**E.12**

47. Solve the inequality x^{2} - x > 12.

**Answer: **

48. Solve the inequality x^{3} - x^{2} ≤ 6x.

**Answer: **

49. Solve the inequality
.

**Answer:** [-2, 1)

50. Solve the inequality and write your answer in interval notation,

**Answer: **(-1/4, 0)

51. A Web-based embroidery company makes monogrammed napkins. The pro t
associated with

producing x orders of napkins is governed by the equation

P(x) = -x^{2} + 130x - 3000

Determine how many orders the company should accept to make a pro t.

**Answer:** 31 to 99 orders will yield a pro t. (i.e. (30, 100)).

**E.13**

52. State the order of the matrix 2

**Answer:** 3 x 2, (i.e 3 rows by 2 columns )

53. Solve for the indicated variables.

**Answer:** x = 6, y = 3

54. Let and
. Find 2A - 3B and BA.

**Answer:** , and
.

55. The IRS allows and individual to deduct business expenses in the following
way: $0.45 per

mile driven, 50% of entertainment cost, and 100% of actual expenses. Represent
these deductions as

a row matrix A. In 2006, Joe had the following business expenses: $2, 700 in
entertainment, $15, 200

actual expenses, and he drove 7523 miles. Represent Joe's expenses as a column
matrix B. Multiply

these matrices (AB) to find the total amount of business expenses Joe can claim on
his 2006 tax form.

**Answer: .**

56. Find the inverse (if it exists) of the matrix

**Answer:**

**E.14
**

57. Find the fifth term in the expansion of (s - 3y)

58. Apply the binomial theorem to expand (2z - 3y)

59. The 54th and 4th term of an arithmetic sequence are -61 and 64, respectively. Find the 23rd

term in the sequence.

60. Find the sum of the first 11 terms of the Arithmetic sequence 9, 17, 25, 33, ...

61. Find the first four terms and the 10th term of the sequence given by .

62. Give the first four terms of the geometric sequence for which = -5 and r = 4:

63. Find the next three terms of the geometric sequence 27,-9, 3,-1, ...

64. For the sequence . write a formula for the general term an:

65. Find the infinite sum 0.5 + 0.05 + 0.005 +... .

66. Find the sum of the first seven terms of the sequence

67. Use

3x - 4y = 1

4x - 2y = 8

68. Solve the system of equations by substitution or
addition method:

x + y + z = 0

2x + z = -1

x - y - z = 2

**
Answer:** x = 1, y = 2, z = -3

69. Solve the system by the method of your choice:

2u + 5v = 7

3u - v = 5

70. A Honda Accord gets approximately 26 mpg on the highway and 19 mpg in the city. You drove

349.5 miles on a full 16 gallon tank. Assuming you drove on both highway and city, approximately

how many miles did you drive in the city and how many on the highway?

71. Find the determinant

72. Prove by mathematical induction that, for all positive integers n,

STEP 1. First we show that the formula above holds true when n = 1, i.e.

STEP 2. Now we assume that the formula above holds true
for any k < n, that is

STEP 3. If we can show that the formula above holds for k + 1 term, we are done.
So, adding

k + 1 to both sides in step 2 we get,

note that the right hand side is the value
when (k + 1) is substituted for n.

Hence if the formula is true for k, we have proved it is also true for k + 1,
but since k is any

positive integer the formula is true for ALL positive integers n.

...Please see your instructor or tutor for a more detailed reasoning.

**Extras:**

73. Find the center and radius given the following equation of a circle:

x^{2} + y^{2} + 6x + 2y + 6 = 0

**Answer:** Center: (-3,-1) radius: r = 2

74. Use the Remainder Theorem to find P(-5) if P(x) = x^{6} + 6x^{5} + 5x^{3} - 6x^{2} - 24

**Answer:** P(-5) = -3924

75. Find the sum

**Answer: **

***NOTE: **The problems in this document are a
selection of problems from many sources, including College Algebra textbooks,
Mymathlab,

Wileyplus and East field College math faculty. This document should give you an
idea of the topics you need know after completing College

Algebra, this document does not intend to give information on any type of
examination, including the final exam.