math review

graphs of functions

x - input y- output slope intercept form but instead of y, it may say f(x)

circumference and diameter

π = c/d where π is 3.14 c= 2πr

graphing circles

(x-a)^2 + (y-b)^2 = r^2 (a,b) is the center of the cirle

Integers

-integers include negatives -(-2)(-30) are factors of 60 even tho they are (-) -60 is a multiple of each of its factors -60 is divisible by each of its divisors -0 is a multiple of every integer

arc

Part of a circle containing the two points and all points between them. Two points on a circle are always the endpoints of two arcs. see geometry pages for example and terms!

convex polygon

Polygon in which the measure of each interior angle is less than 180

length of the sides of a triangle tip:

The length of each side must be less than the sum of the other two sides. for example the sides of a triangle cannot be for seven and 12 because 12 is greater than 4+7.

special types: Rectangle Square Parallelogram Trapezoid

1. A quadrilateral with four right angles is called a rectangle. The opposite sides and diagonals are congruent. 2. A rectangle with four congruent sides 3. A quadrilateral in which both pairs of opposite sides are parallel, opposite sides and angles are congruent. ALL RECTANGLES ARE PARALLELOGRAMS 4. A quadrilateral in which at least one pair of opposite sides parallel. Two opposite parallel sides of a trapezoid are called basis of the trapezoid. TO FIND THE AREA OF ALL PARALLELOGRAMS INCLUDING RECTANGLES AND SQUARES: BASE X HEIGHT any side can be used as a base. the height is the perpendicular line segment to the opposite base ( base to base) TO FIND THE AREA OF A TRAPEZOID: A=1/2(B1 + B2)(H) B1 & B2 are the lengths of both bases see geometry papers to see two differences

example:

1. If an amount P is to be invested at an annual interest rate of 3.5%, compounded annually, what should be the value of P so that the value of the investment is $1000 at the end of the three years? answer: 902 pg. 247 example is a hard example

How to tell if a two triangles are congruent by comparing some of their sides and angles:

1. It's a three sides of one triangle are congruent to the three sides of another triangle then the triangles are congruent. this proposition is called side to side to side or SSS congruence. 2. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent. This proposition is called side angle side or SAS congruence. 3. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. This is called angle side angle or ASA congruence. Note that if two angles of one triangle are congruent to two angles of another triangle then the remaining angles are also congruent to each other this may be known as angle angle side.

properties of real numbers that you do not understand

1. all division by 0 is undefined, even 0/0 2. adding 2 negatives is negative 3. triangle inequality= absolute value of r+s is less than or equal to the absolute value of r plus the absolute value of s. fill in numbers to check 4. The absolute value of our times the absolute value of S equals the absolute value of RS

algebraic expressions identity

1. ca + cb = c(a+b) 2. ca-cb = c(a-b) 3. (a+b)^2 = a^2 + 2ab + b^2 4. (a-b)^ 2 = a^2 -2ab+b^2 5.a^2-b^2 = (a+b)(a-b) 6.(a+b)^3= a^3 + 3a^2b+3ab^2+b^3 7. (a-b)^3 = a^3 -3a^2b+3ab^2-b^3

examples:

1. consider an experiment with events A, B, and C for which the P(A)= 0.23 P(B)= 0.40 and p(C)= 0.85. Suppose that events A and B are mutually exclusive and events B and C are independent. What is the P(A and B) and P(B or C)? P(A) + P(B) = 0.23 + 0.40 = 0.63 0.40 + 0.85- (0.40)(0.85) = 1.25-0.34 =0.91 2. Suppose that there is a six sided die that is waited in such a way that each time the die is rolled, the probability of rolling any other numbers from 1 to 5 are all equal, but the probability of rolling a six is twice the probability of rolling a one. When you roll a die ones, the 6 outcomes are not equally likely. What are the probabilities are the six outcomes? Let PE cool the probability of rolling a one. And each of the probability of rolling a two, three, four, or five is equal to P, and the probability of rolling a six is equal to 2P. Therefore since the sum of the probabilities of all possible outcomes as one it follows that: 1= P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = p+p+p+p+p+2p=7p so the probability of rolling each other numbers from one to five is one seventh, and I probably rolling a 6 is 2/7. 3. Suppose that you roll the weighted six sided die from the previous example twice. What is the probability that the first role will be an odd number and the second rule be an even number? P(odd) = P(1) + P(3) + P(5) = 3/7 P(even) = P(2) + P (4) + P(6) = 4/7 s0 3/7 X 4/7 = 12/49

what percent of 150 is 12.9? 30% od 350 15 is 60% of what number

12.9/150 times 100. 8.6 .3 times 350 =105 .6z=15. 25

percentages greater than 100

15 is 300% of 5, decimal equivalence of 300 is 3.0 250% of 16 is 40 since (250/100)(16)=2.5 times 16= 40, decimal equivalence of 250% is 2.5

