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Distance Formula

d=√(x₁-x₂)² + (y₁-y₂)²

(EX: Find distance between (5,6) and (1,3)

√(5-1)² + (6-3)²=

√(4)² + (3)²=

√16 + 9=

√25=

5=Distance

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Slope

Slope= Rise/Run=Change in Y/Change in X

(y₂-y₁/x₁-x₂)

(EX: Find slope of (5,6) and (1,3)

6-3/5-(-1)=

3/6=

1/2

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Slope Intercept

y=mx+b

Ex: y=2/3x + 5

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Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

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PEDMAS

Parenthesis, Exponents, Multiplication, Division, Add, Subtract.

EX: 9-2 x (5-3)² + 6÷3=

9-2 x (2)² + 6÷3=

9-2 x (4) +6÷3=

9-8 +2=

9-6=

3

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Quadratic Equation

ax²+bx+c= 0

EX: x²+ 9x+ 18=0

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Quadratic Formula

²x = −b ± √b²-4ac/2a

EX: Solve using quadratic formula x²+ 9x+ 18=0:

x= −9±√(9)² − 4(1)(18)/2(1)

−9 ± √81 − 72/2

−9 ± √9/2

−9 ± √3/2 = -9 + 3/2 and -9 -3/2

-9+3/2= -3 and -9-3/2= -6

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Percent Formula

Part=Percent x Whole

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Multiply Power Exponents

add exponents and keep the same base

EX: X₃ · X₂ = X₅

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Dividing Power Exponents

subtract exponents and keep same base

EX: X₄ ÷ X₂ = X₂

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Raising Power to Powers

multiply the exponents

EX: X² · X³ = X⁶

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Negative Exponent

X⁻ⁿ = 1/Xⁿ

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FOIL

First, Outside, Inside and Last.

EX: (x-3) + (x+5) =

x² + 5x -3x -15=

x² + 2x-15

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Factoring Difference of squares

a²-b² = (a-b) (a+b)

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Area of a Triangle

area= ½ (base)(height)

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Pythagorean Theorem

for all right triangles

(leg₁)² + (leg₂)² = (hypotenuse)² (a²+b²=c²)

Special Triangles

3-4-5

30-60-90

5-12-13

45-45-90

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Area of rectangle

area= length x width

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Area of parallelogram

area= base x height

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Area of square

area = (side)²

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Circumference of a circle

area = 2πr

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