Algebra 101
4
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for n
-3
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for r
Continuous Compounding
A = Pe^(rt)
transversal
A line that intersects two or more lines.
rectangle
A parallelogram with 4 right angles
plane
A plane is a flat surface that has no boundaries or thickness
√169
13
9988
1362 did not watch in terror as the tsunami closed in, because as Christians, they had complete assurance in their perpetuity. If 19/22 of the assembled throng watched in terror, how many people were in the assembled throng?
8626
1362 did not watch in terror as the tsunami closed in, because as Christians, they had complete assurance in their perpetuity. If 19/22 of the assembled throng watched in terror, how many watched in terror?
5n + 4(2n + 3)
13n + 12
-3.1
13x +14y = 0.3 -x -101y = 296 Solve for x
√196
14
√225
15
Right Angle
A right angle is an angle that equals 90
What type of matrix must you have to take a determinant?
A square matrix
Straight Angle
A straight angle is a 180-degree angle
acute triangle
A triangle with three acute angles
Standard Form for a Line
Ax + By = C
Exponential function
a functions that can be represented by y = a(b)x
Axis of symmetry
a line that divides a parabola in two equal halves and goes through the vertex
Solution of an inequality in one variable
a number that makes a true statement when substituted into an inequality
Scientific notation
a number written in the form c x 10n where 1 ≤ c < 10 and n is an integer
vertical angle
a pair of opposite congruent angles formed by intersecting lines
right triangle
a triangle with one right angle
Standard form of a quadratic equation
ax2 + bx + c
Angle
formed by two rays with a common endpoint
Order of operations
rules for evaluating an expression (PEMDAS)
Decay factor
the expression (1 - r) in the exponential decay model y = a(1 - r)t
Quadratic formula
the formula used to find the solutions of a quadratic equation;
Quadrants
the four regions created by the x- and y- axis
Graph of a system of linear inequalities
the intersection area of two or more linear inequalities
Hypotenuse
the longest leg of a right triangle across from the 90 degree angle represented by the letter "c"
Numerator
the top part of a fraction
Zero of a function
the x-value for which f(x) = 0 (or y = 0)
Input
the x-values (domain) of a relationship
Maximum value
the y-coordinate of the vertex of a parabola
Minimum value
the y-coordinate of the vertex of a parabola
Output
the y-values (range) of a situation
3
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for c
0
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for e
-5
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for g
279
31 times the number of yellow marbles was equal to 21 times the number of black marbles. Also, 2 times the number of yellow marbles exceeded the number of black marbles by 99. How many black marbles were there?
√16
4
I start with 4y, add 3 and then divide the result by 4
4/(4y + 3)
12a - 3 + 2b - 6 - 8a + 3b
4a - 9 + 5b
beryllium fluoride
BeF₂
line segment or segment
A part of a line is called a line segment, it has two endpoints. It is named by naming the two endpoints in any order
What is a determinant?
A real number associated with a square matrix.
Sn=a1(1-r^n/1-r)
Geometric Sum
S=a1/1-r
Geometric infinite sum
An=a1R^n-1
Geometric series
Independent Lines
Have one solution; Different slopes
59
James collected pennies and quarters in loose change from the mall floor. After he counted it, he discovered that he had found $6.09. How many pennies did he have?
First degree polynomials are called...
Linear
Mapping Diagram
Links domain to range
phosphine
PH₃
8
(½)⁻³
64/27
(¾)⁻³
64/9
(⅜)⁻²
15d⁹
(−3d)(5d⁵)(−d³)
12m²
(−4m)(−3m)
-3c⁶
(−c)(3c²)
-x⁵
(−x⁷)(x⁻²)
-1
12x +12y = -12 12x - 189y = -12 Solve for x
0
12x +12y = 12 12x - 189y = 12 Solve for y
6(2x - 2)
12x - 12
2.1
15x - 12y = 8.7 -11x + 7y = -9.8 Solve for x
1.9
15x - 12y = 8.7 -11x + 7y = -9.8 Solve for y
√256
16
√289
17
√400
20
√441
21
√484
22
horizontal asymptotes for rational expressions
(BOSTON)-if degree of Bottom is bigger, y=0; if degrees are same for numerator and denominator, use coefficients a/c; if Top has a larger degree, NO horizontal asymptote
√9
3
I start with x, add 4 and then multiply the result by 3
3(4x)
Equivalent expressions
two expressions that are equal
Elimination
used to solve a system of equations by adding the two equations in order to cancel out one of the variables
Substitution
used to solve a system of equations by substituting the expression for one variable in for that variable for the other equation
-1
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for a
2
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for b
-2
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for i
end behavior
what happens to the y values as the x values approach positive or negative infinity
exterior angles
when a side of a polygon is extended, a special angle is formed " outside " the polygon
equalaingular
when all angles are congruent
equilateral
when all sides are congruent
0.9
x + y = 0 x - y = -1.8 Solve for y
Quadratic Formula
x = (-b plus or minus) the square root of b^2 -4ac) / 2a from y = ax^2 + bx + c
Slope-Intercept Form for a Line
y = mx + b
What is the line of reflection for inverses?
y = x
Vertex Form of a Quadratic Function
y=a(x-h)2+k
What must be true to multiply two matrices?
The columns of the first must match the rows of the second matrix.
T₁P₂V₂ over T₂V₁
P₁
T₂P₁V₁ over V₂T₁
P₂
Second degree polynomials are called...
Quadratic
Fourth degree polynomials are called...
Quartic
What must be true to add two matrices?
The dimensions must be the same. (Rows and Columns)
Matrix
Rectangular array of numbers in rows and columns
Function
Relation in which one element of domain is paired with EXACTLY one element in range
Solve by graphing: y > 4x - 1 and y ≤ -x +4
See board
51mph
The train made the trip in 9 hours while the bus made all but 39 miles of the trip in 10 hours. How fast did the train travel?
complementary angles
Two angles whose sum is 90 degrees
Mutually inclusive
Two events that can happen at the same time.