The measures of the interior angles of a triangle add up to

180

congruent circles chord circumference

2 circles with equal radii any line segment joining two points on a circle distance around the circle which is similar to the perimeter of a polygon

example of polynomial

2x squared - 7xy cubed -5 -3 terms -first term is 2x squared where the coefficient is 2 and the degree is 2 -second term is -7xy cubed where -7 is the coefficient and the term is 4 -the third term is -5 with a term of 0 and is a constant term the degree of the polynomial is the greatest so 4! if there are multiple "x" in a polynomial, there is still only one variable since it is all x

solving quadratics by facotring

2x^2 - x - 6 = 0 1. factor it out to get (2x+3)(x-2)=0 2. since it is equal to 0, one of them has to be equal to zero so if you set them both equal to 0 then you can find two different solutions the answer is: -3/2 and 3 TRY 5x^2 + 3x -2 = 0 answer: 2/5 and -1

4 angles add to ..... 2 angles add to .....

360, 180

solving linear equations in two variables

3x + 2y = 8. this is a system of equations and there are two ways to solve.

use elimination

4x + 3y = 13 x+2y =2 1. multiply the second by 4 to get x to have a coefficient of 4 2.now subtract to get rid of the x's to get -5y=5 so y= -1 the solution of the system is (4,-1)

percent decrease

500 to 400 500-400/500(base) so 20% decrease base is initial # before the change view pg 299

geometry

:)

data analysis

:)))

polygon

A closed figure formed by three or more line segments all in the same plane, the line segments are called sides. Each side is joined to two other sides at its and points and these are called vertices.

frequency distribution vs. relative frequency

A frequency distribution is a table or graph that presents the categories or numerical values along with their corresponding frequencies. The relative frequency of a category or a numerical value is the corresponding frequency divided by the total number of data. Relative frequencies may be expressed in terms or percents fractions or decimals. A relative frequency distribution is a table or graph that represents the relative frequencies or the categories or numerical values.

regular polygon

A polygon in which all sides are congruent and all interior angles are congruent. For example an octagon has eight sides so the sum of the measure of the interior angles of an octagon is 8-2×180 = 1080. Therefore in a regular octagon the measure of each angle is 1080 divided by 8 = 135.

inscribed and circumscribed

A polygon is inscribed in a circle of all vertices lie on the circle or equivalently the circle is circumscribed about the polygon. note : if the center of the circle is on one of the sides of the inscribed triangle, that side is the diameter of the circle. If one side of an inscribed triangle is a diameter of the circle then the triangle is a right triangle.

Equilateral triangle Isosceles triangle Right triangle

A triangle with three congruent sides. The measures of the three interior angles are equal in each measure 60 Triangle with at least two congruent sides. If a triangle has two congruent sides on the angles opposite the two congruent sides are congruent. the opposing sides of the two congruent angles are also congruent A triangle with an interior right angle. The side opposite the right angle is called the hypotenuse the other two sides are called legs.

the area of a triangle

A=1/2bh b= length of base h= height of the triangle any side of the triangle can be the base and the height is is the vertex opposite the base (perpendicular line segment)

circular cylinder right circular cylinder

Consist of two bases that are congruent circles lying in a parallel plane in a lateral surface a circular cylinder who's axis is perpendicular to its bases. The height of a right circular cylinder is the perpendicular distance between the two bases the height of a right circular cylinder is equal to the length of the axis V= πr ^2 h. radius: height X area of the base. the radius is of the base surface area: sum of the areas of the two bases and the area of its lateral surface A= 2(πr^2) + 2πrh for example, if a right circular triangle has a height of 6.5 and a base with radius 3 then its volume is = π (3^2)(6.5)= 58.5π and area: = 2π(3^2) + 2π (3)(6.5) = 57π

Quadrilateral

Every quadrilateral has four sides and four interior angles club. The measures of the angles add up to 360.

