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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
