in order to convert a percentage to a decimal you need to divide by ______
100
in order to decimal to a percentage you need to ______ by 100
multiply
if you want to convert a fraction to a percentage you need to make it =
x over 100
the _______ tells how many times the root needs to be multiplied by itself
index
what is 4 to the power of 1/2 or 4^1/2
2
1/a^n can also be written as a to the ______
-n
what property of equality says that a=a
reflexive
for each real number a, for each real number b, if a= b, then b=a
symmetric
what property of equality ways for each real number a, for each real number b, for each real number c, if a=b and b=c, then a=c
transitive
what is the closure property of addition -for every real number a, for every real number b ______________ is a real number
a+b
what is the closure property of multiplication for every real number a, for every real number b _________ is a real number
ab
the __________property of multiplicaiton for every real numver a, for every real number b ab= ba
commutative
the _________property of addition says that for every real number a, for every real number b for every real number c (a+b) + c = a + (b+c)
associative
the associative property of multiplicaiton for every real number a, for every realy number b for every real number c (ab)c = ______
a(bc)
the __________property of additon says that fro every real number a, ther is a real number such that a + -a = -a+ a = 0
inverse
the inverse property of multiplication says that for every real number a, a cannot = 0 ther is a real number a^____such that a X a ^____ = a^____ X a =1
-1
the _______says for every reals number a, for every real number b and for every real number c, a(b+c) = ab + ac
distributive
a _________ number is a number that can be written in the form of a + bi
complex
in complex numbers the square root of -1 = ______
i
the square of a real number cannot be ___________
negative
the square of 0 is _____
0
the square of both a positive number and a negative real number is _____________
positive
i^2 = _____________
-1
every real number is a ______________
complex
the least common multiple is the smallest quantity divisible by ______ number of the set
every
the greatest common factor is the largest __________that is common to all member of the set
factor
y2-y1 divided by x2- x1 = the ____________
slope
the value of y where a point intersects the x axis = __________
0
the value of x where a point intersects the Y axis= ___________
0
to find the x intersept we need to make __________= 0
y
the ____________ says y-y1= m(x-x1)
point slope formula
what is the linear equation where a, b and c are constants b cannot = 0
ax+ by = c
when you have a linear equation such as ax + by = c you may use ___________ or _____________ to solve the problem, (you may first have to multiply through one of the equation to make either the x or y value equal)
addition subtration
the possible solution of a quadratic equatin ax^2 + bx + c= 0 are called the_______
roots
x= -b (+ or -) square root of (b^2-4ac) divided by 2a, is called the _____________ and can be used to find the roots of a problem
quadratic formula
once you find the roots of a radical equation you must check them to see if any are __________roots (which means they are not equal when plugged back into the original formula) these roots must be ___________
extranous excluded
the graph of y= ax^2 + bx + c is a curve know as a ____________
parabola
the x value of the vertex of a parabola is the equation
-b/2a
the y value of the vertex of parabola is the equation
(4ac-b^2)/4a
in a quadratic formula if the a value of the parabola is _______0 the parabola open upward
greater
in a quadratic formula if the a value of the parabola is less than 0 the parabola opens ___________
downward
if a=0 in a quadratic formula, the quadratic is reduced to a linear function and a ____________
straight line
to solve a system of equations you must first make the two equations ___________to each other, then use the discrimant to find if the system has any real roots
equal
in a quadratic equation in 2 unknowns has the general formula ax^2 + bxy + cy^2+dx ey+ f = 0 the graph is called an __________ (if a, b and c are not zero)
ellipse
in a quadratic equation in 2 unknowns has the general formula ax^2 + bxy + cy^2+dx +ey+ f = 0 the graph is called an __________or a __________ or __________(b=0 and a=c)
point circle does not exist
in a quadratic equation in 2 unknowns has the general formula ax^2 + bxy + cy^2+dx +ey+ f = 0 the graph is called an __________ (b^2-4ac greater then 0)
