variable
a symbol used to represent a quantity that can change
coefficient
the number that is multiplied by the variable in an algebraic expression
algebraic expression
an expression that contains at least on variable
constant
a value that does not change
evaluate
to find the value of a numerical or algebraic expression
substitute
to replace a variable with a number or another expression in an algebraic expression
equation
a mathematical sentence that shows that two expressions are equivalent
solve
to find an answer or a solution
solution
a value or values that make an equation true
inverse operation
operations that undo each other: addition and subtraction, or multiplication and division
isolate the variable
to get a variable alone on one side of an equation or inequality in order to solve the equation or inequality
Addition Property of Equality
the property that states that if you add the same number to both sides of an equation, the new equation will have the same solution
Subtraction Property of Equality
the property that states that if you subtract the same number from both sides of an equation, the new equation will have the same solution
Multiplication Property of Equality
the property that states that if you multiply both sides of an equation by the same number, the new equation will have the same solution
Division Property of Equality
the property that states that if you divide both sides of an equation by the same nonzero number, the new equation will have the same solution
inequality
a mathematical sentence that shows the relationship between quantities that are not equivalent
algebraic inequality
an inequality that contains at least on variable
solution of an inequality
a value to values that make an inequality true
solution set
the set of values that make a statement true
term
the parts of an expression that are added or subtracted
like term
two or more terms that have the same variable raised to the same power
equivalent expression
equivalent expressions have the same value for all values of the variables
simplify
to write a fraction or expression in simplest form
ordered pair
a pair of numbers that can be used to locate a point on a coordinate plane
coordinate plane
a plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis
x-axis
the horizontal axis on a coordinate plane
y-axis
the vertical axis on a coordinate plane
x-coordinate
the first number in an ordered pair; it tells the distance to move right or left from the origin
y-coordinate
the second number in an ordered pair; it tells the distance to move up or down from the origin
origin
the point where the x-axis and y-axis intersect on the coordinate plane; (0,0)
graph of an equation
a graph of the set of ordered pairs that are solutions of the equation
integers
the set of whole numbers and their opposites
opposites
two numbers that are an equal distance from zero on a number line (additive inverse)
absolute value
the distance of a number from zero on a number line; shown by | |
power
a number produced by raising a base to an exponenet
exponential form
a number is in exponential form when it is written with a base and an exponent
exponent
the number that indicates how many times the base is used as a factor
base
when a number is raised to a power, the number that is used as a factor is the base
scientific notation
a method of writing very large or very small numbers by using power of 10
rational number
any number that can be expressed as a ratio of two integers
relatively prime
two numbers are relatively prime if their greatest common factor (GCF) is 1
reciprocal
one of two numbers whose product is 1; also called multiplicative inverse
least common denominator (LCD)
the least common multiple of two or more denominators
principal square root
the nonnegative square root of a number
perfect square
a square of a whole number
irrational number
a number that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal
real number
a rational or irrational number
Density Property
the property that states that between any two real numbers, there is always another real number
population
the entire group of objects or individuals considered for a survey
sample
a part of the population
biased sample
a sample that does not fairly represent the population
random sample
a sample in which each individual or object in the entire population has an equal chance of being selected
systematic sample
a sample of a population that has been selected using a pattern
stratified sample
a sample of a population that has been divided into subgroups
stem-and-leaf plot
a graph used to organize and display data so that the frequencies can be compared
back-to-back stem-and-leaf plot
a stem-and-leaf plot that compares two sets of data by displaying one set of data to the left of the stem and the other to the right
mean
the sum of a set of data divided by the number of items in the data set; average
median
the middle number, or the mean (average) of the two middle numbers, in an ordered set of data
mode
the number or numbers that occur most frequently in a set of data; when all numbers occur with the same frequency, we say there is no mode
outlier
a value much greater or much less than the others in a data set
variability
the spread of values in a set of data
range
the difference between the greatest and least values in a data set
quartile
three values, one of which is the median, that divide a data set into fourths
box-and-whisker plot
a graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median
bar graph
a graph that uses vertical or horizontal bars to display data
frequency table
a table that lists items together according to the number of times, or frequency, that the items occur
histogram
a bar graph that shows the frequency of data within equal intervals
line graph
a graph that uses line segments to show how data changes
scatter plot
a graph with points plotted to show a possible relationship between two sets of data
correlatoin
the description of the relationship between two data sets
line of best fit
a straight line that comes closet to the points on a scatter plot
point
an exact location in space
line
a straight path that extends without end in opposite directions
plane
a flat surface that extends forever
segment
a part of a line between two endpoints
ray
a part of a line that starts at one endpoint and extends forever
angle
a figure formed by two rays with a common endpoint called the vertex
right angle
an angle that measures 90 degrees
acute angle
an angle that measures less than 90 degrees
obtuse angle
an angle whose measure is greater than 90 degrees but less than 180 degrees
complementary angles
two angles whose measures add to 90 degrees
supplementary angles
two angle whose measures have a sum of 180 degrees
vertical angles
a pair of opposite congruent angles formed by intersecting lines
congruent
having the same size and shape
parallel lines
lines in a plane that do not intersect
perpendicular lines
lines that intersect to form right angles
transversal
a line that intersects two or more lines
Triangle Sum Theorem
the theorem that states that the measures of the angles in a triangle add up to 180 degrees
acute triangle
a triangle with all angles measuring less than 90 degrees
right triangle
a triangle containing a right angle
obtuse triangle
a triangle containing one obtuse angle
equilateral triangle
a triangle with three congruent sides
isosceles triangle
a triangle with at least two congruent sides
scalene triangle
a triangle with no congruent sides
polygon
a closed plan figure formed by three or more line segments that intersect only at their endpoints
regular polygon
a polygon with congruent sides and angles
trapezoid
a quadrilateral with exactly one pair of parallel sides
parallelogram
a quadrilateral with two pairs of parallel sides
rectangle
a parallelogram with four right angles
rhombus
a parallelogram with all sides congruent
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