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Algebra Answers

 This page was last updated on 15-Jun-02
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 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

 21.  a Back

 22.  1 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

 40.  y = mx + b 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

 46.  -1 Back

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

 48.  C = Pi(d) Back

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

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

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