By Ron Larson
This market-leading textual content maintains to supply scholars and teachers with sound, continually established causes of the mathematical thoughts. Designed for a one-term direction that prepares scholars for extra learn in arithmetic, the hot 8th variation keeps the positive aspects that experience consistently made collage Algebra a whole resolution for either scholars and teachers: fascinating functions, pedagogically potent layout, and leading edge expertise mixed with an abundance of rigorously constructed examples and exercises.
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Extra resources for College Algebra (8th Edition)
12x 8x x 115. ENGINEERING A uniformly distributed load is placed on a one-inch-wide steel beam. 71͒ 2. 93͒ 2. 112. GEOMETRY Find the area of the shaded region in each figure. Write your result as a polynomial in standard form. (a) (b) 4x − 2 4x x 18 ft 4x (a) Use the bar graph to estimate the difference in the safe loads for these two beams when the span is 12 feet. (b) How does the difference in safe load change as the span increases? 3x 10x Safe load (in pounds) S 10x (c) (d) 4x + 2 x−1 2x + 8 x−1 4x + 2 x+4 1600 1400 1200 1000 800 600 400 200 6-inch beam 8-inch beam x x+4 2x + 8 4 8 12 Span (in feet) 16 36 Chapter P Prerequisites 116.
The edge of each cut-out square is x inches. Find the volume of the box when x ϭ 1, x ϭ 2, and x ϭ 3. 20 − 2x 16 in. 16 − 2x x x Volume of a Box x x Solution The volume of a rectangular box is equal to the product of its length, width, and height. From the figure, the length is 20 Ϫ 2x, the width is 16 Ϫ 2x, and the height is x. So, the volume of the box is Volume ϭ ͑20 Ϫ 2x͒͑16 Ϫ 2x͒͑x͒ 20 in. ϭ ͑320 Ϫ 72x ϩ 4x 2͒͑x͒ ϭ 320x Ϫ 72x 2 ϩ 4x 3. 13 When x ϭ 1 inch, the volume of the box is Volume ϭ 320͑1͒ Ϫ 72͑1͒2 ϩ 4͑1͒3 ϭ 252 cubic inches.
3x 2 y Ϫ2 y ϭ 3x 2 2 y2 ϭ 4 9x Note how Property 3 is used in the first step of this solution. The fractional form of this property is a b Ϫm 17 Rewriting with Positive Exponents Rewrite each expression with positive exponents. a. xϪ1 b. 1 3xϪ2 c. 12a3bϪ4 4aϪ2b 2 Ϫ2 d. 3xy Solution a. xϪ1 ϭ 1 x Property 3 1 1͑x 2͒ x 2 ϭ ϭ Ϫ2 3x 3 3 3 Ϫ4 3 12a b 12a и a2 ϭ c. 4aϪ2b 4b и b4 The exponent Ϫ2 does not apply to 3. b. 2 Ϫ2 d. 3xy . b ϭ a Exponents and Radicals m Property 3 ϭ 3a5 b5 Property 1 ϭ 3Ϫ2͑x 2͒Ϫ2 yϪ2 Properties 5 and 7 ϭ 3Ϫ2xϪ4 yϪ2 Property 6 ϭ y2 32x 4 Property 3 ϭ y2 9x 4 Simplify.
College Algebra (8th Edition) by Ron Larson