{"id":1134,"date":"2015-11-12T18:35:31","date_gmt":"2015-11-12T18:35:31","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=1134"},"modified":"2017-03-31T22:10:13","modified_gmt":"2017-03-31T22:10:13","slug":"solutions-48","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-48\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\r\n\"Graph\r\n\r\n2.\u00a0Possible answers include [latex]\\left(-3,7\\right)[\/latex], [latex]\\left(-6,9\\right)[\/latex], or [latex]\\left(-9,11\\right)[\/latex].\r\n\r\n3.\r\n\"\"\r\n\r\n4.\u00a0[latex]\\left(16,\\text{ 0}\\right)[\/latex]\r\n\r\n5. a.\u00a0[latex]f\\left(x\\right)=2x[\/latex] <\/span>\r\nb. [latex]g\\left(x\\right)=-\\frac{1}{2}x[\/latex]<\/span>\r\n\r\n6.\u00a0[latex]y=-\\frac{1}{3}x+6[\/latex]\r\n\r\n7.\r\n

a.\u00a0[latex]\\left(0,5\\right)[\/latex]<\/p>\r\n

b. [latex]\\left(5,\\text{ 0}\\right)[\/latex]<\/p>\r\n

c. Slope -1<\/p>\r\n

d. Neither parallel nor perpendicular<\/p>\r\n

e. Decreasing function<\/p>\r\n

f. Given the identity function, perform a vertical flip (over the t<\/em>-axis) and shift up 5 units.<\/p>\r\n\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0The slopes are equal; y-intercepts are not equal.\r\n\r\n3.\u00a0The point of intersection is [latex]\\left(a,a\\right)[\/latex]. This is because for the horizontal line, all of the y<\/em>\u00a0coordinates are\u00a0a<\/em>\u00a0and for the vertical line, all of the x<\/em>\u00a0coordinates are a<\/em>. The point of intersection will have these two characteristics.\r\n\r\n5.\u00a0First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation [latex]y=mx+b[\/latex] and solve for b<\/em>. Then write the equation of the line in the form [latex]y=mx+b[\/latex] by substituting in m<\/em>\u00a0and b<\/em>.\r\n\r\n7.\u00a0neither parallel or perpendicular\r\n\r\n9.\u00a0perpendicular\r\n\r\n11.\u00a0parallel\r\n\r\n13.\u00a0[latex]\\left(-2\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 4}\\right)[\/latex]\r\n\r\n15.\u00a0[latex]\\left(\\frac{1}{5}\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 1}\\right)[\/latex]\r\n\r\n17.\u00a0[latex]\\left(8\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, }28\\right)[\/latex]\r\n\r\n19.\u00a0[latex]\\text{Line 1}: m=8 \\text{ Line 2}: m=-6 \\text{Neither}[\/latex]\r\n\r\n21.\u00a0[latex]\\text{Line 1}: m=-\\frac{1}{2} \\text{ Line 2}: m=2 \\text{Perpendicular}[\/latex]\r\n\r\n23.\u00a0[latex]\\text{Line 1}: m=-2 \\text{ Line 2}: m=-2 \\text{Parallel}[\/latex]\r\n\r\n25.\u00a0[latex]g\\left(x\\right)=3x - 3[\/latex]\r\n\r\n27.\u00a0[latex]p\\left(t\\right)=-\\frac{1}{3}t+2[\/latex]\r\n\r\n29.\u00a0[latex]\\left(-2,1\\right)[\/latex]\r\n\r\n31.\u00a0[latex]\\left(-\\frac{17}{5},\\frac{5}{3}\\right)[\/latex]\r\n\r\n33.\u00a0F\r\n\r\n35. C\r\n\r\n37. A\r\n\r\n39.\r\n\"\"\r\n\r\n41.\r\n\"\"\r\n\r\n43.\r\n\"\"\r\n\r\n45.\r\n\"\"\r\n\r\n47.\r\n\"\"\r\n\r\n49.\r\n\"\"\r\n\r\n51.\r\n\"\"\r\n\r\n53.\r\n\"\"\r\n\r\n55.\r\n\"\"\r\n\r\n57.\r\n\"\"\r\n\r\n59.\u00a0[latex]g\\left(x\\right)=0.75x - 5.5\\text{}[\/latex] 0.75\u00a0[latex]\\left(0,-5.5\\right)[\/latex]\r\n\r\n61.\u00a0[latex]y=3[\/latex]\r\n\r\n63.\u00a0[latex]x=-3[\/latex]\r\n\r\n65.\u00a0no point of intersection\r\n\r\n67.\u00a0[latex]\\left(\\text{2},\\text{ 7}\\right)[\/latex]\r\n\r\n69.\u00a0[latex]\\left(-10,\\text{ }-5\\right)[\/latex]\r\n\r\n71.\u00a0[latex]y=100x - 98[\/latex]\r\n\r\n73.\u00a0[latex]x<\\frac{1999}{201}x>\\frac{1999}{201}[\/latex]\r\n\r\n75.\u00a0Less than 3000 texts\r\n\r\n\u00a0","rendered":"

