And our final answer would be 72.


Yup thats correct


Really, I just guessed, but I'm happy it's correct.


I wasn't sure the method, so I just used my gut feeling.


Thats correct


all angles add up to 180 so u do


90 + 54 + (k/2) = 180 and just solve for k


is it like this?


Close but not quite there let me draw it for you


alright!


whatstht


that


Its honestly a bit weird that they put BD as the altitude


ut


but


just know that BD is the height


where's d


oh but then where do we see it


on the triangle


or we don't?


I don't think we need it


how would we find bc nd bd


Give me a second


Okay nevermind I figured it out


You need to use the altitude theorem


oh no


So BD = leg(other leg) / hypotenuse


oh that's not bad


let me redraw it I drew it wrong at first my bad


np!


where is c


why is it inside


abc is the angles


oh so we know angle b but not a and c


so were solving for angle?


Give me a second, the wording of this problem is very confusing


did i not come with a photo?


huh


did the problem not come with a drawing?


no but there is a explanation


Ok i understand it now just let me write out the work


Okay yeah so u need the altitude postulate


BD = Leg (other leg) / hypotenuse


it says that AC is 23 greater then AB


so 15 + 23 = 38


now you have to rearrange that postulate in order to get BC/BD


its some algebra manipulation do u understand?


U first need to cross multiply


So its BD(AC) = AB(BC)


Then u divide by BD on both sides and its


AC = AB(BC)/BD


and u want just BC/BD


so you divide by AB on both sides


and BC/BD = AC/AB


do you kinda understand?


great ill write it out


the worrding of the problem is a bit confusing I apologize


OK, so I'm kind of confused. What do I fill in now for like


this looks like, but this is VD and um what do I feel for the leg leg hypotenuse.


Okay so one leg is AB and one leg is BC


as u can see in the drawing


One leg is AB and the other leg is PC.


yeah


Yeah, cause we can't use the AC cause that's a hypotenus, so


a B.


times BC


over


AC


So then we would multiply it.


And then what would we get?


so u cross multiply


do you remmeber that like cross multiplying ratios


Yeah, I know how to do that. So it would be BDAC.


and then it would just be ABBC.


yes


Can you write that?


so I can like see how to write it.


there u go


Now do we distribute


You cannot distribute because each side is like its own unit


So remember


so it wouldn't just be BDAC.


u want BC / BD


So I would divide


with, I'm saying like


after that, would the answer be like this?


or no


No you cannot do that


Oh, OK


think of each side like


its own variable


Yeah, you can't


add unlike variables.


its like (y)(z) = (c)(a)


if that makes sense


OK, so we would have to get


yes


what is it BC over BD cause that's what the question I asked for. So this is multiplication, so we could just divide it.


So we have


this on the other side.


There we go


yup


and know u just plug in ac and ab


What is the value of BC over BD, so it's just AC over AB.


So I would have to plug in


over 5


BC over BBC


um


I don't know what to do for.


BC over BD. I already found AC over AP.


thats all you need


because the expresisn


Also they're the same


is saying that they are equivalent


Oh wait, that's 15, not 5.


OK.


yes BC/BD = AC/AB


yeah, I got it.


so BC/BD = 38/15


any more problems?


one moment im writing the formula


ok im uploading the nect


lets clear the board first


please add the questions


the answer choices


Okay give me a second to solve it


Okay so first


X and Y are same-side interior angles


have you learned that?


yes


so we set them =


No they arent equal to each other


They are supplementary


oh


x + y = 180


are they coressponding


No they are not corresponding


Well think about it like this


that angle across from y is equal to y


and remember two angles create that straight line


so y + x = 180


Okay now you know that y < 65


so 180 - 65 = 115 then that means


x has to be greater than 115


because they need to add up to 180


do you understand


OK, I learned this before, but I learned it when it gave us one number, so it would give us like a number and we would subtract it from 180 to get like the answer.


and then we would use the theorems to find out which one is which, but this one, it doesn't give us like any angle.


is it okay if i talk on the mic?


Yeah, of course


Hello, can you hear


Can you hear me


yes


Yeah


OK, so basically, the 65 is the angle that's given.


Oh, OK


So if Y


But that says it's less than 65.


yeah, it's less than the stress, so it's kind of like a weird um


concept that you need to learn. So


basically, uh, if you know that X and Y need to equal 180.