rectangular solid/ rectangular prism

Has six rectangular surfaces called faces. Adjacent faces are perpendicular to each other. Each line segment that is the intersection of two faces is called an edge and each point I watch the edges intersect is called a vertex. google photo

histogram

Histograms are graphs of frequency distributions that are similar to bar graphs, but they must have a number line for the horizontal access, which represents a numerical value. And a histogram, there are no regular spaces between the bars. Any spaces between bars and histogram indicate that there are no data in intervals represented in the spaces.

cube

I rectangular solid with six Square faces in which length = width = height volume = l X W X h surface area= 2(lw + lh + wh)

tables notes

If relative frequency is expressed in a table and percentages are used, they will add up to 100%. If the relative frequencies were expressed as decimals or fractions instead of percents, the total will be one.

if no side lengths are given, but if angles are ... (isosceles)

If the hypotenuse is y and the two legs are labeled X than using the Pythagorean theorem, Y squared = X squared plus X squared which is equal to Y squared equals 2X squared and then can be solved to be Y equals the square root of X.

line graphs

Is useful for showing the relationship between two numerical variables especially of one of the variables as time. The points are connected by a line segment. A unit of time will be on the horizontal axis. it can also be named a time series.

combinations

Similar to permutations, except you do not want to count different orders or use all options given such as having A, B, C, D, E but having one as ABC. An example follows: Suppose you want to select a 3-person committee from a coupe of 9 students. How many ways are there to do this? since the 3 students are not ordered: 9!/3!(9-3)! = 9!/3!6! = (9)(8)(7)/(3)(2)(1) = 84

3-D

Solids, cubes, cylinders, spheres, pyramids, and cons

Permutations and factorials

Suppose he wants to determine the number of different ways to four letters ABC and D can be placed an order from 1st to 4th. It would be done by doing 4 X 3 X 2 X 1 of 4! which is a factorial. How many different five digit positive energy hours can be formed using the digits 123456 and seven if not in the digits can occur more than once in the integer? 7!/(7-5)! *WRITE TOP OUT FULLY TO BE ABLE TO CROSS THINGS OUT IN NUMERATOR & DENOMINATOR

multiplication principle

Suppose there are two choices to be made sequentially and that the second choice is independent of the first choice. Suppose also that they are K different possibilities for the first choice and T different possibilities for the second choice. The multiplication principle states are under those conditions there are K X M different possibilities for the pair of choices. This can be done with more than two possibilities.

similar triangles

The same shape, but not the same size. see geometry paper notes here!

finite set infinite set empty set subset list set intersection union disjoint/mutually exclusive

Their numbers can be completely counted cannot completely count all numbers no members If A and B are sad and all of the members of a are also members of B then a is a subset of B. Zero is a subset of every set. like a finite set, having members that can all be listed but with two differences. In a list, the members are ordered that is rearranging the members of a list makes it a different list. Also elements can be repeated in a list and the repetitions matter. For example, the last one to three to annaliese 1223 are different lists each with four elements and they are both different from the list 123 which has three elements. In contrast to a list with the elements of us that are given, repetitions are not counted as additional elements in the order of the elements does not matter. For example the site 1232 and the stat 312 are the same set which has three elements. If s & t are sets, then the intersection of S and T is the set of all elements that are in both and is the noted by an upside down U. the union of S&T is the set of all elements that are in either S&T or both and is denoted by U. if sets S&T have no elements in common

concentric circles

Two or more circles with the same center

compound interest "annual interest rate, compounded annually"

V= P(1+r/100) ^t

simple interest

V=P(1+rt/100)

segmented bar graph/stacked bar graph

each rectangular bar is split (in the same bar) to represent two things

annual interest rate, compounded n times per year

v= P (1+r/100n) ^ nt

scatterplots

a value on the x and y and is used to see a trend in the data between the two variables. A prediction that can be made based off a trend line is the approximate number of minutes by which a bicyclist will lower their finishing time for each increase of 10 training index units. This prediction is derived from the ratio of the change in finishing time do the change in training index or the slope of the trend line. to find the slope, use any 2 points on the line. do y2-y1/x2-x1. To compute the decrease in minutes per 10 units, we multiply 0.26 by 60 to get approximately 16 minutes. If we want to know how much the finishing time decreases for an increase of 10 units, we multiply the rate by 10 to 0.26 hours per 10 units.