T₁P₂V₂ over T₂P₁
V₁
T₂P₁V₁ over T₁P₂
V₂
Mapping
a diagram that uses arrows to connect the input with the corresponding output values
scale drawing
a drawing that is similar but either larger or smaller than the actual object
Scatter plot
a graphing of points to determine if data has a relationship
vinculum
a horizontal line placed over a mathematical expression, used to indicate that it is to be considered a group
Variable
a letter used to represent a number
Linear inequality in two variables
a line in which the equal sign is replaced with an inequality symbol
line
a line is a straight curve that has no ends
diagonal
a line segment that joins two nonconsecutive vertices
Boundary line
a line that borders the shaded region on the graph of linear inequalities
Horizontal
a line that goes left-right parallel to the ground
Vertical line
a line that goes up and down perpendicular to the ground
Line of best fit
a line used to model a trend in a set of data
regular polygon
a polygon that has all equal sides and all equal angles
Monomial
a polynomial with only one term
Trinomial
a polynomial with three terms
Ray
a portion of a line that extends from one point infinitely in one direction
trapezoid
a quadrilateral with exactly one pair of parallel sides
Unit rate
a rate in which the denominator is 1
Function
a relationship in which all of the x-values are paired with only one possible y-value
Graph of an equation in two variables
forms a line on a coordinate plane
Graph of an inequality in two variables
forms a shaded area on a coordinate plane with a boundary line
point
a specific location in space with no size or shape
scalene triangle
a triangle with no congruent sides
obtuse triangle
a triangle with one obtuse angle
equilateral triangle
a triangle with three congruent sides
isosceles triangle
a triangle with two equal sides
Distributive property
a(b + c) = ab + ac
Domain of a function
all the possible x-values of a function
Compound interest
interest that is earned on both the initial amount and the previously earned interest
intersecting lines
lines that cross at one point
Slope Formula
m = (y (sub 2) - y (sub 1))/(x (sub 2) - x(sub 1)), difference of the y's over the difference of the x's
Translation
moves an image the same distance and same direction
Solution of an inequality in two variables
an ordered pair that makes a true statement when substituted into an inequality
acute angle
angle that has a measure greater than 0 and less than 90
obtuse angle
angle that has a measure greater than 90 but less than 180
right angle
angle that has a measure of exactly 90
straight angle
angle that measure exactly 180
interior angles
angles " inside " the polygon
Supplementary
angles that add to be 180 degrees
congruent angles
angles with the same measure
a¹²
a⁶⋅a⁶
1
a⁷/a⁷
1
a⁷⋅a⁻⁷
What is the discriminant?
b^2 minus 4ac
vertex
common endpoint in an angle
scientific notation
concise way to write very small or very large numbers
vertices
endpoints of line segments ( sides of a polygon )
alternate exterior angles
non- adjacent angles found on opposite sides of the transversal on the exterior line that intersects two parallel lines
Irrational numbers
numbers than cannot be written as a fraction
Integers
numbers that belong to the set ... -3, -2, -1, 0, 1, 2, 3 ...
Rational numbers
numbers that can be expressed as a fraction
degree of a poly
numerical factor of the term with the highest degree
Inverse operations
opposite operations (+ and - or * and / )
Line Segment
part of a line containing two endpoints and all points in between
relation
set of ordered pairs
radical
the check mark part of the radical expression, √ .
Ratio
the comparison of two numbers using division
Absolute value
the distance a number is from zero
Circumference
the distance around a circle
Perimeter
the distance around a figure
Reasonable Domain
the domain that takes into account the restrictions of a situation
Best-fitting line
the equation of a line that best follows a set of data
Growth factor
the expression (1 + r) in the exponential growth model y = a(1 + r)t
Hyperbola
the graph of an inverse relationship
Degree of a polynomial
the greatest degree of the terms of a polynomial
Base of an exponential function
the growth rate of an exponential function
x-axis
the horizontal axis on a coordinate plane
Median
the middle number of a set of data that has been ordered from least to greatest
Vertex of a parabola
the minimum or maximum point of a parabola
degree
the most common unit of measure for angles
Coordinates
the ordered pair that represents a point (x, y)
Relation
the pairing of inputs with outputs
Reasonable Range
the range that takes into account the restrictions of a situation
Growth rate
the rate at which an exponential function is increased
Decay rate
the rate at which an exponential function is reduced
Common ratio
the ratio of a term in a geometric sequence with the previous term
Correlation
the relationship between a set of data; it can be positive, negative, constant, or no correlation
Real numbers
the set of all rational and irrational numbers
Legs of a right triangle
the sides that make up the 90 degree angle of a right triangle
Rate of change
the slope of a line
Roots
the solution to an equation
Graph of an inequality in one variable
the solution to an inequality that can be represented on a number line
Degree of a monomial
the sum of the exponents of the variables
Zero term
the value before a function rule has been applied to the situation
Independent variable
the variable (input) that determines the dependent variable (output)
Dependent variable
the variable (output) that depends on the value of the independent variable (input)
"b" in y = a•bx
the variable used to represent the growth rate in an exponential function
"b" in y = mx + b
the variable used to represent the y-intercept in a linear function
roots vs radicals
these terms are opposites and are used to solve equations or inequalities containing them. The square root of 9 is the opposite of 3 squared or (-3) squared.
simplify
to rewrite an expression without parentheses or negative exponents
protractor
tool used to measure angles
31mL
The chemist needed 100 mL of a solution that was 26% iodine. She had a solution that was 49% iodine, and another that was 15 2/3% iodine. How many mL should he use of the solution that was 49% iodine?
Transformation
a new image created by applying a rule to the coordinates of the original image
Perfect square
a number that has a whole number square root
rhombus
a parallelogram with 4 congruent sides
x log base n of y =
log base n of y ^ x This is the power property of logarithms.
