Math 1009
Quadratic Equations by Taking Roots
Ex: (x+2)² = 25 √ (x+2)² = ± √ 25 Find square root on both sides. x+2 = ± 5 Remove Parenthesis. x+2 =5 or x-2= -5 x=3 x= -7
Linear Applications
Example: 20% of 40? Let x represent the unknown quantity. Looking for a number which 40 is 20% of. Write an equation in x that describes the conditions. 20% of what number is 40? ↓ .....↓....... ↓.......... ↓... ↓ 20% * .........x = 40 20% * x =40 The equation written out. 0.2 * x =40 Write 20% as a decimal. 0.2 * x = 40 Divide both sides of the equation by 0.2 0.2 0.2 x=40 = 200 Divide to obtain the final answer. 0.2 40 is 20% of 200.
Quadratic Equations
Form: ax²+bx+c=0 Ex: 3x²+7x=20 3x²+7x-20=0 Set equation equal to zero. (3x-5) (x+4)=0 Factor. And set equal to zero. 3x-5=0 x+4=0 A=0 , B=0 3x=5 x=-4 x=5/3
Linear Inequalities
Goal: to get the variable by itself ( ):NOT included ,(open dot) [ ]: INCLUDED ; (closed dot) Ex: 8x-11 ≤ 3x-13 -3x ...........-3x _____________________ 5x-11 ≤ ..........-13 +11 .............+11 ______________________ 5x ≤ ............-2 -5x................ - 5 x ≤ -2 ........5 = (-∞,-2] ...........5 Graph: <------*-------]
