{"id":1396,"date":"2021-12-02T19:37:49","date_gmt":"2021-12-03T00:37:49","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/chapter\/midterm-two-version-b-2\/"},"modified":"2022-11-02T10:35:12","modified_gmt":"2022-11-02T14:35:12","slug":"midterm-two-version-b-2","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/chapter\/midterm-two-version-b-2\/","title":{"raw":"Midterm 2: Version B","rendered":"Midterm 2: Version B"},"content":{"raw":"Find the solution set of the system graphically.\n
    \n \t
  1. [latex]\\left\\{\n\\begin{array}{rrrrr}\nx&+&y&=&5 \\\\\n2x&-&y&=&1\n\\end{array}\\right.[\/latex]<\/li>\n<\/ol>\nFor problems 2\u20134, find the solution set of each system by any convenient method.\n
      \n \t
    1. [latex]\\left\\{\n\\begin{array}{rrrrrrr}\n4x&+&3y&=&8&& \\\\\n&&x&=&4y&+&2 \\\\\n\\end{array}\\right.[\/latex]<\/li>\n \t
    2. [latex]\\left\\{\n\\begin{array}{rrrrr}\n5x&-&3y&=&2 \\\\\n3x&+&y&=&4\n\\end{array}\\right.[\/latex]<\/li>\n \t
    3. [latex]\\left\\{\n\\begin{array}{rrrrrrr}\nx&+&y&+&z&=&3 \\\\\nx&&&-&2z&=&-7 \\\\\n&&-2y&+&4z&=&20\n\\end{array}\\right.[\/latex]<\/li>\n<\/ol>\nReduce the following expressions in questions 5\u20138.\n
        \n \t
      1. [latex]5 - 3\\left[4x - 2(6x - 5)^0 - (7 - 2x)\\right][\/latex]<\/li>\n \t
      2. [latex]3a^2(a + 3)^2[\/latex]<\/li>\n \t
      3. [latex](x^2 + x + 5)(x^2 + x - 5)[\/latex]<\/li>\n \t
      4. [latex]\\left(\\dfrac{x^{4n}x^{-6}}{x^{3n}}\\right)^{-1}[\/latex]<\/li>\n<\/ol>\nFor problems 9\u201312, factor each expression completely.\n
          \n \t
        1. [latex]14axy - 6az - 7xy + 3z[\/latex]<\/li>\n \t
        2. [latex]a^2 + 2ab - 15b^2[\/latex]<\/li>\n \t
        3. [latex]2x^3 + 8x^2 - x - 4[\/latex]<\/li>\n \t
        4. [latex]27x^3 + 8y^3[\/latex]<\/li>\n<\/ol>\nSolve the following word problems.\n
            \n \t
          1. The sum of the ages of a father and his daughter is 38. Six years from now, the father will be four times as old as his daughter. Find the present age of each.<\/li>\n \t
          2. A 90 kg mixture of two different types of nuts costs [latex]\\$370[\/latex]. If type A costs [latex]\\$3[\/latex] per kg and type B costs [latex]\\$5[\/latex] per kg, how many kg of each type were used?<\/li>\n \t
          3. A student lab technician is combining a 10% sulfuric acid solution to 40 ml solution at 25% to dilute it to 15%. How much of the 10% solution does the student need to add?<\/li>\n<\/ol>\nMidterm 2: Version B Answer Key<\/a>","rendered":"

            Find the solution set of the system graphically.<\/p>\n

              \n
            1. [latex]\\left\\{ \\begin{array}{rrrrr} x&+&y&=&5 \\\\ 2x&-&y&=&1 \\end{array}\\right.[\/latex]<\/li>\n<\/ol>\n

              For problems 2\u20134, find the solution set of each system by any convenient method.<\/p>\n

                \n
              1. [latex]\\left\\{ \\begin{array}{rrrrrrr} 4x&+&3y&=&8&& \\\\ &&x&=&4y&+&2 \\\\ \\end{array}\\right.[\/latex]<\/li>\n
              2. [latex]\\left\\{ \\begin{array}{rrrrr} 5x&-&3y&=&2 \\\\ 3x&+&y&=&4 \\end{array}\\right.[\/latex]<\/li>\n
              3. [latex]\\left\\{ \\begin{array}{rrrrrrr} x&+&y&+&z&=&3 \\\\ x&&&-&2z&=&-7 \\\\ &&-2y&+&4z&=&20 \\end{array}\\right.[\/latex]<\/li>\n<\/ol>\n

                Reduce the following expressions in questions 5\u20138.<\/p>\n

                  \n
                1. [latex]5 - 3\\left[4x - 2(6x - 5)^0 - (7 - 2x)\\right][\/latex]<\/li>\n
                2. [latex]3a^2(a + 3)^2[\/latex]<\/li>\n
                3. [latex](x^2 + x + 5)(x^2 + x - 5)[\/latex]<\/li>\n
                4. [latex]\\left(\\dfrac{x^{4n}x^{-6}}{x^{3n}}\\right)^{-1}[\/latex]<\/li>\n<\/ol>\n

                  For problems 9\u201312, factor each expression completely.<\/p>\n

                    \n
                  1. [latex]14axy - 6az - 7xy + 3z[\/latex]<\/li>\n
                  2. [latex]a^2 + 2ab - 15b^2[\/latex]<\/li>\n
                  3. [latex]2x^3 + 8x^2 - x - 4[\/latex]<\/li>\n
                  4. [latex]27x^3 + 8y^3[\/latex]<\/li>\n<\/ol>\n

                    Solve the following word problems.<\/p>\n

                      \n
                    1. The sum of the ages of a father and his daughter is 38. Six years from now, the father will be four times as old as his daughter. Find the present age of each.<\/li>\n
                    2. A 90 kg mixture of two different types of nuts costs [latex]\\$370[\/latex]. If type A costs [latex]\\$3[\/latex] per kg and type B costs [latex]\\$5[\/latex] per kg, how many kg of each type were used?<\/li>\n
                    3. A student lab technician is combining a 10% sulfuric acid solution to 40 ml solution at 25% to dilute it to 15%. How much of the 10% solution does the student need to add?<\/li>\n<\/ol>\n

                      Midterm 2: Version B Answer Key<\/a><\/p>\n","protected":false},"author":90,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-1396","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":1392,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/chapter"}],"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\/chapters\/1396\/revisions"}],"predecessor-version":[{"id":1397,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1396\/revisions\/1397"}],"part":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1392"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1396\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1396"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapter-type?post=1396"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1396"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}