-12-29T19:15:39","modified_gmt":"2019-12-30T00:15:39","slug":"mid-term-1-prep-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/mid-term-1-prep-answer-key\/","title":{"raw":"Mid Term 1: Review Questions Answer Key","rendered":"Mid Term 1: Review Questions Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. True<\/li>\r\n \t
  2. Undefined<\/li>\r\n \t
  3. 15<\/li>\r\n \t
  4. 16<\/li>\r\n \t
  5. 12<\/li>\r\n \t
  6. 19<\/li>\r\n \t
  7. True<\/li>\r\n \t
  8. \u221218<\/li>\r\n \t
  9. 18<\/li>\r\n \t
  10. \u221216<\/li>\r\n \t
  11. 16<\/li>\r\n \t
  12. \u221216<\/li>\r\n \t
  13. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\\r\n-(-6) - \\sqrt{(-6)^2-4(8)(-2)} \\\\\r\n6 - \\sqrt{36+64} \\\\\r\n6-10 \\\\\r\n-4\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&3x&-&12&-&27&=&7&-&5x&-&30 \\\\\r\n+&5x&+&12&+&27&&&+&5x&+&12 \\\\\r\n&&&&&&&&&&+&7 \\\\\r\n&&&&&&&&&&+&27 \\\\\r\n\\midrule\r\n&&&&&8x&=&16&&&& \\\\\r\n&&&&&x&=&2&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\left(\\dfrac{1}{R} = \\dfrac{1}{r_1}+\\dfrac{1}{r_2}\\right)(Rr_1r_2) \\\\ \\\\\r\nr_1r_2 = Rr_2 + Rr_1 \\\\ \\\\\r\nr_1r_2 = R(r_2 + r_1) \\\\ \\\\\r\nR=\\dfrac{r_1r_2}{r_2 + r_1}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x+3}{8} - \\dfrac{3}{4} = \\dfrac {x+6}{10}\\right)(40) \\\\ \\)\r\n\\(\\begin{array}{rrrrrcrrrr}\r\n&5(x&+&3)&-&3(10)&=&4(x&+&6) \\\\\r\n&5x&+&15&-&30&=&4x&+&24 \\\\\r\n-&4x&-&15&+&30&&-4x&-&15 \\\\\r\n&&&&&&&&+&30 \\\\\r\n\\midrule\r\n&&&&&x&=&39&&\r\n\\end{array}\\)<\/li>\r\n \t
  17. Need graph drawn. \\(y=5\\)<\/li>\r\n \t
  18. \\(\\begin{array}{ll}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\\r\nm&=&\\dfrac {\\Delta y}{\\Delta x}\\\\ \\\\\r\n\\dfrac{2}{3}& =& \\dfrac{y-2}{x- -1}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrrcl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&2(x&+&1)& =& 3(y&-&2) \\\\\r\n&&2x &+& 2& = &3y& -& 6 \\\\\r\n&&-3y& + &6 &&-3y &+ &6 \\\\\r\n\\midrule\r\n2x&-&3y&+&8&=&0&& \\\\ \\\\\r\n&&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{8}{3}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{ll}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&& \\text{1st slope} \\\\ \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\nm&=&\\dfrac{11--1}{2--2} \\\\ \\\\\r\nm&=&\\dfrac{12}{4} \\\\ \\\\\r\nm&=& 3 \\\\ \\\\\r\n&& \\text{2nd slope} \\\\ \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n3&=&\\dfrac{y--1}{x--2}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&3(x&+&2)&=&y&+&1 \\\\\r\n&&3x&+&6&=&y&+&1 \\\\\r\n&&-y&-&1&&-y&-&1 \\\\\r\n\\midrule\r\n3x&-&y&+&5&=&0&& \\\\\r\n&&&&y&=&3x&+&5\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  20. \r\n\r\n[caption id=\"attachment_1976\" align=\"alignnone\" width=\"300\"]\"Line Use slop intercept method.[\/caption]<\/li>\r\n \t
  21. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\nd^2& =& \\Delta x^2 + \\Delta y^2\\\\\r\nd^2 &=& (15-7)^2 + (3 - -3)^2\\\\\r\nd^2& =& 8^2 + 6^2 \\\\\r\nd&=&10\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\phantom{1}\\)\r\n\\(x=\\dfrac{x_1+x_2}{2}=\\dfrac{7+15}{2}=11 \\\\ \\)\r\n\\(y=\\dfrac{y_1+y_2}{2}=\\dfrac{-3+3}{2}=0 \\\\ \\)\r\n\\((11,0)\\)<\/li>\r\n \t
  23. True<\/li>\r\n \t
  24. True<\/li>\r\n \t
  25. \\(\\{r, s, t\\}\\)<\/li>\r\n \t
  26. True<\/li>\r\n \t
  27. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\\r\n3x&-&6&-&36x&>&60 \\\\\r\n&+&6&&&&+6 \\\\\r\n\\midrule\r\n&&&&-33x&>&66 \\\\\r\n&&&&x&<&-2\r\n\\end{array}\\)\r\n\r\n[caption id=\"attachment_2002\" align=\"aligncenter\" width=\"300\"]\"- (\u2212\u221e, \u22122)[\/caption]<\/li>\r\n \t
