# how to use barcode in c#.net Final Exam in Software Generation QR Code 2d barcode in Software Final Exam

Final Exam
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148 If the discriminant in a quadratic equation is a negative real number, it means that (a) the equation has two different real roots (b) the equation has one real root with multiplicity 2 (c) the equation has one imaginary root with multiplicity 2 (d) the equation has two different imaginary or complex roots (e) the equation has no roots at all, real or complex 149 A mapping is a bijection if and only if it is (a) reflexive (b) a function (c) one-to-one and onto (d) a subset of its co-domain (e) transitive 150 Consider the following pair of equations as a two-by-two system: y = a1x + b1 and y = a2x + b2 where a1, a2, b1, and b2 are real numbers, and neither a1 nor a2 are equal to 0 What are the smallest and largest numbers of elements that the solution set of such a system can have Assume that the two equations are not identical, and are not some constant multiple of each other (a) None, and one (b) None, and two (c) None, and infinitely many (d) One, and infinitely many (e) Two, and infinitely many
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APPENDIX
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Worked-Out Solutions to Exercises: s 1 to 9
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These worked-out solutions do not necessarily represent the only way a problem can be figured out If you think you can solve a particular problem in a quicker or better way than you see here, by all means go ahead! But always check your work to be sure your alternative answer is correct
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1
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1 There are several ways to figure this out, but they re all a little messy You can count the days out loud and write hash marks on a sheet of paper, or you can use a calendar and write numerals on it day by day, starting with 0 on June 24 and working up If you want to avoid all that counting, you can figure out the number of days of interest in June, July, August, September, and October, and then add them up Remember that in any year, June has 30 days, July has 31 days, August has 31 days, and September has 30 days In June, you have 30 24 = 6 days of interest; in July you have all 31 days; in August you have all 31 days; in September you have all 30 days; in October you have 2 days of interest The total is therefore 6 + 31 + 31 + 30 + 2 = 100 days 2 Remember that 1 = I, 5 = V, 10 = X, 50 = L, and 100 = C The answers are as follows, broken down into sums for clarification (a) 200 = 100 + 100 = C + C = CC (b) 201 = 100 + 100 + 1 = C + C + I = CCI (c) 209 = 100 + 100 + 9 = C + C + IX = CCIX (d) 210 = 100 + 100 + 10 = C + C + X = CCX 3 Remember that M = 1,000, C = 100, X = 10, V = 5, and I = 1 The answers are as follows, broken down into sums for clarification (a) MMXX = 1,000 + 1,000 + 10 + 10 = 2,020 (b) MMXIX = 1,000 + 1,000 + 10 + 9 = 2,019
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