math review Flashcards
Real Number
Any number found in the real world, both rational and irrational
Why? |x+ y| <= |x|+|y|
Because y could be a negative number resulting in subtraction in the first half and a higher number on the right. Proof using x=10 and y=-2 vs 2
Composite Number
Any integer greater than 1 that isn’t a prime number
Sq Rt + Number
every positive number has two square roots but generally we refer to the pos sq root only
Square x, x>1
Will result in a bigger number
Square x, x<1
Will result in a smaller number ie squaring a decimal- helps to think in fractions cuz we are increasing the denominator
Sq Rt of - #
Will result in imaginary number, i
i^2
-1
231 in scientific notation
2.31 * 10^2
0.0231 in scientific notation
2.31 * 10^-2
Dividing Decimals
move decimal in dividend and divisor until divisor is an integer (698.12/12.4) becomes (6981.2/124)
x/0 =
undefined
x isnt 0 & y isn’t 0, x/y
i/(y/x)
x isnt 0, x^-1
1/x
x isnt 0, (x^y)^z
x^yz
x isnt 0, (xz)^y
z^yz^y
z isnt 0, (x/z)^y
x^y/z^y
z isnt 0, x^(y/z)
(xy)^1/2 = (x^1/2)^y
2.310^14(1/3.910^4)
Ratio of x to y
x/y
How many solutions do two linear equations that are not equivalent have?
One at most
How many solutions do two linear equations have if they are equivalent?
2
ex: 3x-y=6 & 6x-2y=12
x^3-2x^2+x=-5(x-1)^2
x^3-2x^2+x+5(x-1)^2=0
x^3-2x^2+x+5(x-1)^2=0
x(x^2-2x+1)+5(x-1)^2=0
(x+5)(x-1)^2=0
x=-5 x=1
a^2-b^2 factors to???
(a-b)(a+b)
ex: (9x^2-25) -> (3x-5)(3x+5)
Quadratic Formula
x=[-b+-sqrt(b^2-4ac)]/2a
*roots are going to be 2 distinct numbers unless sqrt(b^2-4ac) <= 0 which means our only rot will be -b/2a
Multiplying or dividing inequality by a negative number
This will recers the order or chang the direction of the inequality
i.e. 6>2
*-1 *-1
-6<-2