Adding and Subtracting fractions

adding with same denominator: add top and keep bottom adding with different denominator: find common denominator the convert numerator, add top and keep bottom

data can be quantitative, or numerical such as the ... of individuals or categorical, or nonnumerical such as...

age, height eye color, who people voted for

real numbers

all rational and irrational numbers includes integers, decimals, and fractions, placed on real number line. to the left is more negative like the - square root of 5 is less than -2. another example is 1 is less than the square root of 2 and that is less than 2

acute triangle.... obtuse triangle... right triangle...

angle measure of less than 90 angle measure between 91 and 180 angle measure of 90

when two lines intersect at a point, they form ...... and where they cross is called the.....

angles, vertex

example: x^2-9 over 4x-12

answer: x+3 over 4. x cannot equal 3 because the denominator would then equal 0.

Pythagorean Theorem

a²+b²=c² c is the hypotenuse length a & b are the leg lengths

bar graphs

better for comparison

angles with the same measure are

congruent angles

Two triangles have the same shape and size

congruent triangles , two triangles are congruent if their vertices can be matched up so that the corresponding angles in the corresponding sides are congruent. example on papers for geometry

applications

converting! example 1: if johns present salary s is increased by 14%, then his new salary can be written at 1.14s example 2: A mixture of 12 g of vinegar and oil is 40% vinegar, where all of the measurements are by weight. How many grams of oil must be added to the mixture to produce a new mixture that is only 25% vinegar? (.40)(12)/12+x =0.25 example 3: a batch of computer parts consist of an identical parts, where and is a multiple of 60. Working alone and it's constant rate machine a takes three hours to produce a batch of computer parts. Working alone at a constant rate machine be takes two hours to produce a batch of computer parts. How long will it take the two machines at their respective constant rates to produce a batch of computer parts? Since machine a takes three hours to produce a batch, machine a can produce 1/3 of the batch in one hour. similarly, Machine B can produce 1/2 of the batch in one hour. If we let X represent the number of hours it takes both machines to produce the batch than the two machines will produce one / X of the batch in one hour. When the two machines work together adding their individual production rates 1/3 and 1/2 gives their combined production rate 1 / X. therefore 1/3 + 1/2 = 1/x which is equivalent to 2/6 + 3/6 = 1/x so 5/6 equals 1/x so x = 6/5 which is an hour and 12 minutes example 4: add a fruit stand, apples can be purchased for $.15 each in pairs for $.20 each. at these rates a bag of apples and pears was purchased for $3.80. if the bag contain 21 piece of the fruit how many of the pieces were pears? 0.15a + 0.20p = 3.80 and a+p =21 1. a=21-p so substitue in a and distribute 2. 0.05p = 0.65 so p = 13 so there were 13 pears

Fractions

denominator= cannot be 0 numerator and denominator: rational numbers n is a rational number because it can always me n/1 multiplying a whole fraction by a number means you multiple the numerator and denominator by that #

absolute value

distance between a number and zero. absolute value of 3 and -3 is 3

percent

don't confuse 0.01 with 0.01%. 0.01 =1% but 0.01%=0.0001

solving quadratic equalitons

know the quadratic formula

If E and F are two events of an experiment, we consider two other events related to E and F.

event 1: the event that both E and F occur, that is, outcomes in the set E (upside down U) F event 2: the event that E or F, or both, occur, that is, outcomes in the set E U F 4 rules: 1. P(either E or F, or both, occur)= P(E) + P(F) - P(both E and F occur) 2. If E and F are mutually exclusive, then P(both E and F occur) = 0, and therefore, P(either E or F, or both, occur) = P(E)+P(F) 3. E and F are said to be independent if the occurrence of either event does not affect the occurrence of the other. If two events are independent then P(E)P(F). For example if a fair six sided die is rolled twice, the event of rolling a three on the first role in the event of rolling a three on the second roll are independent and the probability of rolling a three on both roles is 1/6 X 1/6. mutually exclusive means two events cannot occur at the same time AND, + are clues 3 rules restated: 1. P (E or F) = P(E) + P(F) - P(E and F) 2. P ( E or F) = P (E) + P(F) if E and F are mutually exclusive 3. P (E and F)= P(E)P(F) if E and F are independent

