Smith 1
Joshua R. Smith
Dr. Joseph Walker
LITR201 World Literature through the Renaissance
Dr. Walker,
I have decided to answer the age old question of being human
and what this means I will be analyz
Parallel and Perpendicular Lines
Parallel Lines:
slopes are equal
y-intercepts are different
Perpendicular Lines
meet at right angles
slopes are negative reciprocals
number reciprocal
2
3
5
1
9
3
2
1
Solving Radical Equations
Remember that squaring and taking the square root are opposite
operations just like adding and subtracting are opposite operations.
If you want to get rid of a square, you ca
Simplifying Radical Expressions
There are 3 ways to think about these problems:
1) Find factors that are perfect squares, cubes, etc.
72 x3 36 *2* x2 * x 36 * x2 * 2 x 6 x 2 x
2) Use fractional expone
The EASIEST Way to Calculate The Slope Between 2 Points
A few things to remember before we start:
Ordered pairs are always (x, y) so the x-value is the first coordinate and the
y-value is the second c
Radical Signs and Fractional Exponents
Radical signs: When we use a radical sign like
the expression inside
the radical sign (16) is called the radicand and the small number in the crook
of the radica
Substitution
A system of linear equations may be solved by substitution. This is usually the
best method to use when one of the equations is already solved for a variable.
y = 2x + 3
This equation is
The Pythagorean Theorem
The Pythagorean Theorem is specific to right triangles triangles that
have one right angle.
c
b
The side opposite the right angle is
called the hypotenuse and is always
labeled
Solutions to Systems of Linear Equations in Two Variables
A system of linear equations is just two or more equations that are graphed on
the same graph.
A solution to a system of equations is the poin
Solving for y in an equation
Many times, its most convenient when the equation of a line is solved for y.
Case 1:
y = 3x + 2
Happy day! Its already solved for y
5x + y = 8
Subtract 5x from each side
C
Using Systems of Equations
Learning to set up word problems involving systems of equations is a matter of
learning to read carefully, to extract data from the given situation and to apply a
mathematic
Writing a Quadratic Equation Given the Solutions
Hint: These are sometimes easiest to do if you write UP the page, starting
with the solutions at the bottom where they would be if you had solved the
q
Writing the Equation of a Line
Given the slope and y-intercept:
Slope = 5; y-intercept is (0, 2) then the equation is y = 5x 2.
Given the slope and a point on the line:
Slope = and the line passes thr
The Square Root Property
Remember:
Every positive number has 2 square roots a positive one and a negative
one.
Squaring and taking the square root are opposite operations and undo
each other.
Exampl
Finding the Vertex and Maximum or Minimum of a Parabola
To find the vertex of a parabola you just need the following formula:
Once you calculate a value for x, use that value in the formula of the
par
Multiplying Radicals
When you multiply radicals, you just have to remember that there are innies
(expressions under the radical sign) and outies (expressions outside the radical
sign).
The outies can
Linear Inequalities in Two Variables
Is an ordered pair a solution to a linear inequality?
Plug the x value in for the x and the y value in for the y
If it results in a true statement, the ordered pai
First we need to look at each religion to understand how the two are similar. Buddhism and
Christianity were founded by spiritual masters who offered way to salvation and a life free of sin.
First let
Jesus is the major figure in the New Testament, where he appears as the savior of humankind. He
is also a major prophet in the Quran most people do not know this.
Just as it refers to the birth of Jes
Smith 1
Josh Smith
Dr. Joseph Walker
LIT210
Two Masters or One
First we need to look at each religion to understand how the two are similar. Buddhism
and Christianity were founded by spiritual masters
Group D Presents
Ancient Rome and Aeneas
son of Aphrodite
Christopher Bellone
Christopher Kralicek
Lucinda Miller
Joshua Smith
Overview
Project Type:
Analytical & Informational Multimedia PowerPoint
Common Mistakes
Roots of negative numbers: - a source of confusion!
is not a real number because in order to have a square root you have
to have 2 identical numbers that multiply to give the radicand
Completing the Square
This is what is known as a perfect square trinomial:
x2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)2
Properties of a perfect square trinomial:
1) The leading coefficient is 1
2) Half of
Direct Variation
Direct variation occurs when increasing one item causes something else to
increase in a linear fashion (If two cans of soup cost $6, then four cans of
soup will cost $12).
It does not
Elimination
Elimination always works: If you find that you like this method, you can always use it.
EASY:
x y 20
x y =10
Add the equations together
(this is sometimes called the addition method)
2
Exponents
If a is a real number and n is a positive integer, then
multiplied by itself, n times.
an means a
25 2 2 2 2 2 32
The exponent only affects the number or variable immediately to its
left. If
Solving Systems of Linear Inequalities Graphically
Make your graph big enough so that you can see what youre doing.
Learn the tools that you can use to graph lines and inequalities.
Line drawing tool
Graphing Systems of Inequalities
Graphing a system of linear inequalities is just a matter of plotting two
inequalities on the same graph.
y - 3x + 2
2x + y - 1
Super-impose them. The dark shade
wher
Inverse Variation
Inverse variation occurs when increasing one item causes something else to
decrease in a linear fashion. When you are driving, the faster you go, the
less time it takes to get to you
Ordered Pairs and Linear Equations
Linear Equation: the equation of a line.
It may have one or two variables. 2x + 3y = 6, y = 5, and x = 2 are all equations of lines.
Solutions of linear equations: a