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Unit 1, 2.4 - Coggle Diagram

- - - - where all thee planes intersect
      - consistent dependent
        
        have infinite numbers of solutaion
        
        consistent independent
        
        all systems have one solution
      - Inconsistent variable
        
        where the systems have no solution
        
        Contradiction
        
        makes the equation of equality false
- - - - A,b,and, c are really numbers of algebraic expression.
      - equivalent expressions
      - a=b and a+c=b+c
      - Multiplication property of equality
        
        a,b,and c are real numbers
        
        c can't equal zero
        
        a=b and ac=bc
        
        Distributive property
        
        a(b+c)=ab+ac
        
        a,b,c are real numbers
      - least common denominator
        
        smallest multiple of all variables in an equation/expression
        
        Solving linear equations with fractions
        
        variables in the parentheses must stay the same when finding the lowest common denominator
        
        Solving linear equations involving Decimals
        
        Eliminate the decimal by using multiplication property of equality
        
        Rational Numbers
        
        quotient of two integers
        
        Rational expesstion
        
        quotient of 2 polynomials
        
        the denominator is greater than or equal to 1
        
        rational equation
        
        consist of one or more rational expressios
        
        one of the expressions is a ploynomial
        
        contains at least one expression in evolving and non-constant denominator
        
        restricted value
        
        2 more items...
- - - - read understand the problem
      - make a plan
      - carry out said plan
      - Check your work
  - - - a=1/2 h(a+b)
      - Distance formula
        
        d=rt distance=rate*time
        
        Time formula
        
        t=d/t time=distance/time
- - - - method of solving three linear equations
      - Elementary row operations
        
        results in a equivalent system
        
        Shorthand notation
        
        a method to help keep track of elementary row operations
        
        Augmented Matrix
        
        a way of writing elementary wow operations by dropping the variables
        
        Row echolon form
        
        when there is a diagonal of ones with zeroes below it
        
        Reduced row Echelon from
        
        when there are zeros above and below the diagonal of ones
        
        1 more item...
- - - - y=mx+b
      - m=slope
      - b=y intercept
    - - m=0 rise=0
      - y=b
    - - B=o run-0
      - graph is undefined
  - - - y-y1=m(x-x1)
      - Standard form
        
        Ax+by=c
        
        A,B can't both be zero
- - - - system has only one solution
      - lines intersect at a single point
      - Consistent dependent
        
        two equations can be represented by the same graph
        
        have infinite solutions
        
        Ordered pair notation
        
        a way of writing the solutions to a system
- - - - where the horizontal and vertical axis cross at a point called the origin
      - consist of 4 quadrants
      - Intercepts
        
        where the graph crosses or touches the axis
        
        always have a coordinate that is equal to zero
    - - a quadrilateral where the opposite sides are parallel
      - Pythagorean theorem
        
        a^2+b^2=c^2
        
        Distance formula
        
        d(A,B) = (x2-x1)2+(y2-y1)2