# some formulas that are not directly given that may or may not help

https://arbital.com/p/cramsatformulas

by 974 Oct 6 2018 updated Oct 6 2018

i oofed on the other one

Slope Formula:
$\frac {(y_2-y_1)}{(x_2-x_1)}$= $\frac{\Delta y}{\Delta x}=\frac {rise}{run}$

Equation of a Line:
$y=mx+b$

Midpoint Formula:
($\frac {(x_1+x_2)}{2}$, $\frac {(y_1+y_2)}{2}$)

Distance Formula:
$\sqrt {(x_2-x_1)^2+(y_2-y_1)^2}$

Length of an Arc:
$L_{arc}=(2πr)(\frac {xº}{360})$

Area of an Arc Sector:
$L_{arc sector}=(πr^2)(\frac {xº}{360})$

$x=\frac {-b \pm \sqrt {b^2-4ac}}{2a}$

Completing the Square:
$ax^2+bx=0 \rightarrow a(x+d)^2+e=0$
$d=\frac{b}{2a}$
$e=c-\frac{b^2}{4a}$

Trigonometry:
$sin(x)=\frac {o}{h}$
$cos(x)=\frac {a}{h}$
$tan(x)=\frac{o}{a}$

Arithmetic Sequences:
$t_1, t_1+d, t_1+2d, …$

Geometric Sequences:
$t_1, t_1\cdot r, t_1\cdot r^2,…$

Exponent Rules:
$x^a\cdot{x^b}=x^{a+b}$
$(x^a)^b=x^{a\cdot{b}}$
$x^0=1$
$\frac {x^a}{x^b}=x^{a-b}$
$(xy)^a=x^a\cdot{y^a}$
$\sqrt{xy}=\sqrt{x} \cdot {\sqrt{y}}$
$x^{-b}=\frac {1}{x^b}$

Foil:
$(x+a)(x+b)=x^2+(b+a)x+ab$

Difference of Squares:
$a^2-b^2=(a+b)(a-b)$

Factoring:
$a^2+2ab+b^2=(a+b)(a+b)$
$a^2-2ab+b^2=(a-b)(a-b)$

Pythagorean Theorem:
$a^2+b^2=c^2$