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**Algebra Answers**

** **This page was last updated on
15-Jun-02

1. Begin with the expression in the innermost parentheses or brackets and work your way out. Simplify all numbers with exponents, working from left to right; then perform all multiplications and divisions from left to right; then perform all additions and subtractions, from left to right. **parentheses, exponents, multiply, divide, add, subtract **__Back__

2. A **set** is a collection of objects or things. *Ex: {2,4,6,8}*
A **union** of two sets A and B, written A U B, is the set consisting of all the elements that are in A __OR__ B. *Ex: if A={0,1,2} and B={2,3}, then A U B = {0,1,2,3}*

An **intersection** of two sets A and B, written A W B, is the set consisting of all the elements that are in A __AND__ B. *Ex: **if A={0,1,2} and B={2,3}, then A *W* B = {2}*

A is a **subset** of B, written A z B, if all the elements in set A are also in set B.

*Ex: if A={2,4} and B={1,2,3,4}, then A is a subset of B. *** **__Back__

3. {1,2,3,4,5...} ** **__Back__

4. {0,1,2,3,4,5...} ** **__Back__

5. {...-3,-2,-1,0,1,2,3...} ** **__Back__

6. {a/b, when a and b are integers and b does NOT = 0} *Ex: 3/4 is a real and rational number {...-3, -2, -1, 0, 3/4, 1, 2, 3...} *** **__Back__

7. {all sets of x, such that x is real, but not rational} *Ex: square roots are real and irrational *** **__Back__

8. {all sets of x, such that x is rational or x is irrational} *i.e., all numbers, rational and irrational *** **__Back__

9. {all sets of x, such that x is a positive integer greater than 1 whose only positive divisors are itself and 1} *i.e., {2,3,5,7,11...} *** **__Back__

10. a+b=b+a ab=ba ** **__Back__

11. a+(b+c)= (a+b)+c a(bc)=(ab)c ** **__Back__

12. a+0=a a*1=a ** **__Back__

13. a+(-a)=0 a(1/a)=1 ** **__Back__

14. a(b+c)=ab+ac ** **__Back__

15. a to the r+s power ** **__Back__

16. a to the r*s power ** **__Back__

17. a to the r power * b to the r power ** **__Back__

18. 1/a to the r power ** **__Back__

19. a to the r power / b to the r power ** **__Back__

20. a to the r-s power ** **__Back__

23. a squared + 2ab + b squared ** **__Back__

24. a squared - 2ab + b squared ** **__Back__

25. a squared - b squared ** **__Back__

26. (a+b)(a squared - ab + b squared) ** **__Back__

27. (a-b)(a squared + ab + b squared) ** **__Back__

28. ax squared + bx + c = 0 ** **__Back__

29. Each side = x; Perimeter = 4x; Area = x squared ** **__Back__

30. Length = L Width = W; Perimeter = 2L + 2W; Area = LW ** **__Back__

31. Three sides to a triangle are labelled a, b and c; the hypotenuse is h.
Perimeter = a + b + c; Area = 1/2bh ** **__Back__

32. x = 0.15 * 63 ** **__Back__

33. x * 42 = 21 ** **__Back__

34. c squared = a squared + b squared ** **__Back__

35. x = {-5, 5} ** **__Back__

36. ax + by = c ** **__Back__

37. Make y=0 in the linear equation ** **__Back__

38. Make x=0 in the linear equation ** **__Back__

39. m = (y2 - y1) / (x2 - x1) ** **__Back__

41. y - y1 = m (x - x1) ** **__Back__

42. Vertical lines have no slope ** **__Back__

43. Horizontal lines have 0 slope ** **__Back__

44. Parallel lines each have the same slope, i.e. m1 = m2 ** **__Back__

45. For perpendicular lines, the product of their slopes will be -1, i.e. m1*m2 = -1 ** **__Back__

47. Pi = C/d (circumference of a circle divided by the diameter) ** **__Back__

49. r = d/t, where d = distance and t = time ** **__Back__

50. d = rt, where r = rate of speed and t = time ** **__Back__