By Earl Swokowski, Jeffery A. Cole
The newest variation within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well liked by teachers and scholars alike: its exposition is obvious, the time-tested workout units function numerous purposes, its uncluttered format is attractive, and the trouble point of difficulties is acceptable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage variation, 12E, successfully prepares scholars for extra classes in arithmetic via its first-class, time-tested challenge units.
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Additional info for Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition
S O L U T I O N If we write 6x 2 Ϫ 7x Ϫ 3 ϭ ͑ax ϩ b͒͑cx ϩ d͒, then the following relationships must be true: ac ϭ 6, bd ϭ Ϫ3, ad ϩ bc ϭ Ϫ7 and If we assume that a and c are both positive, then all possible values are given in the following table: a 1 6 2 3 c 6 1 3 2 Thus, if 6x 2 Ϫ 7x Ϫ 3 is factorable, then one of the following is true: 6x 2 6x 2 6x 2 6x 2 Ϫ Ϫ Ϫ Ϫ 7x 7x 7x 7x Ϫ Ϫ Ϫ Ϫ 3 3 3 3 ϭ ϭ ϭ ϭ ͑x ϩ b͒͑6x ϩ d͒ ͑6x ϩ b͒͑x ϩ d͒ ͑2x ϩ b͒͑3x ϩ d͒ ͑3x ϩ b͒͑2x ϩ d͒ We next consider all possible values for b and d.
025 E I3 or 2. 48 ϫ 10Ϫ4 Many calculators use scientific form in their display panels. For the number c ϫ 10n, the 10 is suppressed and the exponent is often shown preceded by the letter E. For example, to find ͑4,500,000͒2 on a scientific calculator, we could enter the integer 4,500,000 and press the x 2 (or squaring) key, obtaining a display similar to one of those in Figure 6. 025 ϫ 1013. Thus, ͑4,500,000͒2 ϭ 20,250,000,000,000. Calculators may also use scientific form in the entry of numbers.
7 (a) x is negative. Exer. 9–14: Rewrite the number without using the absolute value symbol, and simplify the result. 9 (a) ͉ Ϫ3 Ϫ 2 ͉ (b) ͉ Ϫ5 ͉ Ϫ ͉ 2 ͉ (c) ͉ 7 ͉ ϩ ͉ Ϫ4 ͉ (c) q is less than or equal to . 10 (a) ͉ Ϫ11 ϩ 1 ͉ (b) ͉ 6 ͉ Ϫ ͉ Ϫ3 ͉ (c) ͉ 8 ͉ ϩ ͉ Ϫ9 ͉ (d) d is between 4 and 2. 11 (a) ͑Ϫ5͉͒ 3 Ϫ 6 ͉ (b) ͉ Ϫ6 ͉͑͞Ϫ2͒ (c) ͉ Ϫ7 ͉ ϩ ͉ 4 ͉ (e) t is not less than 5. 12 (a) ͑4͉͒ 6 Ϫ 7 ͉ (b) 5͉͞ Ϫ2 ͉ (c) ͉ Ϫ1 ͉ ϩ ͉ Ϫ9 ͉ (b) y is nonnegative. 7 Ϫ 23 ͉ (c) ͉ 51 Ϫ 13 ͉ Exer. 15 – 18: The given numbers are coordinates of points A, B, and C, respectively, on a coordinate line.
Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition by Earl Swokowski, Jeffery A. Cole