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 helping their colossal constructions. 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 learn of the elemental kind of expressions for that functionality. Readers are inspired to ascertain the elemental kinds, see how they're built, and view the position of every part. through the textual content, there are instruments sections positioned on the ends of chapters to assist readers collect the abilities they should practice simple algebraic manipulations.
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Extra resources for Algebra: Form and Function
W/5 = 20 35. y − 5 = 20 36. 20 = 5 − x PROBLEMS 37. The value of a computer t years after it is purchased is: Value of the computer = 3500 − 700t. (a) What is value of the computer when it is purchased? (b) Write an equation whose solution is the time when the computer is worth nothing. 38. 25 each. Write an equation whose solution is the number of ice cream cones he can buy, and find the number. 39. Hannah has $100 in a bank account and deposits $75 more. Write an equation whose solution is the amount she needs to deposit for the balance to be $300, and find the amount.
Example 5 Solution Give a solution to each equation. x+1 =1 (a) 5 (c) 9 − z = z − 9 x−7 =0 3 3 (d) t − 5t2 + 5t − 1 = 0 (b) (a) The only way a fraction can equal one is for the numerator to equal the denominator. Therefore, x + 1 must be 5, so x = 4. (b) The only way a fraction can equal zero is for the numerator to be zero. Therefore x = 7. (c) The left side is the negative of the right side, so the equation requires a number to equal its own negative. The only such number is zero. So 9 − z and z − 9 are both zero, and z = 9.
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). 21. 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.
Algebra: Form and Function by Deborah Hughes-Hallett, William G. McCallum, Eric Connally
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