We're gonna pretend, we're gonna pretend that like, say why is equal to 65.


All right, we're gonna pretend. So X is gonna be equal to 180.


minus 65


So X is gonna have to be equal to 115, right?


But um


says it's not actually good to 65. You know that it's gonna be all the numbers less than 65, you kinda


you, do you understand that


Yeah, no, that makes sense.


And if you, so say you shrink down, so say you shrink down, so say if you go wise is less than 65, what say you say why 64, right? Cause it could be 64. That means X would need to be greater than 116.


So it has to be just greater.


greater than 115, yeah


So it's


OK, yeah, that makes sense to me.


yeah, yeah, yeah.


it's a little it's a little confusing


but um


that's kind of the way that I would think about it.


Yeah


Um.


Yeah. Do you have any other problems


Yeah, I do, but I kind of like wanna talk about it.


like, OK, so


you know, we do 180 and then it says why is less than 65, so you can do that and then do 180 minus 65.


So that's what


X is, cause that's what we have left.


and it's bigger than that


and then


X just has to be greater than 115.


OK.


That, that's, that's, that's basically what it.


I have another one.


So like if you wanna


the board


Yeah, the


OK


So


OK, yeah.


I forgot how big a rectangle can be.


Um.


you actually don't even these ankles to the


small.


But like how


how big is a rectangle supposed to be? Because I know, uh triangle is supposed to add up to 180.


Um, basically


the, the angles, well, it's, it's not how big it is, like length or width or anything like that. It's the


all the angles within a rectangle add up to 360, and then all the angles are gonna try and go out of 40, but for this problem, you actually don't need to be able at all.


Do you understand?


So wait, do I understand that um all of rectangles add up to 360.


Uh, 360, but no, uh no, I'm asking, do you understand like.


uh


do you, this problem doesn't need the because


talking about the area


Oh, OK


Yeah


but yeah, basically you can also just remember like for any other songs that you.


Wait, is it because the area is inside and then the like


it


the um what is it? It's outside.


Mhm.


The angle


Yeah, yeah. OK, wait, I understand cause this is talking about the outside.


right?


So it can be more than 360 degrees.


Yeah, yeah, like the length and this is, yeah.


we're, um, OK, but let me, here, let me draw it out for you


OK, so we're gonna draw ABCD, so A.


E.


C.


Are you like walking home? What does that sound?


um


no, I'm


I


It's my um audio


better?


I apologize


Yeah, now it is. It was like scratching like it sounded like it was raining.


OK


or something


Yeah


No, no, no, no, you're fine. Like I was just like, what was that?


OK, so this is ABCD. So we're gonna read the poem. So, ABCD is similar to EFGH. So let's draw both, both of them.


again


Uh


G


H


So


when I was talking about the angles, so all these angles right here, you see how these are all right angles?


So that means it's 9090, 90, 90. So they all add up to their 60.


you understand


But it's for both of them, no matter, no matter the length of any um


of of the width or the length, no matter that, the angles are always gonna add up to 360.


So like you could have


So in a triangle, why do we only add up to 180. And here, why do we have like 4 90s.


I get, well, basically, so say there's the rectangle right here


Like what you, you'll see watch. So say


if we just cut this in half, sorry, it's a bad line, but if you just cut this in half, then you can see it's two triangles, right?


Yeah


And


if you like, pretend that there's these, the 90s here, right? Or will they, there will be, right? But if you couldn't have, you see how there's two trials that you could see how there's two 180s right here.


Oh.


OK


Well, my question is why did we put those though?


Oh


Well, you, you don't, I was just trying to explain to you how they are always equal to 180. For this problem that you have, you actually don't need the angles at all.


Yeah, OK, wait, that makes sense. OK, I understand now.


OK. Um, OK. So it's uh, it tells you that the area for ABCD is 648, um.


right? And do you know, do you, have you learned about similar triangles in your class?


so it says ABCD is 648.


Yeah, the area, so


So area is a length times width, so the outside, not the inside.


So


Well


that just means we need to find the length and width.


um


kind of, this problem is more like a a ratio's problem because


it's saying that EFGH and ABCD are similar, and you know how similar means like


if


Two are the same


like 2 parts are the same.


not that they're the same, but like, OK, so say you have 22 recti 22 rectangles.