Probability

experiment for an uncertain outcome. probability of an event is between 0 & 1 RULES: 1. If anna vent is certain to occur then the probability is one 2. If an event is certain not to occur the probability is zero 3. If an event is possible but not certain to occur then the probability is between zero and one 4. The probability that an event will not occur is equal to one - the probability of the event 5. If he is the event then the probability of E is the sum of the probabilities of the outcomes of E 6. The sum of the probabilities of all possible outcomes of an experiment is one

exponents

exponent of 0 is undefined negative # raised to an even power is always positive negative # raised to an odd power is always negative (-3)^2 = (-3)(-3)=9. -3^2=-((3)(3))=9 negative exponents: a^-1 is 1/a and a^-2 is 1/a^2 and so on

functions

f(x) so fill in numbers for x that would work and that would be the domain. for example 2x/x-6 can have all real number except for 6 cuz then it would be divided by 0 and be undefined. so the answer is all real numbers except for 6. try other examples/video

coordinate geometry

first number: x second number: y there can be reflection on the xy plane symmetric across the y, x, or origin

multiply the algebraic expression

foil. multiply and add like terms.

to solve a problem involving ratios, you can often write a proportion and solve it by cross multiplication

have confidence in yourself!

operations with algebraic expressions

if a number can be factored out such as in 4x+12= 4(x+3) solve: 7x^2 + 14x over 2x + 4. common top and bottom can be cancelled. A fraction is not defined when the denominator is equal to 0. the denominator of the original expression was 2(2+x) which is equal to zero when x equals -2 so the original expression is defined for all x does not equal -2

graphing inequalities

if less than or equal to.... on the line or below if greater than or equal to....on the line and above same y=mx=b but instead of an =, an inequality line of symmetry perfectly splits two lines

percent increase

if quantity increases from 600 - 750. percent increase is found by 750-600/600 ( base) so 25% increase. if it doubles in size then the percent increase is 100%

circle graphs/pie charts

illustrate how a whole is separated into parts. it may be used to represent relative frequency and frequency distribution. each part of the circle is called a sector . if a sector is 7%, then it is 7% of 360.

algebraic expression

include a letter to represent an unknown 89/n+p is one term term with no variable is called a constant degree: sum of the exponents of the variables , no exponent means 1. this is how to find the degree of a polynomial. the number 2 alone has a degree of 0 but 2x has a degree of 1

solving linear inequalities

inequalities are the less than, greater than, etc symbols if you multiply or divide by a (-), flip the sign solving for x: try -3x +5 is less than or equal to 17 answer: greater than or equal to -4 4x+9/11 is less than 5 answer:less than 11.5

Integers

least common multiple: the least positive integer that is a multiple of 2 or more numbers greatest common divisor/greatest common factor: greatest positive integer that is a divisor of 2 or more numbers even integers: only if it can be divided by 2 prime numbers: greater than one and is only divisible by 1 and itself, 2 is the only prime even number. composite numbers is the opposite of prime

terms:

line: extends in both directions and never ends line segment: two endpoints congruent line segments: line segments of equal length

measures of position

low, middle, greatest , percentiles, quartiles. the first, second, and third quartile split the data into about 4 equal groups. there are 99 percentiles numbers that divide the data into 100 roughly equal groups. for quartiles, the first is from low to Q1, then Q1 to Q2, then Q2 to Q3, and then Q3 to G. Q2 is equal to the median always. when the data is in order, Q1 is the median of the fist half and Q3 is the median of the second half. for percentiles, it can be p1, p2, p3, p4, p5, ...., etc. but typically w large groups of data, Q1=P25, Q2 = p50 and so on

measures of central tendencies

mean, median, mode the frequency of the number is also known as the weight of the number

percent

means per 100 .3% = 0.3/100 = .003 12% = 12/100= 0.12

mixed numbers

multiply then add

multiplying and dividing fractions

multiply: multiply the numerators and the denominators divide: flip the second (reciprocal) and then multiply the two fractions

graphing quadratic equations

parabola: y=ax^2 + bx + c if a is positive, it opens upward and if a is negative, it opens downward watch video

box/ box and whisker plots

place L, Q1, Q2, Q3, and G. the whiskers are L and G and spread out to these points. can be used side by side to view two different sets of data. m

