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In chapter 1 of my Integrated Math 2 notebook, we learned about Angle Pair Relationships and the many different relationships that an angle can be called. This includes Supplementary, Complementary, Vertical, Congruent, Same-Side Interior, and Alternate Interior Angles.

First we figure out what type of Angle Relationship the angle is classified as.

Then we apply and solve the specific problem easily with the hints the relationship gives us. For example a supplementary angle's "linear pairs" will provide any additional angles degrees and will also prove that an angle is 180 degrees, therefore it'll solve itself.

Lastly, we can solve the missing variable or angle easily (with no strong winds trying to abduct you) since its just an equation now.

So basically its a normal basic algebra equation with shapes.

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In chapter 3 we learned about probability and how much of a chance a certain event has from happening. For me I picture this concept as a Board Game or Card Game or Video Game or Sport Game or any damn game it doesn't matter. So I'll just explain it in Mario Kart 64 terms cause I'm corny like that and there's no way you haven't played that game ( if your sane). Let's just say your in a race with 8 people, which means you have a 12.5% chance of winning 1st place. Your playing as that damn princess who ALWAYS gets kidnapped, and you leading in front of everyone while you swerve through chocolate mountain,your right in the finish line, but than that ugly ass turtle thing throws a blue shell at your face and you combust and within that 1 second that you cant move, like half the players swerve past you and you're no longer 1st place (at all). Since this game is rigged and hates you, and the ai players are coded in a way for your enemy to be that damn turtle and everyone else be behind waiting for you to miserably fail, you quickly realize that your enemy has a higher chance of winning than you do which affected the probability of you winning by quite a bit. Lets just say the chart details the percentage of you and that turtles chance of winning or not, and since you decided to play as that peach girl and your only main enemy is Bowser , that proves that that specific event of you being hit by a blue shell sent from that stupid spiked turtle is mutually exclusive and also associated since that green grouch with a mustache seems to ONLY be obsessed with you. So how do we figure the probability? (you ask yourself behind the screen while you think I'm dodging the question that I should be answering besides wasting my time typing this). ok anyways first we figure out your conditianal probability of you being winning vs that turtles chance. With that, we can also use our context clues to figure out that you playing as peach greatly affected your chance of losing to Bowser , so those two events are associated. if you were to pick some other character like idk that green man luigi and not peach. Bowser would not be your main enemy, therefore those events would be independant because I dont think luigi has beef with Bowser.. so being hit by a blue shell specifically from Bowser right before the finsih line and him winning was mutually exclusive since that could only have happened to you. So the more specific the category is(winning 1st place) the more the chance dwindles down, if you had not been 1st place at that time (lets say you were 2nd place since the blue shell only targets players in 1st place), you wouldn't have been hit, so the probability of you winning would be higher since the choices you made greatly affected the conditions and the probability. We can also use this example for Conditional Probability math problem itself, (Event A) lets say you (peach) have a 4/10 chance of winning the race while Bowser has a 6/10 of winning. This event by itself would be a bit unfair but reasonable. Now if another event were to be added into the mix, the percentages could dwindle down depending on how many events we want to take into account. (Event B) Now there's a 3/10 chance of you getting REALLY mad at the game vs a 7/10 chance of you being able to control your temper. Lets say you win as peach (4/10) and for some reason also get mad (3/10). In order to find the percentages you need to multiply both fractions (4/10 x 3/10) which the outcome will be a percentage (0.12) and than finally move 2 digits to the left (12%0.

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In chapter 2, we learned about shapes and how we can prove their similarity, this includes my favorite lessons are dilations since their fun to graph and scale factors since they're pretty simple . First we graph the sides of both the original shape and new shape, Then we make them into a fraction from "new/old" (ex. 24/8 and 18/6).

By dividing the fractions we can finally get the scale factor which will tell us how many times (or how much) the shape expanded in size..

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in chapter 4 we learned about trigonometry and how we can use sine, cosine, and tangent to solve/find variable's answers to right triangles. first we label the hypotenuse, the opposite, and adjacent sides, Whichever one dosent have the side length will be ignored and with the ones remaining, we'll have to figure out if they align with sin (opposite/hypotenuse), cos (adjacent/hypotenuse), or tan's (opposite/adjacent) political values. Then we just make an equation with the tool and angle given to us (ex. sin37) alongside the fraction we made with the tool. From here it really depends on where the variable is placed or if the angle is a 0 (in which you'll have to replace it with a -1 as the exponet. The equation is the simplest part since u just put it into a calculator. Anyways I'm tired, I want to die. goodnight or good morning I dont forking know.