By Deborah Hughes-Hallett, William G. McCallum, Eric Connally
Shape is expounded to operate. An aircraft wing has the shape it does as a result of its lifting functionality. The pillars of the Parthenon and the girders of a skyscraper are formed to the aim of helping their enormous buildings. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial version introduces each one function--linear, energy, quadratic, exponential, polynomial--and offers a learn of the elemental kind of expressions for that functionality. Readers are inspired to ascertain the elemental kinds, see how they're developed, and view the position of every part. in the course of the textual content, there are instruments sections put on the ends of chapters to assist readers collect the talents they should practice simple algebraic manipulations.
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Extra resources for Algebra: Form and Function
1 REORDERING AND REGROUPING Solution 31 Since the bike shop sells q bicycles during a normal month, and since that number triples during a sale month, it sells 3q bicycles during a sale month. Similarly, the price is (1/2)p during a sale month. Thus, 1 Revenue during sale month = (3q) p . 2 By regrouping and reordering the factors in this product we get Revenue during sale month = (3q) 1 p 2 1 3 = 3 · qp = qp. 5, times the original revenue. Example 3 In a population of 100 prairie dogs there are b births and d deaths over a one-year period.
If xyz = 100, find the value of (3x)(2y)(5z). x 22. If xyz = 20, find the value of (2z)( )(6y). 4 23. Rewrite the expression a + 2(b − a) − 3(c + b) without using parentheses. Simplify your answer. 24. A car travels 200 miles in t hours at a speed of r mph. If the car travels half as fast but three times as long, how far does it travel? ) (a) If in January 2009 the amount (in billions of gallons) flowing into the reservoir is A and the amount flowing out is B, write an expression for the amount of water in the reservoir at the end of January 2009.
B) Is the expression 2x + 6 equivalent to the expression x + 3? Solution (a) If we divide both sides of the first equation by 2, we have 2x + 6 = 10 2x + 6 10 = 2 2 x + 3 = 5. dividing both sides by 2 Therefore, the two equations are equivalent. Dividing both sides of an equation by 2 produces an equivalent equation. You can verify that x = 2 is the solution to both equations. (b) The expression 2x + 6 is not equivalent to x + 3. This can be seen by substituting x = 0 into each expression. The first expression becomes 2x + 6 = 2(0) + 6 = 6, but the second expression becomes x + 3 = 0 + 3 = 3.
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