By Deborah Hughes-Hallett, William G. McCallum, Eric Connally
Shape is expounded to operate. An aircraft 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 aiding their big constructions. 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 provides a examine of the elemental kind of expressions for that functionality. Readers are inspired to envision the elemental kinds, see how they're developed, and look at the function of every part. in the course of the textual content, there are instruments sections positioned on the ends of chapters to assist readers collect the abilities they should practice uncomplicated algebraic manipulations.
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Additional info for Algebra: Form and Function
In Problems 113–115, write an equation whose solution is the given value. 113. The number of tons of wheat it can afford to buy if it spends a total of $100 million, wheat costs $300 per ton, and it must buy 5 fighter planes at $15 million each. 114. The price of fighter planes if it bought 3 of them, 10,000 tons of wheat at $500 a ton, and spent a total of $50,000,000. 115. The price of a ton of wheat if it buys 20 fighter planes and 15,000 tons of wheat for a total expenditure of $90,000,000, and a fighter plane costs 100,000 times a ton of wheat.
B) Is 8x − 4 equivalent to 2x − 1? 61. Which of the equations in parts (a)–(d) are equivalent to x−3 2x − (x + 3) = 4 + ? 10 Give reasons for your answers. x−3 (a) 2x − x + 3 = 4 + 10 64. −11 = √ 1 s 5 r = 16 5 1 = B 14 69. Suppose x = 5 is a solution to the equation b(x − r) = 3. Square both sides of this equation and then add 4 to both sides. Give the resulting equation and find a solution. 70. Show that x = 5 is a solution to both the equations 2x − 10 = 0 and (x − 3)2 − 4 = 0. Does this mean these equations are equivalent?
Rewrite the expression in Problem 73 in terms of w and q. In Problems 76–82, both a and x are positive. What is the effect of increasing a on the value of the expression? Does the value increase? Decrease? Remain unchanged? 76. ax + 1 77. x + a 78. x − a 79. 80. x + 1 a x +1 a 81. 5k (e) 10k 4 (f) 1 2k/5 Verify the identities in Problems 95–96. 95. 96. 1 (a 2 1 (a 2 + b) + 12 (a − b) = a + b) − 12 (a − b) = b 97. Find the expression for the volume of a rectangular solid in terms of its width w where the length l is twice the width and the height h is five more than the width.
Algebra: Form and Function by Deborah Hughes-Hallett, William G. McCallum, Eric Connally