By Deborah Hughes-Hallett, William G. McCallum, Eric Connally

Shape is expounded to operate. An plane wing has the shape it does due to its lifting functionality. The pillars of the Parthenon and the girders of a skyscraper are formed to the aim of assisting their substantial buildings. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial variation introduces every one function--linear, energy, quadratic, exponential, polynomial--and offers a research of the elemental type of expressions for that functionality. Readers are inspired to check the elemental types, see how they're built, and think about the function of every part. through the textual content, there are instruments sections positioned on the ends of chapters to assist readers gather the abilities they should practice simple algebraic manipulations.

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Extra resources for Algebra: Form and Function

Example text

T + 3 = t2 + 9, t = 3 11. x+3 = x2 −9, x = −3 12. x + 3 = x2 − 9, x = 4 13. 14. a+3 a−3 = 1, a = 0 3+a = 1, a = 0 3−a 21. Which of the following are equations? (a) (b) (c) (d) 3(x + 5) = 6 − 2(x − 5) ax2 + bx + c = 0 5(2x − 1) + (5 − x)(x + 3) t = 7(t + 2) − 1 22. (a) Construct a table showing the values of the expression 1 + 5x for x = 0, 1, 2, 3, 4. (b) For what value of x does 1 + 5x = 16? 15. 4(r − 3) = 4r − 3, r = 1 23. (a) Construct a table showing the values of the expression 3 − a2 for a = 0, 1, 2, 3, 4.

3x − 10 = 20 3x = 30 add 10 to both sides x = 10 divide both sides by 3. We check to see that 10 is a solution: 3(10) − 10 = 30 − 10 = 20. (b) In the expression on the left side of the equal sign, we first add 3 to x and then multiply by 2. To solve for x in the equation, we undo these operations in the reverse order. We first divide by 2 and then subtract 3 from both sides to produce equivalent equations. 2(x + 3) = 50 x + 3 = 25 divide both sides by 2 x = 22 subtract 3 from both sides. We check to see that 22 is a solution: 2(22 + 3) = 2(25) = 50.

5 times their weight in pounds, w, divided by the square of their height in inches, h. 4. The volume of a cone with radius r and height h is represented by the expression Volume of cone = 1 2 πr h. 3 Which has greater volume: a short fat cone with height 2 and radius 3 or a tall thin cone with height 5 and radius 1? The surface area of a cylinder with radius r feet and height h feet is 2πr 2 + 2πrh square feet. In Exercises 5–8, find the surface area of the cylinder with the given radius and height.

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