Classwork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations


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1 Classwork #0: Final Review: Solving Equations, Word Problems, Linear Equations, Sstems of Linear Equations Solving Equations: Isolate the variable! Things to watch for: when ou have parentheses the inequalit sign when or b a negative 0 = 0 means 0 = means Solve. If it is an inequalit, include a graph..) w w.) (m + ) = .).) v + <  or v + <.) m = m + m.) 0 a = ( a) Solving Word Problems Use a chart! Distance Problems D = R T Same direction Opposite direction Round trip Miture Problems Volume %/$ = amount Volumes: and (total).) Two cars leave town at the same time heading in the same direction. One car travels 0mph and the other travels at 0mph. After how man hours will the be 0 miles apart? Distance Rate Time Slow Car Fast Car
2 .) Two cars leave town at the same time heading in the opposite direction. One car travels 0mph and the other travels at 0mph. After how man hours will the be 0 miles apart? Distance Rate Time Slow Car Fast Car.) Raisins cost $ per pound and nuts cost $ per pound. How man pounds of each should ou use to make a 0lb miture that costs $ per pound? Raisins Nuts Miture Equations of Lines: Start with slope: m = Parallel means slope Perpendicular means, slope Plug in m and point (, ) into Solve for b Plug m and b into Covert to standard form, if necessar 0.) Find the slope of the line passing through the pair of points: a) (, ) and (, ) b) (, ) and (, ) SlopeIntercept Form Standard Form Intercepts
3 .) Write the equation in slopeintercept form. State the slope (m) and intercept (b).) Write the equation of the line with slope of.) Graph the line b finding the slope and intercept..) Write the equation in standard form and find the and intercepts. and intercept in standard form..) Graph the line b finding the and intercepts ) Write the equation of the line with slope  and passing through the point (, ) in standard form..) Write the equation of the line passing through the points (, ) and (, ) in slopeintercept form.) Write the equation of the line parallel to.) Write the equation of the line perpendicular =  + and passing through the point (, ) in to = and passing through the point (, ) standard form. in standard form. 0
4 .) Solve for a and b using the substitution method a b a b.) Solve for and b using the addition/elimination method: Classwork #: Rules of Eponents When ou are Adding/Subtracting terms  Onl combine the like terms  Leave variables alone  Onl add/subtract coefficients E: + + Multipling Terms  Multipling coefficients together  Add eponents on the like variable epressions E: (a b )(a b ) Dividing Terms E:  Divide/reduce coefficients  Subtract eponents on like variables st st Raising Terms to a Power  Raise the coefficient to the power  Multipl the eponents E: (w z ) Watch out for negative eponents: E: p  E: (w  )(w  ) E: Simplif: Leave all answers in positive eponents.) (bc )(b c)(b c  ).) (m  n ).) ( ) ( )
5 .) mn mn.) z z.) t r
6 Absolute Value: Isolate the, and write equations! Things to watch for:  In an inequalit, ou must:  get the on the left side  if it is < or, it is a (a sandwich)  if it is > or, it is a (a sandwich) Solve each absolute value equalit:.) p.) r Solve and graph each absolute value inequalit:.) d.) k Graphing Linear Inequalities  Get alone  Graph using slope and intercept  Line: > or < means or means  Shading: < or means > or means.) Graph the linear inequalit:
7 .) Graph the set of linear inequalities and shade the solution region. Square Roots:  Adding/Subtracting: You can onl add and subtract terms with like radicals  0 Multipling: multipl outside numbers together, and inside numbers together. Then reduce Dividing: ou can t have a radical on the Simplif:. g g h.).) h 0 gh.. b.).).) 0. m.) Solve for b: b For , solve and check our solution(s):.).)
8 Classwork #: Scientific Notation Converting from Standard Notation to Scientific Notation  Place the decimal point so that ou have digit to the left of the decimal point..  Count the number of places ou need to move the decimal to get back to our original number. This number will be the eponent on the 0.  If ou are moving to the left, this eponent will be  If ou are moving to the right, this eponent will be Write in scientific notation:.),000.) ) 0.0.). 0.) Multipling Numbers in Scientific Notation  Multipl coefficients (decimal terms)  Add the eponents  Check that our answer is still in scientific notation.) (. 0 )(.0 0 ).) (. 0  )(. 0  ).) (. 0  )(. 0 ) Dividing Numbers in Scientific Notation  Divide coefficients (decimal terms)  Subtract the eponents  Check that our answer is still in scientific notation.) ) ) Taking Numbers in Scientific Notation to a Power  Raise the coefficient to the given power  Multipl the eponents  Check that our answer is still in scientific notation.) (. 0 ).) ( 0  ) .) ( 0 ).) ( 0  )
9 Solve b factoring.) k k =.) m = 0 Solve b using square roots.) w =.) = 0 0.) m = 0.) ( 0) = 0 Solve b using the quadratic formula: Write down the formula:.) 0 + = 0.) m +m = Without graphing, find the information for each parabola:.) f ( ).) f ( ) Verte: ; Ais of Smmetr: What is the direction of opening? Is the verte a ma or min? Wider or narrower than =? Simplif:.) Verte: ; Ais of Smmetr: What is the direction of opening? Is the verte a ma or min? Wider or narrower than =?.)
10 .) Divide using long division: 0.) Subtract:.) Add:.) Solve:.) Solve: t t.) John can weed the garden in hours. His wife can weed the same garden in hours. How long would it take them to weed if the worked together? John John s Wife
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