  28. \\(\\begin{array}{rrrcrcr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-18& \\le& 4x& - &6& \\le& 2\\\\\r\n+6&&&+&6&&+6\\\\\r\n\\midrule\r\n\\dfrac{-12}{4}&\\le&&\\dfrac{4x}{4}&&\\le&\\dfrac{8}{4}\\\\ \\\\\r\n-3&\\le&&x&&\\le&2\r\n\\end{array}\\)[caption id=\"attachment_2007\" align=\"aligncenter\" width=\"300\"]\"-3, [\u22123, 2][\/caption]<\/li>\r\n \t
  29. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrr}\r\n2x&-&1&<&-7 \\\\\r\n&+&1&&+1 \\\\\r\n\\midrule\r\n&&\\dfrac{2x}{2}&<&\\dfrac{-6}{2} \\\\ \\\\\r\n&&x&<&-3\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n7&<&2x&-&1 \\\\\r\n+1&&&+&1 \\\\\r\n\\midrule\r\n\\dfrac{8}{2}&<&\\dfrac{2x}{2}&& \\\\ \\\\\r\n4&<&x&&\r\n\\end{array}\r\n\\end{array}\\)\r\n\r\n[caption id=\"attachment_2010\" align=\"aligncenter\" width=\"300\"]\"- (\u2212\u221e, \u22123) or (4, \u221e) WRONG IMAGE<\/span>[\/caption]<\/li>\r\n \t
  30. \\(\\phantom{1}\\)\r\n\\(\\left| \\dfrac{3x - 4}{5} \\right| < 1 \\\\ \\)\r\n\\(\\left(-1 < \\dfrac{3x-4}{5}< 1 \\right)(5) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-5&<&3x&-&4&<&5 \\\\\r\n+4&&&+&4&&+4 \\\\\r\n\\midrule\r\n\\dfrac{-1}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{9}{3} \\\\ \\\\\r\n-\\dfrac{1}{3}&<&&x&&<&3\r\n\\end{array}\\)\r\n\r\n[caption id=\"attachment_2012\" align=\"alignnone\" width=\"300\"]\"-1\/3, \\((-\\dfrac{1}{3}, 3)\\)[\/caption]<\/li>\r\n \t
  31. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&3x&-&2y&=&10&& \\\\\r\n+&-10&+&2y&&-10&+&2y \\\\\r\n\\midrule\r\n&\\dfrac{3x}{2}&-&\\dfrac{10}{2}&=&\\dfrac{2y}{2}&& \\\\ \\\\\r\n&&&y&=&\\dfrac{3}{2}x&-&5\r\n\\end{array}\\)\r\n\r\n[caption id=\"attachment_1981\" align=\"alignnone\" width=\"300\"]\"Line Slope intercept method. Check (0, 0): 3(0) \u2212 2(0) < 10. Shade the (0, 0) side.[\/caption]<\/li>\r\n \t
  32. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(y=|x-1|-2\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    4<\/td>\r\n1<\/td>\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\u22121<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
  33. \\(\\begin{array}{rrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&6L&+&2S&=&38 \\\\\r\n+&4L&-&2S&=&12 \\\\\r\n\\midrule\r\n&&&10L&=&50 \\\\\r\n&&&L&=&5 \\\\ \\\\\r\n\\therefore &6(5)&+&2S&=&38 \\\\\r\n&30&+&2S&=&38 \\\\\r\n-&30&&&&-30 \\\\\r\n\\midrule\r\n&&&2S&=&8 \\\\\r\n&&&S&=&4\r\n\\end{array}\\)<\/li>\r\n \t
  34. Insert diagram.\r\n\\(\\begin{array}{rrl}\r\n5x+x&=&36 \\\\\r\n6x&=&36 \\\\\r\nx&=&6 \\\\\r\n\\therefore 5x&=&30\r\n\\end{array}\\)<\/li>\r\n \t
  35. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(d&+&q&=&14)(-10) \\\\\r\n&10d&+&25q&=&260 \\\\ \\\\\r\n&-10d&-&10q&=&-140 \\\\\r\n+&10d&+&25q&=&\\phantom{-}260 \\\\\r\n\\midrule\r\n&&&\\dfrac{15q}{15}&=&\\dfrac{120}{15} \\\\ \\\\\r\n&&&q&=&8 \\\\ \\\\\r\n\\therefore &d&+&8&=&14 \\\\\r\n&&-&8&&-8 \\\\\r\n\\midrule\r\n&&&d&=&6\r\n\\end{array}\\)<\/li>\r\n \t
  36. \\(\\phantom{1}\\)\r\n\\(x, x+2 \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrrr}\r\nx&+&x&+&2&=&x&-&10 \\\\\r\n&&2x&+&2&=&x&-&10 \\\\\r\n&&-x&-&2&&-x&-&2 \\\\\r\n\\midrule\r\n&&&&x&=&-12&& \\\\\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\nnumbers are \u221212, \u221210<\/li>\r\n \t
  37. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{\\underline{1st}}&& \\\\\r\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\r\n\\text{\\underline{2nd}}&& \\\\\r\ny&=&12 \\\\\r\nk&=&\\text{find} \\\\\r\nm&=&3 \\\\\r\nn&=&4 \\\\\r\nd&=&8 \\\\ \\\\\r\n12&=&\\dfrac{k(3)(4)^2}{8} \\\\ \\\\\r\nk&=&\\dfrac{12(8)}{3\\cdot 16} \\\\ \\\\\r\nk&=& 2\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\text{\\underline{3rd}}&& \\\\\r\ny&=&\\text{find} \\\\\r\nk&=& 2 \\\\\r\nm&=&-3 \\\\\r\nn&=&3 \\\\\r\nd&=& 6 \\\\ \\\\\r\ny&=&\\dfrac{(2)(-3)(3)^2}{6} \\\\ \\\\\r\ny&=&-9\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n\r\n