The product of a radical expressions can be obtained by
multiplying the radicands of each radical expression. √(8) times √(2) =√(8)(2) = √16 = 4
6x - 3y = 1, 4x - 2y = 7
no solution
alternate interior angles
non- adjacent angles found on opposite sides of the transversal on the interior line that intersects two parallel lines
Square root
the "b" if b2 = a
Intersection
the place where two equations "cross" each other
Simplify
to perform all indicated operations
Complementary
two angles that add to be 90 degrees
Equivalent equations
two equations that have the same solution
Open sentence
two expressions that are compared to each other
primitive terms
undefined terms. Impossible to define exactly so are defined as best as possible. Point, curve, line, plane
Function notation
uses f(x) instead of y
standard notation
usual way to write numbers
1
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for j
-4
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for m
5
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for s
-6
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for w
6
w + g + m + r + i + a + e + j + b + c + n + s + z = 0 (w +8) = 3z = {g - (-7)} = 2.5s = 2n = -.5a = b = -i = (j + 1) = (r + 5) = -2m = {e - (-2)} Solve for z
-0.9
x + y = 0 x - y = -2 Solve for x
7.2
x - 24y = 180 -12x + 12y = -172.8 Solve for x
-7.2
x - 24y = 180 -12x + 12y = -172.8 Solve for y
-12
x - y = -24.1 x + y = 0.1 Solve for x
12
x - y = -24.1 x + y = 0.1 Solve for y
99.9
x - y = 199.7 12x + 13y = -98.6 Solve for x
-99.8
x - y = 199.7 12x + 13y = -98.6 Solve for y
8.1
x - y = 9 -x + 2y = -9.9 Solve for x
-0.9
x - y = 9 -x + 2y = -9.9 Solve for y
domain
x-coordinates, input
Standard Form Equation for a Circle with center at the origin
x^2 + y^2 = r^2
1
x² = 1
x⁶
x⁵⋅x
Point-Slope Formula
y - y(sub1) = m(x - x(sub 1))
35
The well known man received Christmas gifts of $5 bills and $10 bills for a grand total of $625. The number of $5 bills was 10 less than the number of $10 bills How many $5 bills did he receive?
Equivalent inequalities
two inequalities that have the same solution
67 1/3
Ben could go the 202 miles to the next major city in 2 hours less than it took Jennifer to go the 309 miles to the following major city. Also, 45 times the rate of Ben was 369 mph less than 55 times the rate of Jennifer. What was the rate of Ben?
Obtuse Angle
An angle greater than a right angle but less than a straight angle is called an obtuse angle.
Reflex Angle
An angle greater than a straight line but less than two straight angles is a reflex angle.
Angle
An angle is the opening between two rays as defined by European authors or the set of points determined by two rays as defined by US.
corresponding angles
Angles formed by a transversal cutting through 2 or more lines that are in the same relative position.
adjacent angles
Angles that have a common side and a common vertex
Sn=n(a1+an/2)
Arithmatic Sum
An=a1+(n-1)d
Arithmatic series
Solution of an equation in two variables
an ordered pair that makes a true statement when substituted into an equation
Algebraic expression
contains numbers, variables, and operations (no equal sign)
Reciprocal Identity (2)
cosX=1/secX
Quotent Identity (2)
cotX=cosX/sinX
1/c³
c³/c⁶
c³
c⁶/c³
c⁵
c⁹⋅c⁻⁴
1/c⁵
c⁻⁹⋅c⁴
Verbal model
describes a real-world situation using labels and math symbols
Composition of Functions
f ( g(x)) means that function g is the input to function f
Standard Form for a Quadratic
f(x) = ax^2 + bx + c
Quadratic Function
f(x)=ax2+bx+c
Linear Function
f(x)=x+c
Congruent figures
figures that are the exact same size and shape
Similar figures
figures that have the same shape and are proportional
congruent
figures that have the same shape and same size
similar
figures that have the same shape but not necessarily the same size
indirect measurement
finding the measure of objects that are too large to measure directly ( flag poles )
How do you factor a sum or difference of cubes?
first one, second one, first one squared, product of the two and the last one squared, first sign's the same, second one's not, last one's always plus and here's what you've got!
Reflection
flips a figure about a line
What's the square root of -1?
i
skew lines
lines that lie in different planes, never intersect and are not parallel
parallel lines
lines that never intersect
Sample Set
list of all possible outcomes for a given situation
log base a of x - log base a of y =
log base a of (x divided by y) This is the quotient property of logarithms.
log base a of x + log base a of y =
log base a of (x times y) This is the product property of logarithms.
Terms of an expression
parts of an expression separated by a + or - sign
corresponding parts
parts of congruent triangles that "match"
polynomial function
polynomial equation that represents ordered pairs on a graph
quadratic form
polynomial that can be written as (x^n)2 + b(x^n)1+ c
Opposites
positive and negative
What does the rational exponent mean?
power/root = "power over root"
synthetic sub
process using the coefficients to evaluate a polynomial at a certain value of x
location principle
property for determining roots between consecutive integers given that y-value have changed signs
p⁴
p⁷/p³
depressed poly
quotient when a poly is divided by one of its factors
sides
rays of an angle
Solve by graphing: 3x - y ≤ -6 and x > -3
see board
vertical asymptoptes for rational expressions
set denominator equal to zero and factor; remember to divide out any common factors from numerator!
x-intercepts for rational expressions
set numerator equal to zero and factor, remember to divide out any common factors from denominator!
Quotent Identity (1)
tanX=sinX/cosX
leading coefficient
term with the highest power
Like terms
terms that have the same variable parts
Parabola
the "U" shaped graph of a quadratic equation
Base of a power
the "big" number in a power
Coefficient
the "big" number in a term
Constant of variation
the "k" value in direct (y = kx) or inverse variation (xy = k)
Exponent
the "little" number in a power
Profit
the amount of money made after costs are subtracted
Commission
the amount of money made from making a sale
Volume
the amount of space needed to fill a 3-dimensional figure
Area
the amount of space within a 2-dimensional figure
Half-life
the amount of time needed to reduce a quantity in half
Discount
the amount that can be taken off of the original amount
Scale factor
the amount used to multiply a figure
Product
the answer of multiplication
Sum
the answer to addition
Quotient
the answer to division
Difference
the answer to subtraction
Mean
the average, obtained by adding the scores and then dividing by the number of scores
Initial value
the beginning amount in an exponential function represented by the letter "a" in y = a(b)x
Greatest Common Factor
the biggest term that can be divided into two or more terms
Denominator
the bottom part of a fraction
Leading coefficient
the coefficient of the first term when a polynomial is written so that the exponents decrease from left to right
sides
the connecting line segments of a polygon
Common difference
the constant difference between consecutive terms in a sequence
Ordered Pair
the coordinates of a point (x, y)
Range of a data set
the difference between the biggest and smallest values in a set of data
radicand
the number inside the radical sign √ ← under the line.
index
the number over the radical sign √ indicating the root of the radicand.