hyperbola
in a quadratic equation with 2 unknown which has the formula ax^2 + bxy + cy^2 + dx + ey + f the graph is _____________ or a pair of __________ if ( b^2-4ac= 0) which may be coincident or it does not exist
parabola parallel line
when solving a system of equation involving quadratics and one is linear and the other is quadratic, solve the _______ first , then substitue the found value into the quadratic and solve for the other unknown
linear substitute
when solving a system of equation with 2 quadratic function, first __________ one equation from the other equation to find isolate one variable, solve for that variable, then ______ and solve for the other variable
subtract substitute
in the law of proportion if a/b = c/d then ad =
bc
in the law of proportion if a/b = c/d then b/a =
d/c
in the law of proportion if a/b = c/d then a/c
b/c
in the law of proportion if a/b = c/d then (a+b)/ b =
(c+d)/d
in the law of proportion if a/b = c/d then (a-b)/b =
(c-d)/d
a point has no ________or thickness
size
a series adjacent points that connect
line
a collection of points lying on a flat surface that extend indefinitely in any direction
plane
the set of all points on a half line and the dividing point itself
ray
three or more points are said to be ___________if an only if they lie on the same line
collinear
the absolue value of the difference of the coordinates of any two points on the real number line
distance
a line that divides a line segment into two congruent segments
bisector
the union of two rays having the same end point
angle
if all points lie in the same plane they are __________
coplanar
two angles with a common vertex and a common side but no common interior points
adjacent
two angles with a common vertex and with sides that are 2 pairs of opposite rays
vertical
an angle whose measure is larger than 0 degrees but smaller than 90 degrees
acute
an angle whose measure is 90 degrees
right angle
an angle whose measure is larger than 90 degrees but less than 180 degrees
obtuse angle
an angle whose measure is 180 degrees
straight
an angle whose measure is greater than 180 degrees and less than 360 degrees
reflex
two angles whose sum totals 90 degrees
complimentary
two angles whose sum totals 180 degrees
supplementary
angles that are equal
congruent
a ray _________ divides the angle into 2 angles that have equal measure
bisect
two lines are said to be ______________ if they intersect and form right angles
perpendicular
distance from a ___________ to a _________ is the measure of the perpendicular line segment from the point to that line
point line
two or more distinct lines are said to be ____________ if and only if they are coplanar and they do no intersect
parallel
two distinct straight lines can intersect at most at only one point
one
if a triangle has two congruent sides then it is an _________triangle
isosceles
_____________ of angles is an equivalance relation - it is reflexive, symmetric and transitive
congruence
a ___________is a figure with the same number of sides as angles
polygon
is a polygon whose sides are equal in measure
equilateral polygon
is a polygon whose angles are equal in measurement
equiangular polygon
is a polygon that is both equilateral and equangular
regular polygon
when calculating the number of sides in a polygon make 360 degrees/ n = ______________
exterior angle
the perimeter of a polygon is equal to the ________of sides X the _____________ of sides
length number
the segment from the center of the polygon perpendicular to as side of the polygon
apothem
the __________ of a regular polygon is the segment joining an vertex with the center of the polygon
radius
use ____________= 1/2a X p (where a = apothem and p = the perimeter)
area of a polygon
the perimeter of two similar polygons have the same ratio as teh measure of any pair of corresponding line segments of the polygon
ratio
a closed three sided figure is called a ____________
triangle
that points of intersection on a triangle are called its _____________
vertices
when proving 2 polygons are similar -what is the formula you use (hint: n= the number of sides)
((n-2) (180))/n
a triangle with no equal sides
scalene
a triangle with having at least 2 equal sides
isosceles
a triangle whose sides are equal
equilateral
a triangle whose angles all equal 60 degrees
equiangular
the sum of the interior angles of a triangle = ___________
180
