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

Shape is expounded to operate. An plane 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 assisting their substantial buildings. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial variation introduces each 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 varieties, see how they're built, 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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X + 1) + (x + 2) + (x + 3) 18. (2x)(5x) + (3x)(2x) + 5(3x) + x(3x) PROBLEMS 19. If a + b + c = 12, find the value of 25. The area of a rectangle is 50 square meters. If the length is increased by 25% and the width is increased by 10%, what is the new area? (a + 5) + (b − 3) + (c + 8). 26. Quabbin Reservoir in Massachusetts provides much of Boston’s water. At the start of 2009 the reservoir contained 412 billion gallons of water. 20. If x + y + z = 25, find the value of (y − 10) + (z + 8) + (x − 5).

10. 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.

How much money will they have left after seeing two movies? Can they afford to see a third movie? An airline has four different types of jet in its fleet: • p 747s with a capacity of 400 seats each, • q 757s with a capacity of 200 seats each, • r DC9s with a capacity of 120 seats each, and • s Saab 340s with a capacity of 30 seats each. Answer Problems 102–103 given this information. 102. Write an expression representing the airline’s total capacity (in seats). 103. To cut costs, the airline decides to maintain only two types of airplanes in its fleet.