Mode
the number(s) that occur the most in a set of data
Whole numbers
the numbers 0, 1, 2, ...
Corresponding parts
the parts of a figure that have the same relative position
Percent of change
the percent a quantity increases/decreases; p% = amount of increase/decrease divided by original
Percent of decrease
the percent of change when the new amount is less than the original amount
Percent of increase
the percent of change when the new amount is more than the original amount
Breakeven point
the point in which cost = profit
Midpoint
the point on a line that is equidistant from the endpoints
x-intercept
the point where the graph crosses the x-axis; the y-value will always be zero
y-intercept
the point where the graph crosses the y-axis; the x-value will always be zero
Linear regression
the process that finds the best-fitting line to model a set of data (can be done on the calculator)
Undefined slope
the slope of a vertical line
"a" in y = a•bx
the variable used to represent the initial amount in an exponential function
"m" in y = mx + b
the variable used to represent the slope of a line
y-axis
the vertical axis on a coordinate plane
Slope
the vertical change (rise) over the horizontal change (run) in a line
Factor completely
to factor a polynomial until there are no other factorable parts
Factoring
to find the factors of a polynomial
Evaluate
to find the value of an expression by substituting a numbers in for the variables
Perpendicular lines
two lines that intersect at a 90 degree angle
Parallel lines
two lines that never intersect
System of linear equations
two or more equations using the same variables
Linear system
two or more linear equations that have the same variables
System of linear inequalities in two variables
two or more linear inequalities using the same variables
Absolute Value Equation with vertex (h, k)
y = a(x - h)^2 + k
Vertex Form for a Quadratic
y = a(x - h)^2 + k
Intercept Form for a Quadratic
y = a(x - p)(x - q)
range
y-coordinates, output
Point Slope Equation
y-y1=m(x-x1)
inverse variation
y=k/x
direct variation
y=kx
joint variation
y=kxz, y varies jointly with x and z
Parent linear function
y=x
Parent quadratic function
y=x2
-2
z = -8x 3x = -2y 3x - 7y + 2z = 5 Solve for x
3
z = -8x 3x = -2y 3x - 7y + 2z = 5 Solve for y
16
z = -8x 3x = -2y 3x - 7y + 2z = 5 Solve for z
11PM the next day
At 3PM a passenger train left Newport heading southwest at a rate of 29.3125 mph. At what time would it arrive at Frankensburg, which was 938 miles away?
28 5/6 mph
At 4 PM a passenger train headed southwest to a city called Earlsentown, and arrived at 10PM the next morning. How fast did the train travel?
33mph
At 6AM a freight train headed west. 7 hours later, an express train headed east at a rate of 29mph. How fast did the freight train travel if they met at 6PM and started out 1851 miles apart?
40mph
At 7AM, the express train headed south at a speed of 28mph. 4 hours later, the freight train headed north from the same station. If they were 548 miles apart at 6PM, how fast did the freight train travel?
3:30PM
At 9AM the train headed west at a speed of 32mph. At noon, a bus left the same place and headed east at a rate of 48mph. At what time were the train and bus 376 miles apart?
7AM the next morning
At what time did the express train travel 250 miles if it was traveling at a rate of 12.5mph and started at 11AM?
Standard form of a linear equation
Ax + By = C
√144
12
√49
7
Solving Absolute Value Inequalities
GOLA; Greater than - OR, Less than - AND
Domain
Set of inputs (x- value)
Relation
Set of pairs of input and output values
Formula
an equation that can be used to find a specified value
Identity
an equation that is true for all values
Proportion
an equation that states to ratios are equal
Literal equation
an equation where letters are used to represent numbers
Linear equation
an equation whose graph is a straight line
synthetic division
process for dividing polynomials by a linear factor using the coefficients
9
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for k
-196
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for q
√200
10√2
√121
11
-2(n - 5)
-2n + 10
8.4
-3x + 4y = -27.1 2x - 3y = 15 Solve for y
3x + 6y - 8x - y
-5x + 5y
-25
-5²
-2.6
-6x + 3y = -68.4 9x - 2y = 96.1 Solve for y
When solving a matrix equation, use...?
"A inverse times B" meaning A^-1 times B
-1
(-1)²³
1
(-1)³²
Difference of 2 squares
A2-B2=(A-B)(A+B)
dichlorodifluoromethane
CCl₂F₂
potassium chlorate
KClO₃
supplementary angles
Two angles whose sum is 180 degrees
Reciprocal Identity (3)
tanX=1/cotX
9x⁶
(3x³)²
1
(-1)⁸
2x + 3y = 7, x - 2y = -7
(-1, 3)
-1/1000
(-10)⁻³
10,000p¹²
(-10p³)⁴
2/3 ÷ -4/3
- 1/2
0
0⁴
√1
1
Pythagorean Identity (3)
1+cot^2(X)=csc^2(X)
Pythagorean Identity (2)
1+tan^2(X)=sec^2(X)
How do you find the inverse of a function?
1. "y = " form, 2. switch x and y, 3. solve for y
Methods to Solve a Quadratic
1. Graphing, 2. Factoring, if factorable, 3. Completing the Square, 4. Quadratic Formula
2^(-3)
1/(2^3) = 1/8
1
1⁻⁵
3(4 - 2n) + 8n
2n + 12
2(n + 4)
2n + 8
-1
2p = c = (a - 4) = x = (d - 1) 31 = .5x + a + x + 4 + p + x + c + x + 1 + d Solve for a
3
2p = c = (a - 4) = x = (d - 1) 31 = .5x + a + x + 4 + p + x + c + x + 1 + d Solve for c
3(n - 3)
3n - 9
2x²
3x² - x²
√48
4√3
125
5
√25
5
-( -5 - 4m)
5 + 4m
6.4
64x - 46y = 8,982 601x + 106y = 27,228 Solve for x
-10.6
64x - 46y = 8,982 601x + 106y = 27,228 Solve for y
6(n +3)
6n + 18
(5 * 16) + 2
82
Compound Interest Formula
A = P(1 + r/n)^(n x t), r is the rate, n is the number of times compounded, t is time
Sum of 2 Cubes
A3+B3=(A+B)(A2-AB+B2)
Difference of 2 Cubes
A3-B3=(A-B)(A2+AB+B2)
Elimination- Linear Combination
Add equations together to eliminate a variable
Domain for an Exponential Function?
