Algebra Period 3

Check this out!! They earned MAJOR extra credit!! How about you????


SO??? As Mr. Kaiser said last night at the awesome talent show, "Our school has talent."

Math 6 H Periods 1, 6 & 7

I found this image and immediately thought of our feast this Friday.

What do you think this plate is for? What is missing?

Math 6 H Periods 1, 6 & 7 (Tuesday)

Computing with Percents 9-3
The statement 20% of 300 is 60 can be translated into the following equations
20/100(300) = 60 or 0.20 •300 = 60

EQUATION METHOD:
Notice the following relationship between the words and the symbols
20% of 300 is 60
0.20 • 300 = 60

WRITE THE PROBLEM OUT AND THEN DIRECTLY UNDER THE "IS" WRITE AN EQUAL SIGN. DIRECTLY UNDER THE WORD 'OF" WRITE A MULTIPLICATION SIGN. iF YOU ARE GIVEN A % CHANGE IT FIRST TO A DECIMAL. THEN BRING DOWN ALL THE OTHER NUMBERS GIVEN IN YOUR PROBLEM. LET x OR n REPRESENT YOUR VARIABLE... THAT IS THE "WHAT " PART OF YOUR PROBLEM.

A similar relationship occurs whenever a statement or a question involves a number that is a percent of another number

What is 8% of 75?
Let n represent the number asked for
What number is 8% of 75?
n = 0.08 • 75

solve
What percent of 40 is 6?
let n represent the percent asked for.

What percent of 40 is 6?
n% • 40 = 6
n% • 40 = 6
n% (40)/40 = 6/40
n% = 6/40
n/100 = 6/40
(100) n/100 = (100) 6/40
n=15 so 15% of 40 is 6

140 is 35 % of what number?
let n represent the number asked for
140 is 35% of what number?
140 = 0.35 • n
140 = 0.35n
140/0.35 = 0.35n/0.35 divide carefully!! Watch those decimals!!
400 = n
so 140 is 35% of 400

Always check to see if your answer is logical.

PROPORTION METHOD

In these types of percent problems you are always know three parts of the following proportion

n/1oo = a/b
or better yet
n/100 = is/ of

The n represents the %

Read the problems carefully and you can easily determine which is the "is" and which represents the 'of"
For example:
What percent of 40 is 6?
What percent -- from the problem above indicates that we DO NOT know the n
of 40-- hmm... then 40 must be the 'of' and
similarly is 6 means that 6 represents the 'is'

n/100 = 6/40 solve as a proportion
and you get n= 15 but since it asked us to state the 5 your answer is 15%

140 is 35 % of what number?
In this problem I notice 35% right away so that is the n!!
Then I read the problem again and notice 140 is... hmmm.. THat says 140 must be the is

35/100 = 140/ x I do not know the 'of'

Solve again
x = 400

Algebra Period 3 (Monday)

Quadratic Equations Review

CHAPTER 13 reminds you of the several different ways to SOLVE QUADRATICS
Solving a quadratic means to find the x intercepts of a parabola.
There are different ways of asking the exact same question:

Find the.....
x intercepts = the roots = the solutions = the zeros of a quadratic

We'll answer this question one of the following ways:
1) Read them from the graph (read the x intercepts) That’s were y = 0 or where the parabola crosses the x-axis!!
but...graphing takes time and sometimes the intercepts are not integers

2) Set y or f(x) = 0 and then factor (we did this in Chapter 6)
but...some quadratics are not factorable

3) Square root each side (+ or - square root on the answer side)
but...sometimes the variable side is not a perfect square (it's irrational)

4) If not a perfect square on the variable side, complete the square, then solve using #3 method
Now this method ALWAYS works, but...it takes a lot of time and can get complicated

5) Quadratic Formula (works for EVERY quadratic)
Really easy if you just memorize the formula and how to use it! :)


Each time you will find the ROOTS

Pre Algebra Period 2 (Monday)

Introduction to Geometry: Points, Lines, & Planes 9-1
Point:(symbol is a dot or just a letter) Location in space - no size
Ray: (arrow pointing to the right) - one endpoint and one direction- Named by its endpoint first
Line: (generally, line with arrows on both ends above 2 points on the line) - Series of points that goes on infinitely in both directions - named either direction
Line segment: (a line with no arrows on either end) - a piece of a line with 2 endpoints in either direction
Lines can be parallel (2 vertical lines) or intersecting in the same plane
Parallel lines are lines in the same plane that never meet
If they intersect at exactly 90 degrees, then they are perpendicular
If they don't intersect but are in two different planes, they are skew