      \r\n \t
    1. <\/li>\r\n<\/ol>","rendered":"
        \n
      1. True<\/li>\n
      2. Undefined<\/li>\n
      3. 15<\/li>\n
      4. 16<\/li>\n
      5. 12<\/li>\n
      6. 19<\/li>\n
      7. True<\/li>\n
      8. \u221218<\/li>\n
      9. 18<\/li>\n
      10. \u221216<\/li>\n
      11. 16<\/li>\n
      12. \u221216<\/li>\n
      13. \"\begin{array}{l}<\/li>\n
      14. \"\begin{array}{rrrrrrrrrrrr}<\/li>\n
      15. \"\begin{array}{l}<\/li>\n
      16. \"\phantom{1}\"
        \n\"\left(\dfrac{x+3}{8} - \dfrac{3}{4} = \dfrac {x+6}{10}\right)(40) \\\"
        \n\"\begin{array}{rrrrrcrrrr}<\/li>\n
      17. Need graph drawn. \"y=5\"<\/li>\n
      18. \"\begin{array}{ll}<\/li>\n
      19. \"\begin{array}{ll}<\/li>\n
      20. \n
        \"Line
        Use slop intercept method.<\/figcaption><\/figure>\n<\/li>\n
      21. \"\begin{array}{rrl}<\/li>\n
      22. \"\phantom{1}\"
        \n\"x=\dfrac{x_1+x_2}{2}=\dfrac{7+15}{2}=11 \\\"
        \n\"y=\dfrac{y_1+y_2}{2}=\dfrac{-3+3}{2}=0 \\\"
        \n\"(11,0)\"<\/li>\n
      23. True<\/li>\n
      24. True<\/li>\n
      25. \"\{r, s, t\}\"<\/li>\n
      26. True<\/li>\n
      27. \"\begin{array}{rrrrrrr}
        \n
        \"-
        (\u2212\u221e, \u22122)<\/figcaption><\/figure>\n<\/li>\n
      28. \"\begin{array}{rrrcrcr}
        \n
        \"-3,
        [\u22123, 2]<\/figcaption><\/figure>\n<\/li>\n
      29. \"\begin{array}{ll}
        \n
        \"-
        (\u2212\u221e, \u22123) or (4, \u221e) WRONG IMAGE<\/span><\/figcaption><\/figure>\n<\/li>\n
      30. \"\phantom{1}\"
        \n\"\left| \dfrac{3x - 4}{5} \right| < 1 \\\"
        \n\"\left(-1 < \dfrac{3x-4}{5}< 1 \right)(5) \\\"
        \n\"\begin{array}{rrrrrrr}<\/p>\n
        \"-1\/3,
        \"(-\dfrac{1}{3}, 3)\"<\/figcaption><\/figure>\n<\/li>\n
      31. \"\begin{array}{rrrrrrrr}
        \n
        \"Line
        Slope intercept method. Check (0, 0): 3(0) \u2212 2(0) < 10. Shade the (0, 0) side.<\/figcaption><\/figure>\n<\/li>\n
      32. \n\n\n\n\n\n\n\n\n\n\n
        \"y=|x-1|-2\"<\/caption>\n
        \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
        4<\/td>\n1<\/td>\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\u22121<\/td>\n<\/tr>\n
        \u22121<\/td>\n0<\/td>\n<\/tr>\n
        \u22122<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
      33. \"\begin{array}{rrrrrr}<\/li>\n
      34. Insert diagram.
        \n\"\begin{array}{rrl}<\/li>\n
      35. \"\begin{array}{rrrrrl}<\/li>\n
      36. \"\phantom{1}\"
        \n\"x, x+2 \\\"
        \n\"\begin{array}{rrrrrrrrr}
        \n\"\phantom{1}\"
        \nnumbers are \u221212, \u221210<\/li>\n
      37. \"\begin{array}{ll}<\/li>\n<\/ol>\n

        <\/p>\n

          \n
        1. <\/li>\n<\/ol>\n","protected":false},"author":14,"menu_order":31,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1966","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1966\/revisions"}],"predecessor-version":[{"id":3731,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1966\/revisions\/3731"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1966\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1966"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1966"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1966"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}