a triangle with one obtuse angle (angle greater than 90 degrees) is
obtuse
a triangle with three acute angles (less than 90 degrees)
acute
a triangle with a 90 degrees angle
right
the side of a right triangle opposite the right angle
hypotenuse
in the pythagorean theorm a^2 + b^2 = c^2, c is called the ______
hyotenuse
the __________of a triangle is a line segment from a vertex of the triangle perpendicular to the opposite side
altitude
what is the formula for the area of a triangle
1/2bh
a line segment connecting a vertex of a triangle and the midpoint of the opposite side is called a __________ of a triangle
median
a line that joins the midpoint of two sides of a triangle is called the__________
mildline
___________is a quadrilateral whose opposite sides are parallel
parallelogram
2 angles that have their vertices at the endpoints of the same side of a parallelogram are called ____________________
consecutive angles
how do you calculate the area of a parallelogram -what is the formula
bh
a parallelogram with right angles and equal diagonals
rectangle
what is the formula to calculate the area of a rectangle
lw
a parallelogram that has tow adjacent sides that are equal and whose sides are perpendicular to each other
rhomus
wha tis the formula for the area of a rhomus- (hint d= diagonal)
1/2 (d1 + d2)
a rhomus with a right angle
square
to calculate the diagnol of a square you multipy any ______by the _______________of 2
side square root
what is the formula for the area of a square
s^2
what is the formula for a square if you only know the length of the diaganol
1/2 (d)^2
what is a quadrilateral with 2 and only 2 sides parallel
trapezoid
how do you calculate the area of a trapezoid (hint h= altitude -perpendicular segment)
1/2h (b1 + b2)
what type of trapezoid has its non parallel sides equal
isosceles
a set of points in teh seame plane equidistant from a fixed point- called its center
circle
a __________of a circle is a line segment drawn from the center of the circle to any point on the circle
radius
a portion of a circle is called an ________ of the circle
arc
a line that intersects a circle in tow point is called the _______
secant
a line segment joining two poing on a circle is called a ________
chord
the measure of a minor arc is the measure of the __________that intercepts the arc
central angle
a __________________ is a circle passing through all the vertices of a polygon
circumscribed circle
what are the 2 formulas to calculate the circumference of a circle
pi(d) 2(pi)r
what is the formula for the area of a circle
(pi)r ^2
what is the formula the formula for an arc if you know the radius and the n= central angle
(n/360) X 2pi r
the volume of a cube is
a^3
the surface area of a cube is what formula
6a^2
wha tis the volume of a right circular cylinder with a radius of r and a height of h
pi r^2 h
what is the surface area of a right circular cylinder with a radius of r and a height of h
2pi r^2 + 2pi rh
what is the volume of a sphere with a radius r
4/3 pi r^3
what is the surface area of a sphere with a radius r
4pi r^2
what is the area of a pyramid or cone (hint B= area of Base)
1/3Bh
what is the volume of a cone
1/3 pi r^2 h
what is the square of ((x1-x2) + (y1-y2)) =
distance between 2 points
a __________is any process that assigns a ___________value of y to each number of x
function single
in a function the x value is the ___________variable
dependent
when you see f of g replace the x in f(x) with the ___________
g value
when you find the inverse of a function switch the x value with a ____, solve for y
y
in a logarithm the answer following the = sign is the __________
exponent
log base b to the 1 = ____________
0
log base b to the b = ____________
1
log base b to the b^x =
x
when calculating the probability of mutually exclusive event y (can not occur simultaniously) you need to ______their seperate probabilities (uses the word "or")
added
when calculating the probability of independent events you need to __________ (words like and &" followed by" )
multiply
the difference between the largest and smallest numbers in a set is called the ___________
range
operation in steps = if an event a ways and followed by b ways followed by c ways the total number of ways it can be done is
a x b x c
positions= number of position can be calculated by finding the ______ of the total number of items
factoral
to calculate a permutation (order does not matter) what is the formula
n!/ (n-r)!
what is the formula for a combination (where order matters)
n!/(r!(n-r)!)