things to review

prime divisors, prime factorization

polynomial of 2 and 3 degrees are known as

quadratic and cubic polynomials

measures of dispersion

range, interquartile range, and standard deviation. measure the spread of the data. range: shows the maximum spread of the data. the range is directly effected by outliers. interquartile range: not usually affected by outliers, this is the difference between the third and first quartile. measures the spread of the middle half of the data standard deviation/ population standard deviation: unlike the other two, it depends on each number in the list of data. measures how far each numbers falls from the mean. The more the data are spread away from the mean, the greater the standard deviation in the more the data are clustered around them in the lesser the standard deviation. 1. compute the mean 2. find difference between the mean and each of the values 3. square each of the differences 4. find the average of the squared differences 5. take the nonnegative square root of the average of the squared differences example: 0, 7, 8, 10, 10 1. 7 2. 7, 0, 1, 3, 3 3. 49, 0 ,1 , 9, 9 4. 13.6 5. 3.7

rules of exponents

rule of exponents: 2^3c+1 = 2^10 then 3c+1 = 10 so c = 3 rule 1: a number raised to a negative exponent turns to 1/ the number and exponent rule 2: (3^2)(3^4)=3^6 rule 3: 5^7/5^4= 5^3 rule 4: 7^0=1, 0 is not defined rule 5: (x^a)(y^a)= (xy)^a rule 6: (x/y)^a= x^a/y^a rule 7: (x^a)^b=x^ab extra: (-x)^2 = x^2 extra: square root of x^2 + y^2 does not equal x+y

calculating distance between two points

use pythagorean theorem. form a triangle on the graph using the given line segment as the hypotenuse and find intersecting point find the length of the vertical and horizontal part using your three points c= the square root of a^2 + b^2 to find the length

more measures of dispersion

sample standard deviation: computed by dividing the sum of the square differences by n -1 instead of n. It is preferred for a sample of data that is taken from a larger population of data. example: 600 applicants for several post office jobs were rated on a scale from 1 to 50 points. The ratings had a mean of 32. 5 points and a standard deviation of 7.1 points. How many standard deviations above or below the mean is a rating of 48 points? A rating of 30 points? A rating of 20 points? 1. one standard deviation above the mean: 32.5 + d so 32.5 + 7.1 = 39.6 2. Two standard deviations above the mean: 32.5 +2d so 32.5 + 2(7.1)= 46.7 so to solve: 32.5 + ?(7.1) = 48 so it is 2.2 standard deviations above the mean rating of 30 points: -0.4 rating of 20 points: -1.8 The negative sign indicates that the rating is 0.4 standard deviation BELOW the mean! TO SUMMARIZE: 48 points is 15.5 points above the mean or approximately 2.2 standard deviations above the mean... 30 points is 2.5 points below the mean or approximately zero. Four standard deviations below the mean... 20 points is 12. Five points below the mean or approximately 1.8 standard deviations below the mean. 32. Five points is zero points from the mean or 0 stand deviations from the mean From the last example, 2.2, -0.4, and -1.8 are all between -3 and three. So the corresponding ratings 48, 30, and 20 are all within three standard deviations of the #MIN. This goes along with the fact that in any group of data, most of the data are within three standard deviations of the mean. A number line to display the data would go from -3 to 3 with the mean being at zero.

fractional expressions

simplify 1/square root 2 divided by 3/square root 5 answer: square root of 5 over 3 square root of 2

graphing linear equations and inequalities

slope: rise over run y2-y1/x2-x1 parallel lines: slopes are equal perpendicular lines: slopes are negative reciprocals

roots

square root of 100 is 10 square root of -100 is -10 square root of 0 is 0 rule 1: (square root of a) squared is a rule 2: square root of 4 is the square root of 2 squared so answer is 2 rule 3: square root of 3 times square root of 10 = square root of 30 rule 4: square root of 5 divided by the square root if 15 = the square root of 5/15

decimals

to the right of the decimal: tenths, hundredths, thousandths to show a repeating decimal: place a bar over the repeating portions a decimal doesnt have to terminate or repeat such as 1.2345326743643. THESE ARE IRRATIONAL NUMBERS: DO NOT TERMINATE NOR REPEAT

a .... is the simplest polygon with three sides a quadrilateral has ... sides a pentagon has ... sides

triangle 4 5 to find the sum of the measures of the interior angles of an n-sided polygon: (n-2)(180) since 180 is the sum of the interior angles of a triangle. n-2 gives the number of angles of the polygon

graphing equations

use elimination or substitution to get to y=mx+b and graph