McDougal 1
Zak McDougal
Mrs. Roach
Classics in American Literature
25 March 2009
The Luscious Life of Lou
His poise and his humility in accepting his fate made him one of baseballs most revered
figures (Lou Gehrig 3). This described one of the greatest Ne
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 be multiplied together, the innies can be multiplied to
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
5
negative
reciprocal
3
2
1
5
9
9
1
9
How to determine
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 can take the square root.
If you want to get rid of squar
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 exponents to make your life easier!
1
18 2
x x *x x
19
18
* x
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 coordinate.
When you subtract, you are finding the diffe
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 radical sign (4) is called the index. That symbol would be re
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 already solved for y.
3x + 2y = 13
Rewrite the second e
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 side c. It is always the
longest side of the triangle.
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 point (or points) that are on both lines.
x y 8
x y 2
the
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
Case 2:
y = - 5x + 8
The x-term comes after the = and th
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
mathematical system to the data in order to obtain a desired answ
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
quadratic and then reversing yourself step by step throu
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 through (5, 4)
That means m = and x = 5 and y = 4
y = mx +
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.
Example 1:
The square root
of x2 is x.
64 has both a + and
a
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 pair is a solution.
If it results in a false statement, it
Finding the Intercepts of a Parabola
Y-intercept: Parabolas with an x squared term always either open upward
or downward and they only cross the y-axis in one place. Consequently, they
only have one y-intercept.
As usual, you calculate the y-intercept by
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 analyzing Oedipus attempts to outrun
prophecy and his fate. I
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 lets look at Christianity. God created one man and one wom
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 Jesus, the Quran has a very positive outlook about His lif
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 who offered way to salvation and a life free of
sin. F
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 Project
Purpose:
Describe myth's historical basis/or
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 (- 4).
If you choose + 2 it doesnt work because (+ 2)(+
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 the coefficient of x is equal to the square root of the
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 apply when the increase is irregular (One can of soup
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)
2x = 30
Now divide by 2
x = 15
Substitute 15 into either
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 you want it to affect more than one thing, you need to
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
Paint bucket for shading
For choosing solid or dashed l
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
where they overlap is the answer!
As usual, watch out for t
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 your destination.
These problems are almost always set up