Angle Relationships & Parallel Lines 9-2
angle: (angle opening to the right) two rays that meet at the same endpoint
named by either just the vertex, or 3 points on the angle in either direction with vertex in middle
adjacent angles share one ray
vertical angles are opposite each other and congruent (equal)
Complementary sum to 90 degrees and
supplementary sum to 180 degrees
acute is greater than 0 and less than 90
90 degrees is right angle
obtuse is greater than 90 but less than 180
180 is a straight angle (line)
to write the measure of an angle you write m<
Transversal: a line that intersects two other lines

Corresponding angles are formed by this transversal
These angles are on the same side of the transversal and also are both above or both below the line
When the two lines that are intersected are parallel, corresponding angles are congruent

Alternate interior angles are between the two lines (inside the two lines) and on opposite sides of the transversal (alternate sides) These angles are also congruent if the lines are parallel.

Same side interior: If angles are both inside and on the same side of the transversal, they are supplementary (sum to 180 degrees)

You can have lots of corresponding angles if you have a transversal intersecting more than 2 parallel lines - in fact they would be infinite if you kept adding another parallel line!
It's amazing that by just knowing one angle, you know all 8 angles with one transversal and two parallel lines! (I will show this in class on Tuesday!)

Math 6 H Periods 1, 6 & 7 (Monday)

Percent and Fractions 9-1

The word “percent” is derived from the Latin “per centum” meaning “per hundred” or “out of one hundred” so 28% means 28 out of 100

A percent is a ratio that compares a number to 100. Therefore you can write a percent as a fraction with a denominator of 100, so 28% is also 28/100

Our book’s example is as follows;
During basketball season, Alice made 17 out of 25 free throws, while Nina made 7 out of 10. To see who did better, we compare the fractions representing each girl’s successful free throws. 17/25 or 7/10
We have calculated this type of problem before.. this time when we compare fractions use the common denominator 100, even if 100 is not the LCD of the fractions.
17/25 = 68/100 and
7/10 = 70/100

Since Alice makes 68 free throws per 100 and Nina makes 70 per hundred, Nina is the better free throw shooter.
the ratio of a number to 100 is called a percent. We write percents by using the symbol %
so
17/25 =68% and
7/10= 70%

Rule
To express the fraction a/b
as a percent, solve the equation

a/b = n/100

for the variable n and write n%


Express 17/40 as a percent
n/100 = 17/40 multiply both sides by 100 100 ( n/100) = 17(100)/40
n = 17(100)/40 n = 85/2 n= 42½

Therefore, 17/40 = 42 1/2 %


Rule
To express n% as a fraction, write the fraction

n/100 in lowest terms


Express 7 ½ % as a fraction in lowest terms

7 ½ % = 7.5% = 7.5/100 How do we get rid of the decimal?
multiply the numerator and the denominator by 10
7.5(10)/100(10) simplify

Since a percent is the ratio of a number to 100, we can have percents that are greater than or equal to 100%

1 = 100/100 = 100%

165/100 = 165 %

Write 250% as a mixed number in simple form

250% = 250/100

250/100 = 2 50/100 = 2 1/2

The town of Wonderful spends 42% of its budget on education. What percent is used for other purposes?
the whole budget is represented by 100%. Therefore, the part used for other purposes is

100 - 42 or 58%


Percents and Decimals 9-2

By looking at the following examples, you will be able to see a general relationship between decimals and percents

57% = 57/100
0.79 = 79/100 = 79%
113% = 113/100 = 1 13/100
0.06 = 6/100 = 6%

Rules

To express a percent as a decimal, move the decimal point two places to the left and remove the percent sign

57% = 0.57
113% = 1.13

To express a decimal as a percent, move the decimal point two places to the right and add a percent sign

0.79 = 79%
0.06 = 6%


In 9-1 you learned one method of changing a fraction into a percent. Here is an alternative method

Rule
To express a fraction as a percent, first express the fraction as a decimal
and then as a percent

Express 7/8 as a percent

Divide 7 by 8
7/8 = 0.875 = 87.5%

Express 1/3 as a percent
divide 1 by 3
0.33333….. it’s a repeating decimal
express the decimal as a percent 0.333… = 33 1/3%
so, to the nearest tenth of a percent = 33.3% but it is much more accurate to keep the 1/3 and write 33 1/3%