All real numbers
Range for a Logarithmic Function?
All real numbers
Angle
Angle comes from the Latin word "angulum" meaning corner. It is formed by two rays that have a common endpoint.
Point Slope Standard Form
Ax+Bx=C
tetrachloride
CCl₄
Column Matrix
Consists of one column
Mutually Exclusive
Events that cannot occur at the same time
ammonium chloride
NH₄Cl
sodium hypochlorite
NaClO
sodium hydroxide
NaOH
sodium monohydrogen
Na₂HPO₄
Does every matrix have an inverse?
No. If the determinant equals 0, there will not be an inverse.
Probability
The likelihood that an event will occur. The probability that an event will occur is 0, 1, or somewhere between 0 and 1.
Median
The middle number in a set of numbers that are listed in order
24
Will bought $120 worth of $5 pizzas...how many pizzas did he buy?
Can you take a cube root of a negative number?
Yes, and the answer will be negative. A negative number raised to an odd power equals a negative.
zinc nitride
Zn₃N₂
relative max
a "peak" in a graph
relative min
a "valley" in a graph
Write log base a of b = c in exponential form .
a ^ c = b
polygon
a closed plane figure formed by three or more line segments
How do you know that two functions are inverses of each other?
f ( g(x)) = g (f(x)) = x
the sum of radical expressions can be obtained
if and only if the radicands are the same.
6x + 3y = 3, 8x + 4y = 4
infinite number of solutions
1/p⁴
p³/p⁷
Reciprocal Identity (1)
sinX=1/cscX
Pythagorean Identity (1)
sin^2(X)+cos^2(X)=1
1/(x^-2)
x^2
3
√(x² - 5x + 3 + x - (-(√36))) + ⁵√1⁴ = √(x² - 4x + 4) + ⁴√(216(6))
3
√(x² - 5x +3 + x + 36) + ⁵√1⁴ = √(x² - 4x + 4) + ⁴√(216(6))
2
√(√((x² - 4x + 20)²)) - ⁴√4² + (-(2√-1√-1√-1√-1)) - (-(¹⁰√32²))
√100
10
-0.3
101x + 203y = 10.3 -25x - 100y = 5.5 Solve for x
0.2
101x + 203y = 10.3 -25x - 100y = 5.5 Solve for y
1/3 (33 - x)
11 - 1/3x
2.9
13x +14y = 0.3 -x -101y = 296 Solve for y
√324
18
√361
19
1
1⁻⁸
8
2
√4
2
√529
23
√576
24
√625
25
Quadratic function - an equation that can be written in the form ax2 + bx + c
...
1000
10
Polynomial
a monomial or sum of monomials
-18
2y = z = 3v = -.5w = (9 + x) 41w + 15x + 61y + 17z + 201v = 292.5 Solve for w
2
2x = -15y -xy + 0.1(xy) = 2z 2z - 2y + 3x = z - 17.3 Solve for y
31.7
2x = -15y -xy + 0.1(xy) = 2z 2z - 2y + 3x = z - 17.3 Solve for z
0
2x = 0
0
2x = x
Can't simplify further
2x³y² + 5x⁵y⁶
3
2y = z = 3v = -.5w = (9 + x) 41w + 15x + 61y + 17z + 201v = 292.5 Solve for v
0
2y = z = 3v = -.5w = (9 + x) 41w + 15x + 61y + 17z + 201v = 292.5 Solve for x`
4.5
2y = z = 3v = -.5w = (9 + x) 41w + 15x + 61y + 17z + 201v = 292.5 Solve for y
9
2y = z = 3v = -.5w = (9 + x) 41w + 15x + 61y + 17z + 201v = 292.5 Solve for z
1
2⁰
¼
2⁻²
⅛
2⁻³
½
2⁻¹
1/16
2⁻⁴
1/32
2⁻⁵
√8
2√2
√12
2√3
√24
2√6
27
3
189
31 times the number of yellow marbles was equal to 21 times the number of black marbles. Also, 2 times the number of yellow marbles exceeded the number of black marbles by 99. How many yellow marbles were there?
Circle
360-degree angle
24u⁸
3u²⋅8u⁶
I start with x, multiply it by 3 and then add 6
3x + 6
1/9
3⁻²
⅓
3⁻¹
√18
3√2
√27
3√3
64
4
2k - 3m + n + 3k - m - n
5k - 4m
7 + 4t + 6 + t
5t + 13
Now put the terms together: 2x + 3 + 3x + 5
5x + 8
16x²y³
5x²y³ + 11x²y³
1/25
5⁻²
√50
5√2
√75
5√3
216
6
√36
6
6(n - 3)
6n -18
I start with x, multiply it by 6 and then subtract y
6x - y
√108
6√3
343
7
Can't simplify further
7a + 7a²
√98
7√2
512
8
√64
8
5x - 3 + 2x + 10 + x
8x + 7
√128
8√2
729
9
√81
9
-3(3 + n)
9 - 3n
quadrilateral
A polygon with 4 sides
parallelogram
A quadrilateral with two pairs of parallel sides
Ray
A ray is sometimes called a half line. It has one endpoint at the beginning called the origin
Perpendicular
A ray that makes a square corner. Two lines which are at right angles at their point of intersection are called perpendicular lines. Represented by the symbol
7
After putting some money into her savings jar and walking away, Janet suddenly changed her mind and began to count her money. She found that she had $42. She also discovered that the number of five-dollar bills was 21 deficient of the number of quarters. How many five-dollar bills did she have?
28
After putting some money into her savings jar and walking away, Janet suddenly changed her mind and began to count her money. She found that she had $42. She also discovered that the number of five-dollar bills was 21 deficient of the number of quarters. How many quarters did she have?