Solutions to Try Its<\/h2>\n

1.
\n\"Graph<\/p>\n

2.\u00a0Possible answers include [latex]\\left(-3,7\\right)[\/latex], [latex]\\left(-6,9\\right)[\/latex], or [latex]\\left(-9,11\\right)[\/latex].<\/p>\n

3.
\n\"\"<\/p>\n

4.\u00a0[latex]\\left(16,\\text{ 0}\\right)[\/latex]<\/p>\n

5. a.\u00a0[latex]f\\left(x\\right)=2x[\/latex] <\/span>
\nb. [latex]g\\left(x\\right)=-\\frac{1}{2}x[\/latex]<\/span><\/p>\n

6.\u00a0[latex]y=-\\frac{1}{3}x+6[\/latex]<\/p>\n

7.<\/p>\n

a.\u00a0[latex]\\left(0,5\\right)[\/latex]<\/p>\n

b. [latex]\\left(5,\\text{ 0}\\right)[\/latex]<\/p>\n

c. Slope -1<\/p>\n

d. Neither parallel nor perpendicular<\/p>\n

e. Decreasing function<\/p>\n

f. Given the identity function, perform a vertical flip (over the t<\/em>-axis) and shift up 5 units.<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0The slopes are equal; y-intercepts are not equal.<\/p>\n

3.\u00a0The point of intersection is [latex]\\left(a,a\\right)[\/latex]. This is because for the horizontal line, all of the y<\/em>\u00a0coordinates are\u00a0a<\/em>\u00a0and for the vertical line, all of the x<\/em>\u00a0coordinates are a<\/em>. The point of intersection will have these two characteristics.<\/p>\n

5.\u00a0First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation [latex]y=mx+b[\/latex] and solve for b<\/em>. Then write the equation of the line in the form [latex]y=mx+b[\/latex] by substituting in m<\/em>\u00a0and b<\/em>.<\/p>\n

7.\u00a0neither parallel or perpendicular<\/p>\n

9.\u00a0perpendicular<\/p>\n

11.\u00a0parallel<\/p>\n

13.\u00a0[latex]\\left(-2\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 4}\\right)[\/latex]<\/p>\n

15.\u00a0[latex]\\left(\\frac{1}{5}\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, 1}\\right)[\/latex]<\/p>\n

17.\u00a0[latex]\\left(8\\text{, }0\\right)[\/latex] ; [latex]\\left(0\\text{, }28\\right)[\/latex]<\/p>\n

19.\u00a0[latex]\\text{Line 1}: m=8 \\text{ Line 2}: m=-6 \\text{Neither}[\/latex]<\/p>\n

21.\u00a0[latex]\\text{Line 1}: m=-\\frac{1}{2} \\text{ Line 2}: m=2 \\text{Perpendicular}[\/latex]<\/p>\n

23.\u00a0[latex]\\text{Line 1}: m=-2 \\text{ Line 2}: m=-2 \\text{Parallel}[\/latex]<\/p>\n

25.\u00a0[latex]g\\left(x\\right)=3x - 3[\/latex]<\/p>\n

27.\u00a0[latex]p\\left(t\\right)=-\\frac{1}{3}t+2[\/latex]<\/p>\n

29.\u00a0[latex]\\left(-2,1\\right)[\/latex]<\/p>\n

31.\u00a0[latex]\\left(-\\frac{17}{5},\\frac{5}{3}\\right)[\/latex]<\/p>\n

33.\u00a0F<\/p>\n

35. C<\/p>\n

37. A<\/p>\n

39.
\n\"\"<\/p>\n

41.
\n\"\"<\/p>\n

43.
\n\"\"<\/p>\n

45.
\n\"\"<\/p>\n

47.
\n\"\"<\/p>\n

49.
\n\"\"<\/p>\n

51.
\n\"\"<\/p>\n

53.
\n\"\"<\/p>\n

55.
\n\"\"<\/p>\n

57.
\n\"\"<\/p>\n

59.\u00a0[latex]g\\left(x\\right)=0.75x - 5.5\\text{}[\/latex] 0.75\u00a0[latex]\\left(0,-5.5\\right)[\/latex]<\/p>\n

61.\u00a0[latex]y=3[\/latex]<\/p>\n

63.\u00a0[latex]x=-3[\/latex]<\/p>\n

65.\u00a0no point of intersection<\/p>\n

67.\u00a0[latex]\\left(\\text{2},\\text{ 7}\\right)[\/latex]<\/p>\n

69.\u00a0[latex]\\left(-10,\\text{ }-5\\right)[\/latex]<\/p>\n

71.\u00a0[latex]y=100x - 98[\/latex]<\/p>\n

73.\u00a0[latex]x<\\frac{1999}{201}x>\\frac{1999}{201}[\/latex]<\/p>\n

75.\u00a0Less than 3000 texts<\/p>\n

\u00a0<\/p>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
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