Mary Jane Sterling - Pre-Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

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31–40Graph the inequality.

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41–50Solve by using the necessary formula.

41. Find the slope of the line through the points (−2, 3) and (4, 9).

42. Find the slope of the line through the points (−4, −3) and (−6, 2).

43. Find the slope of the line through the points (4, −3) and (4, −7).

44. Find the slope of the line through the points (−2, −9) and (2, −9).

45. Find the distance between the points (−8, −1) and (−2, 7).

46. Find the distance between the points (0, 16) and (7, −8).

47. Find the distance between the points (6, −5) and (−4, 3).

48. Find the midpoint of the segment between the points (−5, 2) and (7, −8).

49. Find the midpoint of the segment between the points (6, 3) and (−4, −4).

50. Find the midpoint of the segment between the points and .

51–60Use an appropriate formula to compute the indicated value.

51. Find the perimeter of triangle ABC, whose vertices are A (1, 1), B (1, 4), and C (5, 1).

52. Find the perimeter of the parallelogram DEFG, whose vertices are D (0, 10), E (9, 13), F (11, 7), and G (2, 4).

53. Find the center of the rhombus HJKL, whose vertices are H (0, 3), J (4, 6), K (8, 3), and L (4, 0).

54. Determine which type(s) of triangle ABC is if the vertices are A (1, 1), B (4, 5), and C (9, −5).

55. Determine which type of triangle ABC is if the vertices are A (0, 0), B (0, 12), and C .

56. Find the length of the altitude of triangle ABC, drawn to side AC, with vertices A (0, 0), B (5, 12), and C (21, 0).

57. Find the length of the altitude of triangle DEF, drawn to side DF, with vertices D (2, 3), E (2, 12), and F (42, 3).

58. Find the area of the parallelogram PQRS with vertices P (4, 7), Q (7, 12), R (15, 12), and S (12, 7).

59. Find the area of circle A if the endpoints of its diameter are at (6, 13) and (−8, 21).

60. Find the area of triangle ABC with vertices A (0, 0), B (5, 12), and C (14, 0).

Chapter 2

The object of solving equations and inequalities is to discover which number or numbers will create a true statement in the given expression. The main techniques you use to find such solutions include factoring, applying the multiplication property of zero, creating sign lines, finding common denominators, and squaring both sides of an equation. Your challenge is to determine which techniques work in a particular problem and whether you have a correct solution after applying those techniques.

In this chapter, you’ll work with equations and inequalities in the following ways:

Writing inequality solutions using both inequality notation and interval notation

Solving linear and quadratic inequalities using a sign line

Determining the solutions of absolute value equations and inequalities

Taking on radical equations and checking for extraneous roots

Rationalizing denominators as a method for finding solutions

Keep in mind that when solving equations and inequalities, your challenges will include

Factoring trinomials correctly when solving quadratic equations and inequalities

Choosing the smallest exponent when the choices include fractions and negative numbers

Assigning the correct signs in intervals on the sign line

Recognizing the solution when a factor of the expression is x

Determining which solutions are viable and which are extraneous

Squaring binomials correctly when working with radical equations

Finding the correct format for a binomial’s conjugate

61–70Write the expression using the indicated notation.

61. Write the expression in interval notation.

62. Write the expression in interval notation.

63. Write the interval notation as an inequality expression.

64. Write the interval notation as an inequality expression.