Hnrs. Alg. 2 Ch. 1
do you use a bracket or parenthesis when writing +/- infinity?
ALWAYS a parenthesis
absolute value bars are included in what part of PEMDAS?
P: parenthesis
counterexample
a specific case that shows that a statement is false
distance from 0 on the number line (is always POSITIVE)
absolute value
inverse property
additive: 0 ex. a+(-a)=0 multiplicitive: 1 ex. a x 1/a=1
identity property
additive: a+0=a multiplicitive: a x 1=a
real numbers
all numbers
empty set
an equation that is never true (no solution) ex. lxl=-5
conjunctions use the word...
and
less thAND
and/conjunction
compound inequalities contain the words:
and/or
irrational numbers
any numbers that do not end or repeat
What type of equation is this: 3+10x-9=4(x-2)+1
conditional; true for some, but not all values of the variable
What type of equation is this: 3x-5(2x+4)=6x+2-13x
contradiction; ends with a false statement (no solution)
binomial
ex. 3x (squared)+7x
trinomial
ex. 3x (squared)+7x-1
monomial
ex. 3x (squared), 23, -w, 5b, 1/3x
conjunctions must always be in numerical order to be true
ex. {x/-4<x<6} ex. (-4,6)
only one part of a disjunction must be true for the disjunction to be true
ex. {x/x<-1 or x>4} ex. (-∞, -1) U [4, ∞)
integers
-3,-2,-1,0,1,2,3...
what is the coefficient in: -6m
-6
the degree of a constant is...
0
whole numbers
0,1,2,3,4,5...
constant
1, 2, 3, 4...any number
natural numbers
1,2,3,4,5...
you can express your answer of an inequality in 3 ways:
1. graph 2. set-builder notation {x/x>4} 3. interval notation (-4, ∞)
degree of a monomial: 12gh (squared)
3
2-3xy if x=-2 and y=1/3
4
find the rate if distance is 150 miles and time is 2 hrs. (D=RT)
75 mi/hr.
linear
variable to the power of 1 ex. 3x, x, -2y...
quadratic
variable to the power of 2 ex. 3x (squared)
cubic
variable to the power of 3 ex. 2y (cubed)
What type of equation is this: 8-(x+3)=x+5-2x
identity; ends with true statement (all real numbers)
to solve absolute value equations, you need to...
isolate the absolute value, then write two equations
What type of equation is this: 2x+4=5x-2
linear equation
if an absolute value is less than or equal to a negative number, the answer is always...
no solution!!!
rational numbers
numbers that can be written as fractions, including terminating and repeating decimals, and integers
associative property
of addition: (a+b)+c=a+(b+c)
commutative property
of addition: a+b=b+a of multiplication: ab=ba
disjunctions use the word...
or
greatOR than
or/disjunction
when you multiply and inequality by a negative value, you...
reverse the symbol (ex. -2x>8 becomes x<-4)
solve: 16t=4l3t+8l
t=8
union
the graph of a disjunction is the union of the solution set of the 2 inequalities
solve: lx+4l=17
x=13 and x=-21