Algebra 101

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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

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

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

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


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