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Unit 13 Common Formulas and Equations

Area of a Rectangle

$A = lw$

⠠⠁⠀⠐⠶⠀⠇⠺

Area of a Triangle

$A\ = \ \ \frac{1}{2}bh$

⠠⠁⠀⠐⠶⠀⠼⠁⠌⠃⠰⠃⠓

Area of a Circle

$A = \pi r^{2}$

⠠⠁⠀⠐⠶⠀⠨⠏⠗⠰⠔⠼⠃

Circumference of a Circle

$C = 2\pi r$

⠰⠠⠉⠀⠐⠶⠀⠼⠃⠨⠏⠗

Distributive Law

$a(b + c)\ = \ ab + ac$

⠁⠐⠣⠃⠐⠖⠉⠐⠜⠀⠐⠶⠀⠁⠃⠐⠖⠁⠉

Pythagorean Theorem

$a^{2} + b^{2}\ = {\ c}^{2}$

⠁⠰⠔⠼⠃⠐⠖⠃⠔⠼⠃⠀⠐⠶⠀⠉⠰⠔⠼⠃

Product of a Sum and Difference

$(x - y)(x + y)\ = {\ x}^{2} - y^{2}$

⠐⠣⠭⠐⠤⠽⠐⠜⠐⠣⠭⠐⠖⠽⠐⠜⠀⠐⠶⠀⠭⠰⠔⠼⠃⠐⠤⠽⠔⠼⠃

First Law of Exponents

$a^{n}a^{m}\ = {\ a}^{n + m}$

⠰⠰⠁⠔⠝⠁⠔⠍⠀⠐⠶⠀⠁⠰⠔⠣⠝⠐⠖⠍⠜

Second Law of Exponents

$(ab)^{n}\ = {\ a}^{n}b^{n}$

⠐⠣⠁⠃⠐⠜⠰⠔⠝⠀⠐⠶⠀⠰⠰⠁⠔⠝⠃⠔⠝

Fractional Addition

$\frac{a}{b} + \frac{c}{d}\ = \ \frac{ad + bc}{bd}$

⠰⠰⠷⠁⠨⠌⠃⠾⠐⠖⠷⠉⠨⠌⠙⠾⠀⠐⠶⠀⠰⠰⠷⠁⠙⠐⠖⠃⠉⠨⠌⠃⠙⠾

Fractional Multiplication

$\frac{a}{b} \times \frac{c}{d}\ \ = \ \ \frac{ac}{bd}$

⠰⠰⠷⠁⠨⠌⠃⠾⠐⠦⠷⠉⠨⠌⠙⠾⠀⠐⠶⠀⠰⠰⠷⠁⠉⠨⠌⠃⠙⠾

Fractional Exponent

$a^{\frac{1}{n}}\ = \ \sqrt[n]{a}$

⠁⠰⠔⠷⠼⠁⠨⠌⠝⠾⠀⠐⠶⠀⠰⠰⠩⠔⠣⠝⠜⠁⠬

Negative Exponent

$a^{- n}\ = \ \frac{1}{a^{n}}$

⠰⠰⠁⠔⠣⠐⠤⠝⠜⠀⠐⠶⠀⠰⠷⠼⠁⠨⠌⠁⠔⠝⠾

Power of a Power

$\left( a^{n} \right)^{m}\ = \ a^{nm}$

⠰⠰⠐⠣⠁⠔⠝⠐⠜⠔⠍⠀⠐⠶⠀⠰⠰⠁⠔⠣⠝⠍⠜

Power of a Quotient

$\left( \frac{a}{b} \right)^{n}\ = \ \frac{a^{n}}{b^{n}}$

⠰⠰⠐⠣⠷⠁⠨⠌⠃⠾⠐⠜⠔⠝⠀⠐⠶⠀⠰⠰⠷⠁⠔⠝⠨⠌⠃⠔⠝⠾

Slope Formulas

$m\ = \ \ \ \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

⠰⠍⠀⠐⠶⠀⠰⠰⠷⠽⠢⠼⠃⠐⠤⠽⠢⠼⠁⠨⠌⠭⠢⠼⠃⠐⠤⠭⠢⠼⠁⠾

$m\ = \ \ \frac{\mathrm{\Delta}y}{\mathrm{\Delta}x}$

⠰⠍⠀⠐⠶⠀⠰⠰⠷⠠⠨⠙⠽⠨⠌⠠⠨⠙⠭⠾

Slope Intercept

$y\ = \ \ mx + b$

⠰⠽⠀⠐⠶⠀⠍⠭⠐⠖⠃

Newton's Second Law

$\overrightarrow{F}\ = \ m\overrightarrow{a}$

⠠⠋⠰⠘⠱⠀⠐⠶⠀⠰⠰⠣⠍⠁⠜⠘⠱

Compound Interest

$A\ \ = \ \ \ P\left. \ \left( 1 + \ \frac{r}{n} \right.\ \right)^{nt}$

⠠⠁⠀⠐⠶⠀⠠⠏⠐⠣⠼⠁⠐⠖⠷⠗⠨⠌⠝⠾⠐⠜⠔⠣⠝⠞⠜

Distance Formula

$d\ = \ \sqrt{({x_{1} - x_{2})}^{2} + ({y_{1} - y_{2})}^{2}}$

⠰⠙

⠀⠀⠐⠶⠀⠰⠰⠩⠐⠣⠭⠢⠼⠁⠐⠤⠭⠢⠼⠃⠐⠜⠔⠼⠃⠐

⠀⠀⠐⠖⠐⠣⠽⠢⠼⠁⠐⠤⠽⠢⠼⠃⠐⠜⠔⠼⠃⠬

Quadratic Equation

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

⠰⠭⠀⠐⠶⠀⠰⠰⠷⠐⠤⠃⠸⠖⠩⠃⠔⠼⠃⠐⠤⠼⠙⠰⠁⠉⠬⠨⠌⠼⠃⠰⠁⠾

Tangent Formula

$\tan\theta\ = \ \ \frac{\sin\theta}{\cos\theta}$

⠞⠁⠝⠨⠹⠀⠐⠶⠀⠰⠰⠷⠎⠊⠝⠨⠹⠨⠌⠉⠕⠎⠨⠹⠾

Binomial Expansion Formula of Rational Powers

$(1 + x)^{n}\ = \ \ 1 + \frac{nx}{1!} + \frac{n(n - 1)x^{2}}{2!} + \ldots$

⠐⠣⠼⠁⠐⠖⠭⠐⠜⠔⠝

⠀⠀⠐⠶⠀⠼⠁⠐⠖⠷⠝⠭⠨⠌⠼⠁⠖⠾⠐⠖⠷⠝⠐⠣⠝⠐⠤⠼⠁⠐⠜⠭⠔⠼⠃⠨⠌⠼⠖⠾

⠀⠀⠐⠖⠲⠲⠲