1090
After recovering his pocketbook, elderly Jacob Moore sat down to count the cash in it. After counting, he rediscovered that he had $161,320 in 100-dollar bills and 20-dollar bills. How many 100-dollar bills did he have?
2616
After recovering his pocketbook, elderly Jacob Moore sat down to count the cash in it. After counting, he rediscovered that he had $161,320 in 100-dollar bills and 20-dollar bills. How many 20-dollar bills did he have?
Acute angle
An acute angle is an angle that equals less than 90
Inequality
an open sentence that contains an inequality symbol (<, ≤, >, or ≥)
point
a location
2
2p = c = (a - 4) = x = (d - 1) 31 = .5x + a + x + 4 + p + x + c + x + 1 + d Solve for d
1.5
2p = c = (a - 4) = x = (d - 1) 31 = .5x + a + x + 4 + p + x + c + x + 1 + d Solve for p
ammonia
NH₃
3
2p = c = (a - 4) = x = (d - 1) 31 = .5x + a + x + 4 + p + x + c + x + 1 + d Solve for x
12s - 3t + 2 - 10s - 4t + 12
2s - 7t + 14
2(x + 3)
2x + 6
0
2x + x = 4x
simplifying radicals (square roots only)
1. divide the number inside the radical into two factors, one of which is a perfect square 2. square root the perfect square 3. leave the non-perfect square under the radical
-15
2x = -15y -xy + 0.1(xy) = 2z 2z - 2y + 3x = z - 17.3 Solve for x
-1000p¹²
(-10p⁴)³
1
(-2)⁰
1/9
(-3)⁻²
-27w⁶
(-3w²)³
9w⁶
(-3w³)²
-2x + 3y = 8, x - 5y = -4
(-4, 0)
25
(-5)²
Solve: 3x + 2y = -19 and x - 12y = 19
(-5, -2)
4x + 3y = 3, 2x + y =-3
(-6, 9)
Vertex of a Quadratic Function
(-b/2a, Plug it in)
Vertex
(-b/m,c)
x⁸y⁴
(-x²y)⁴
-x¹⁰y¹⁵
(-x²y³)⁵
Origin
(0, 0)
3x - 7y = 10, x - 4y = 5
(1, -1)
10,000
(1/10)⁻⁵
2x - 3y = 4, 8x + 3y = 1
(1/2, -1)
2x + y = -2, -2x + 5y = -16
(1/2, -3)
6x + y = -2, 4x - 3y = 17
(1/2, -5)
-5y³/x⁷
(10xy⁵)/(-2x⁸y²)
Solve: 8x + 2y = -2 and y = -5x + 1
(2, -9)
10a⁹
(2a³)(5a⁶)
2a⁸
(2a³)³/(4a)
32a¹⁵
(2a³)⁵
Solve: y = -2x - 1 and y = 3x - 16
(3, -7)
2x + y = 6, 3x + 5y = 9
(3, 0)
a/2
(3a²b)/(6ab)
Discriminant
(Square root of) b2-4ac
Associative property
(a+b)+c=a+(b+c)
2
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for e
5
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for f
-7
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for g
198
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for h
-1
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for i
2
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for j
5
(i + 3) = e = 2/9k = -2/7g = .4f = j = -1/98q = 1/99h = (s-3) 17 = i + g + f + e + j + k + q + s + h Solve for s
Standard Form Equation for a Circle with center (h, k)
(x - h)^2 + (y - k)^2 = r^2, circle with center at (h, k) and radius of r
9 ÷ (-3) - 8÷ (-4)
-1
What's i^2?
-1
-2.5 (4p +14)
-10p + -35
-5(2x - 2)
-10x + 10
-1
-1⁵
-2(n -4)
-2n + 8
-1
-2⁰
20.1
-3x + 4y = -27.1 2x - 3y = 15 Solve for x
10.1
-6x + 3y = -68.4 9x - 2y = 96.1 Solve for x
-3²
-9
-3(4 + w) - 6w
-9w + -12
-(n + 12)
-n - 12
12
-x + 2y = -36.2 3x - 4y = 84.4 Solve for x
-12.1
-x + 2y = -36.2 3x - 4y = 84.4 Solve for y
-1.1
-x - y = -100.4 2x + y = 99.3 Solve for x
101.5
-x - y = -100.4 2x + y = 99.3 Solve for y
Mean - the average of a set of data
...
What is the slope for a horizontal line?
0
What ways can you solve a system?
1. graph, 2. substitution, 3. linear combination or elimination, 4. use a matrix equation, if the system is linear
61.8mph
Ben could go the 202 miles to the next major city in 2 hours less than it took Jennifer to go the 309 miles to the following major city. Also, 45 times the rate of Ben was 369 mph less than 55 times the rate of Jennifer. What was the rate of Jennifer?
methyl bromide
CH₂Br
methylene bromine
CH₂Br₂
carbon dioxide
CO₂
How can radical expressions be written without a radical sign?
Change the root to a fraction with the root as the denominator and any exponents on a radicand as the numerator.
Row Matrix
Consists of one row
chromium chloride
CrCl₃
Third degree polynomials are called...
Cubic
1853
During Christmas Season, Salvation Army took in $2,212.70 in 5,450 $1 bills and dimes through red buckets. How many $1 bills did they take in?
3597
During Christmas Season, Salvation Army took in $2,212.70 in 5,450 $1 bills and dimes through red buckets. How many dimes did they take in?
185
During the Christmas Season, Goodwill took in $1,025 worth of old bikes worth $20 apiece and Christmas do-dads worth $5 apiece. In all there were 190 items received. How many Christmas do-dads did Goodwill take in?
5
During the Christmas Season, Goodwill took in $1,025 worth of old bikes worth $20 apiece and Christmas do-dads worth $5 apiece. In all there were 190 items received. How many old bikes did Goodwill take in?
Area of a triangle given coordinates for the three vertices?
Enter three vertices, (x, y) in a 3 X 3 matrix, in rows 1, 2, and 3, with 1's in the last column. Take plus or minus 1/2 of the determinant.
iron sulfide
FeS
43mph
How fast did the train go if it left at noon and by 3PM traveled 129 miles?
water
H₂O
sulfuric acid
H₂SO⁴
sulfurous acid
H₂SO₃
Vertical Line Test
If passes 2 points on graph=> NOT a function
What does the value of the discriminant tell about a quadratic?
