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Chapter 3: Real Numbers and the Coordinate Plane
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Square Roots The square root of a number is another number that when multiplied by itself is equal to the original number I know, so the
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Square Root If a number has a square root, it has two SO…
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Square roots Remember: positive x positive = positive negative x negative = negative Therefore… This is not a real number! (It is imaginary, but we are not getting into that)
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Perfect Squares When the square root comes out as a whole number it is a perfect square
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Use Perfect Squares to Estimate Other Square Roots NOTE: This number is irrational, it can not be written as a fraction and will not stop or repeat, just like Pi. This is true for all non-perfect squares.
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Rational Vs. Irrational Remember rational numbers can be written as a fraction – Repeating decimals – Integers (positive and negative whole numbers) – Fractions – Terminating decimals (the decimal stops) Irrational – Square roots that are not perfect squares – Decimals that don’t stop or repeat
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Square roots in Algebra The square root is the opposite of squaring a number Just like division undoes multiplication, the square root will undo squaring a number Remember to do order of operations backwards (easy operations first)
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Square Roots in Algebra Opposite of multiplying by 16 is dividing by 16 Calculate 816/16=51 Square root and squaring cancel out
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Homework Page 109 9-49 odd
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The Pythagorean Theorem It is a formula! a b c NOTE: The hypotenuse is always the longest side, and the side opposite the right angle NOTE: this only works for right triangles
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Using the Formula Just like every other formula, copy it down and list your variables 5cm 10cm c
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Substitute into the Formula
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Solve the Formula Don’t forget your units!
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Homework Page 114 3-24
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Pythagorean theorem with unknown Leg Variables (a) and (b) are interchangeable, But if you are given the hypotenuse and a leg, you need to find the other leg with algebra 9cm 3cm x Substitute into the formula
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Solving with algebra Opposite of adding 9 is subtracting 9 Don’t forget units!
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Tips Give yourself plenty of space to work Draw pictures to illustrate situations from word problems If the answer is not a perfect square, leave it under the radical sign ( )
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Homework Page 120 3-21
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Graphing in the Coordinate Plane Ordered Pairs: give the location of a point on my plane The first number is the x coordinate The second number is the y coordinate
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Pythagorean theorem with the Coordinate Plane See notes on Pythagorean Theorem for details on solving
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Homework Page 126 11-31
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Equations, Tables, and Graphs All three can be used to represent the same data
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Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)expression 00 1 2 3 4 x
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Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression 00 13 2 3 4 x
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Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression 00 13 26 3 4 x
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Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression 00 13 26 39 4 x
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Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression 00 13 26 39 412 x
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Suppose you save three dollars a week Table: Number of weeks (x) Total savings (y)Expression 00 13 26 39 412 xy
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Suppose you save three dollars a week Look for patterns. What do I do to one column to get the next? Number of weeks (x) Total savings (y)Expression 00 13 26 39 412 xy Rule: Multiply by 3
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Suppose you save three dollars a week Look for patterns. What do I do to one column to get the next? Number of weeks (x) Total savings (y)Expression 003(0) 133(3) 263(2) 393(3) 4123(4) xy3(x) Rule: Multiply by 3
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Graph It Number of weeks (x) Total savings (y) ExpressionOrdered Pair 003(0)(0,0) 133(3)(1,3) 263(2)(2,6) 393(3)(3,9) 4123(4)(4,12) xy3(x)(x,y) Plot these points on the coordinate plan and connect the dots with a straight line.
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For lines you only need 2 points
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Homework Page 133 5-18
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