Flashcards in memorize Deck (77)
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1
if your system of equations has no solution...,
it will graph as two parallel lines because parallel lines never intersect
2
if your system of equations has one solution...,
the two equations will graph as two lines intersecting at a single point because two straight lines have only one intersection
3
if your system of equations has infinitely many solutions...,
it will graph as a single line because their graphs are the same line
4
integers
whole numbers (negative or positive)
5
rationals
fractions, anything expressable as a ratio of integers
6
real #s
integers plus rationals plus special numbers like roots and pi
7
arithmetic sequence
each term equal to previous term PLUS x
8
geometric sequence
each term equal to previous term TIMES x
9
factor
the factors of a number divide into that number without a remainder
10
multiples
the multiples of a number are divisible by that number without a remainder
11
how to find part of a percent of something
part = (percent/100) * whole
12
average of numbers(mean)
sum of terms/number of terms
13
average speed
total distance/total time
14
sum
average * number of terms
15
mode
value in the list that appears most often
16
median
middle value in the list (must be sorted)
17
Fundamental Counting Principle
If an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N*M ways.
18
Probability
probability= # desired outcomes / #total outcomes
19
x^a*x^b =
x^(a+b)
20
(x^a)^b =
x^(a*b)
21
x^0 =
1
22
x^a / x^b =
x^(a-b)
23
(xy)^a =
x^a * y^a
24
rootxy =
rootx * rooty
25
1 / x^b =
x^(-b)
26
(-1)^n =
1 is positive if 'n' is even
1 is negative if 'n' is odd
27
Difference of two squares
a^2 - b^2 = (a+b)(a-b)
28
Distance formula
root[ (x2-x1)^2 + (y2-y2)^1 ]
29
Mid point formula
(x,y) = ( x1+x2 / 2 , y1+y2/2 )
30
slope
y2-y1 / x2-x1 = rise/run
31
Intersecting Lines
Opposite angles are equal. Each pair of angles along the same line add to 180 degrees.
\ a /
\ /
\ /
\ /
b \ / b
/ \
/ \
/ \
/ a \
32
Parallel Lines
Eight angles are formed when a line crosses two parallel lines. The four big angles (a) are equal, and the four smaller angles (b) are equal.
/
___ a_/_ b____
b /a
/
/
___ a_ /_b____
b / a
/
33
pythagorean theorem
a^2 + b^2 = c^2
34
30-60-90 triangles
Hypotenuse (90 degrees): 2x
side across from 60 degrees: x root 3
side across from 30 degrees: x
35
45-45-90 triangles
hypotenuse (90 degrees): x root 2
side across from 45 degrees: x
36
area of a triangle
A = 1/2 * b * h
*works for all triangles
37
equilateral triangles
triangle with three EQUAL sides, all three angles measure 60 degrees each
38
Isosceles Triangle
Has two equal sides, the angles opposite these two equal sides are equal. (To find the third angle, add these two and subtract from 180 degrees, because a triangle is always 180 degrees).
39
Similar Traingle
Two or more triangles are similar if they have the same shape. The corresponding angles are equal, and the corresponding sides are in proportion. For example, if the sides of one triangle are 3-4-5 and the other are 6-8-10 the ratio is 2 to 1 but the angle measurements would remain the same.
40
Area of a circle
A = pi * r^2
41
Circumference of a circle
C = 2 * pi * r
42
How many degrees in a circle?
360
43
How to find Length of Arc
(n degrees/360 degrees) * (2*pi*r)
44
How to find area of a sector
(n degrees/360 degrees) * (pi*r^2)
45
Area of a square
A = bh
46
Area of a rectangle
A = bh
47
Area of a parallelogram
A = length * HEIGHT - not width ************************** the line going through the middle is the height.
____
/ l /
/ l h / w
/_ l__/
L
You do not use the length to figure out the area of a parallelogram.
48
Volume of a rectangular solid
V = length * width * height
49
Volume of a right cylinder
V = pi * radius^2 * height
50
less or greater than or equal to uses a ___________ dot on a number line and a __________ line on a graph
shaded in, solid
51
less or greater than used a _________ dot on number line and a _______ line on graph
open circle (not shaded in), dotted
52
only time a system of inequalities has no solution is when...,
the boundary lines are parallel and the shading is in opposite directions
53
1 cup = _____ oz
8 fl oz
54
1 pint = ____ cups
2 cups
55
1 quart = ____ pints
2
56
1 quart = ____ cups
4
57
2 pints = _____ cups
4
58
1 gallon = _____ quarts
4
59
1 pound = ______ ounces
16
60
1 ton = _____ pounds
2000
61
1 yard = _____ feet
3
62
1 mile = _____ feet
5280
63
1 gallon = _____ quarts
4
64
1 gallon = ____ pints
8
65
1 quart = ____ pints
2
66
1 gallon = _____ cups
16
67
1 pint = ____ cups
2
68
Distance =
rate * time
69
68-95-99.7 Rule
If you take the mean and go one standard deviation above and below the mean you will get 68% of the data.
If you take the mean and go two standard deviations above and below the mean you will get 95% of the data.
If you take the mean and go three standard deviations above and below the mean you will get 99.7% of the data
70
parallel lines have _______ slope
the same
71
perpendicular lines have ____________ lines
opposite reciprocal
(flip the number and change the sign - positive or negative)
72
sine of an angle
opposite/hypotenuse
73
cosine of an angle
adjacent/hypotenuse
74
tangent of an angle
opposite/adjacent
75
cotangent of an angle
adjacent/opposite
goes with tangent
76
secant of an angle
hypotenuse/adjacent
goes with cosine
77