If the discriminant = 0, there is one real solution & graph "sits or bumps" x-axis. If the discriminant > than 0, there are two real solutions & graph crosses x-axis twice. If the discriminant < 0, there are no real solutions, two imaginary solutions & graph does not cross x-axis.
47.8mph
It is 666.9 miles from Enfartsenburg to Jaguar City and 479.1 miles from Enfartsenburg to Kenyantown. A train left Enfartsenburg at 6:30 AM and headed to Jaguar City. 5 1/4 hour later, a bus left from the same place and headed for Kenyantown. The bus reached Kenyantown 14 3/4 hours after the train left the station. The train, however, had arrived 5 hours before that. How fast did the bus travel?
68.4mph
It is 666.9 miles from Enfartsenburg to Jaguar City and 479.1 miles from Enfartsenburg to Kenyantown. A train left Enfartsenburg at 6:30 AM and headed to Jaguar City. 5 1/4 hour later, a bus left from the same place and headed for Kenyantown. The bus reached Kenyantown 14 3/4 hours after the train left the station. The train, however, had arrived 5 hours before that. How fast did the train travel?
43mph
It was 440 miles from Frankensburg to Italizcen and 688 miles from Frankensburg to Howell. At 6AM a bus left Frankensburg to go to Howell. 7 hours later, a train headed from Frankensburg to go to Italizcen, and arrived at 11PM, one hour later than the bus. How fast did the bus travel?
44mph
It was 440 miles from Frankensburg to Italizcen and 688 miles from Frankensburg to Howell. At 6AM a bus left Frankensburg to go to Howell. 7 hours later, a train headed from Frankensburg to go to Italizcen, and arrived at 11PM, one hour later than the bus. How fast did the train travel?
22
James collected pennies and quarters in loose change from the mall floor. After he counted it, he discovered that he had found $6.09. How many quarters did he have?
88
John and Ken counted their hoard of dimes and pennies and discovered that the total value was $10.13. How many dimes did they have?
133
John and Ken counted their hoard of dimes and pennies and discovered that the total value was $10.13. How many pennies did they have?
5AM the next morning
Jonathan knew that from the station his 1 o'clock PM train left from to his destination was 368 miles. If his train traveled 23 mph, at what time did Jonathan arrive at his destination?
23
Joyce collected pennies and dimes in loose change from the mall floor. Upon counting it, she found out that she had $2.79. How many dimes did she have?
49
Joyce collected pennies and dimes in loose change from the mall floor. Upon counting it, she found out that she had $2.79. How many pennies did she have?
111
Larry's wallet contained $30.60 in quarters and dimes. The number of dimes exceeded that of the quarters by 33. How many dimes did Larry have?
78
Larry's wallet contained $30.60 in quarters and dimes. The number of dimes exceeded that of the quarters by 33. How many quarters did Larry have?
parallel lines
Lines in the same plane that do not intersect are called parallel lines. Two lines that run in the same direction
2
Mrs. Clasvin's class had an experiment with marbles. 9 times the number of yellow marbles was 3 more than 3 times the number of red marbles. Also, there was 2½ timed as many red marbles as yellow marbles. How many yellow marbles were there?
Solution of a system of linear equations
an ordered pair that is a solution to all of the equations in the system
5
Mrs. Clasvin's class had an experiment with marbles. 9 times the number of yellow marbles was 3 more than 3 times the number of red marbles. Also, there was 2½ timed as many red marbles as yellow marbles. How many yellow marbles were there?
What do you know about slopes of parallel lines?
Parallel lines have the same slope!
Inconsistent Lines
ParallelI
What do you know about slopes of perpendicular lines?
Perpendicular lines have slopes that are opposite reciprocals of each other!
Completing the Square
Remember to have a coefficient of 1 for the squared term. Take 1/2 of b and square it. Add to both sides. Solve through square roots.
14
Ron received $9.70 in change from the cashier in one-dollar bills and nickels. Upon counting the coins, he discovered that the total number of coins was 23. How many nickels did he have?
9
Ron received $9.70 in change from the cashier in one-dollar bills and nickels. Upon counting the coins, he discovered that the total number of coins was 23. How many one-dollar bills did he have?
Coinciding Lines
Same Line ( All Real )
Range
Set of outputs (y-value)
How do you solve an absolute value equation?
Set the expression from inside the absolute value equal to the positive constant and to the negative constant.
Subsitution
Solving for one variable in one equation & plugging it into the second
69mL
The chemist needed 100 mL of a solution that was 26% iodine. She had a solution that was 49% iodine, and another that was 15 2/3% iodine. How many mL should he use of the solution that was 15 2/3% iodine?
47.5 L
The chemist needed 76 liters of a solution that was 48.5% ammonia. She had a solution that was 96% ammonia, and another that was 20% ammonia. How many mL should he use of the solution that was 20% ammonia?
28.5 L
The chemist needed 76 liters of a solution that was 48.5% ammonia. She had a solution that was 96% ammonia, and another that was 20% ammonia. How many mL should he use of the solution that was 96% ammonia?
520
The fuel man needed 1000mL of a fuel that was 36.2% alcohol. He had a container of a mixture that was 12.2% alcohol and another that was 62.2% alcohol. How much of the mixture that was 12.2% alcohol should he use?
480
The fuel man needed 1000mL of a fuel that was 36.2% alcohol. He had a container of a mixture that was 12.2% alcohol and another that was 62.2% alcohol. How much of the mixture that was 62.2% alcohol should he use?
385mL
The new chemist needed 500mL of a solution that was 14.25% ant-an-thrombi acid. She had a tube that was 2.75% ant-an-thrombi acid, and another that was 52.75% ant-an-thrombi acid. How much of the solution that was 2.75% ant-an-thrombi acid should she use?
115mL
The new chemist needed 500mL of a solution that was 14.25% ant-an-thrombi acid. She had a tube that was 2.75% ant-an-thrombi acid, and another that was 52.75% ant-an-thrombi acid. How much of the solution that was 52.75% ant-an-thrombi acid should she use?
286
The number of green marbles was 583 less than 8 times the number of pink marbles. Also, 6 times the number of pink marbles was 286 less than 4 times the number of gray marbles. Even so, 54 times the number of green marbles was equal to 153 times the number of orange marbles. How many gray marbles were there?
561
The number of green marbles was 583 less than 8 times the number of pink marbles. Also, 6 times the number of pink marbles was 286 less than 4 times the number of gray marbles. Even so, 54 times the number of green marbles was equal to 153 times the number of orange marbles. How many green marbles were there?
198
The number of green marbles was 583 less than 8 times the number of pink marbles. Also, 6 times the number of pink marbles was 286 less than 4 times the number of gray marbles. Even so, 54 times the number of green marbles was equal to 153 times the number of orange marbles. How many orange marbles were there?
142
The number of green marbles was 583 less than 8 times the number of pink marbles. Also, 6 times the number of pink marbles was 286 less than 4 times the number of gray marbles. Even so, 54 times the number of green marbles was equal to 153 times the number of orange marbles. How many pink marbles were there?
Mode
The number that occurs most often in a set of data
625.4442
The pharmacist needed 1,175.0914 mL of a solution that was 0.4684711% iron sulphate. If the pharmacist had a bottle that was 0.7861932% iron sulphate and another that was 0.1986475% iron sulphate. How much should she use of the solution that was 0.1986475% iron sulphate?
539.6572
The pharmacist needed 1,175.0914 mL of a solution that was 0.4684711% iron sulphate. If the pharmacist had a bottle that was 0.7861932% iron sulphate and another that was 0.1986475% iron sulphate. How much should she use of the solution that was 0.7861932% iron sulphate?
What is a circle?
The set of all points (x, y) that are equidistant from a fixed point called the center.
42mph
The train made the trip in 9 hours while the bus made all but 39 miles of the trip in 10 hours. How fast did the bus travel?
45
The well known man received Christmas gifts of $5 bills and $10 bills for a grand total of $625. The number of $5 bills was 10 less than the number of $10 bills How many $10 bills did he receive?
45
The well known man received for Christmas useful items and non-useful items for a total of 99. 5 times the number of useful items was equal to 6 times the number non-useful items. How many non-useful items did he receive?
Solution of a system of linear inequalities
an ordered pair that is a solution to all of the inequalities in the system
54
The well known man received for Christmas useful items and non-useful items for a total of 99. 5 times the number of useful items was equal to 6 times the number non-useful items. How many useful items did he receive?
How do you set up a matrix equation to solve a linear system of equations?
There are three matrices in the equation. A coefficient matrix, where coefficients come from standard form equations, a variable matrix, and a constant matrix.
130
There were 2,330 less green marbles than 21 times the number of blue marbles. And 13 times the number of red marbles was 1,630 more than the number of opaque marbles. Also, 144 times the number of red marbles was equal to 54 times the number of green marbles. How many blue marbles were there?
400
There were 2,330 less green marbles than 21 times the number of blue marbles. And 13 times the number of red marbles was 1,630 more than the number of opaque marbles. Also, 144 times the number of red marbles was equal to 54 times the number of green marbles. How many green marbles were there?
320
There were 2,330 less green marbles than 21 times the number of blue marbles. And 13 times the number of red marbles was 1,630 more than the number of opaque marbles. Also, 144 times the number of red marbles was equal to 54 times the number of green marbles. How many opaque marbles were there?
150
There were 2,330 less green marbles than 21 times the number of blue marbles. And 13 times the number of red marbles was 1,630 more than the number of opaque marbles. Also, 144 times the number of red marbles was equal to 54 times the number of green marbles. How many red marbles were there?
perpendicular lines
Two lines that intersect to form right angles
How many roots does a square root have?
Two, positive and negative roots
T₂P₁V₁ over P₂V₂
T₁
P₂V₂T₁ over P₁V₁
T₂
Factorial
Used in determining the different arrangements of objects. For example: How many ways can you arrange 4 desks? 4! which means 4 x 3 x 2 x 1 = 24 ways
What's the horizontal line test?
Used on an original function to determine if the inverse would be a function. Yes, you may still use the vertical line test on an inverse.
Line
a collection of points that extends indefinitely in two directions
traingles
a figure formed by 3 line segments that intersect only at their end point
plane
a flat surface with no edges, or boundaries
Pythagorean Theorem
a formula used to find the sides of a triangle; a2 + b2 = c2
Rate
a fraction that compares two quantities measured in different units
Linear function
a function that can be represented by a line that is not vertical
Direct variation
a linear relationship that can be modeled with y = kx
root
a number indicating the number of repetitive factors needed to obtain the radicand, ie. square root (xx) cube root (xxx).
Solution of an equation in one variable
a number that makes a true statement when substituted into an equation
square
a parallelogram with four congruent sides and four right angles
Inverse variation
a relationship that can be represented by the equation xy = k
Exponential decay
a situation that decreases by the same percent each time; the growth rate is 0 < b < 1
Exponential growth
a situation that increases by the same percent each time; the growth rate is b > 1
Infinite solutions
a system of equations in which all values are true (the equations are the same line)
No solution
a system of equations in which there are no solutions (the lines are parallel)
Constant term
a term with no variable part; a value that stays the same
Vertical line test
a test in order to determine if graph is a function by seeing if a vertical line can be placed anywhere on the graph and it will only pass through one point
Commutative property
a+b=b+a
Negative exponent
a-n = 1/an
Zero exponent
a0 = 1
(a^2)^6
a^12
(a^6)/(a^2)
a^4
(a^2)( a^6)
a^8
Range of a function
all the possible x-values of a function
product of powers
all the variables are powers of the same variable
function
all x's must be different, x's are used one time only,use vertical line test on the graph
Point-slope form
an equation in the form y - y1 = m(x - x1)
Slope-intercept form
an equation in the form y = mx + b
Function rule
an expression that can be used to represent a functional set of data
Binomial
an expression that contains two terms
Factor
an expression that is part of a product
Power
an expression that represents repeated multiplication (bx)
Equation
an open sentence that contains an equal sign