They're the same shape, different size.


Yeah, like that, it's kind of like that, kind of like that. I'll, I'll actually you'll see, uh, you'll see how it connects a little bit more as I write it out.


So just give me a sec. So, OK, and then the area for this one is 72.


Yeah


OK, and then this is the longest side of ABCD is 36. So would you say that CD right here is 36.


OK


And then we'll say that the, you know how it says the long, what is the length and inches of the longest side?


of EV we'll just say that's GH.


Oh, OK.


So we're gonna make that X right here, because that's what we're trying to find.


OK, wait, I think I have an idea on how to solve it.


Yeah.


OK, let's see


So I'm just gonna do this.


OK, now I have to fill out one more piece of information. Oh yeah, that's 36, so.


36, and now I'll just cross and multiply it. So.


72 x 36 is 25


and then we would divide it by 648 to get X


So


and I got 4. So the shortest side is 4.


Um, yeah, that's correct


I mean, the longest side for EFGH is for, yeah.


That's correct


OK, I have another one.


OK, I'll clear the book


So are you a teacher?


No, I'm not a teacher


Oh, you'at Lincoln High??


Um, no


Oh.


Westwood Academy?


No, I'm


I'attend College Prep, but I've taken these classes before, so I know how to do them.


Oh, you're smart


OK, this one's kind of weird. OK. Um, yeah, let's try it out.


OK. So you see a corresponds to D and C and F are the right angles.


So


um


let me think, so


Yeah, I know


you know, do you know tangent sign, sign, OK. So tangi A is 21/20. So opposite.


yeah


yep


So it's just, so it's opposite, so that's 21. And then adjacent, so that's 20.


And then once signed B, so that's uh adjacent with.


the same cause they're similar, so 21 and 20.


right.


No, no, no, no, they're not the same. The, the, so, OK, when similar, similar means?


Oh, wait, wait, yeah, it's signed, not tan, so it


wouldn't it be opposite over hypotenus?


Yeah, so it'd be this FE down here over this XFL.


So it'd be 21 over X.


for sin D


Uh.


no, cause it's, it, it, they can't be the same because look, it says that AB is 2.9 X, and DE is X. So similar doesn't mean they're equal. Similar does not mean equal. It means that the ratios of their side lengths are the same.


So what does that mean? Does that mean only one length is the same.


No, I'll explain. So here, I'll, we're just gonna go away from the problem real quick and I'll show you this like little example. So these two triangles, I'm going to say that they're similar. So if one side is 10,


this is the longest side. This side will be 5, and save this one is


uh 8. This one is 4. These triangles are similar.


So they're common factors.


Kind of, yeah, like that, kind of like that.


OK


And then, so you see how 10, and then when I said that the side lengths, the ratio is the same, this this long, this is say this is the um short leg right here, 8, this is the short legs, so we'll say S and it's the long leg. The L over S is equal to this one, L over S like this one over here L overs.


Yeah


So 10/8, the ratio of 10/8 is equal to 5/4 you know simplifying fractions. So you see how, you see that, you see that connection right there?


So that's what similar means.


Yeah, that's a similar


So they don't have, how


So then how would we get this one?


yeah, yeah, this one, OK, this one's a little weird. You're gonna have to like


so first let's know, we're gonna know that sine D


is equal to opposite overhypani, so it's FE over X.


OK.


right? And since a corresponds to angle D, we're gonna do sine A. So sine A is equal to 21


to sin


A is equal to 21 over 2.9x. You don't actually need to know X yet.


cause


you'll see


Soy is 2.9


over


X


So 21


since they're similar, you can set the ratios equal to each other.


Why did we do sign in?


because um


I'm trying to show you that like


Oh, so we have to do sign sin D.


so sign D is this FE right here over x. Sign A is 21 hour plan.


Yeah.


OK, so this is kind of the, the, this is what you have here and then


let me, let me think


OK, uh, there's one more thing that we need to solve for.


So you see how um


we, we, we, we need, honestly, because this is 2.9 X, but we need to find this length right here.


We need to find the hypotenuse of the AECD.


or ABC


So that means we need to find.


Um, yeah, you could find, yeah, basically, but you can just do it like this watch. So, so first you're gonna find the hypotenuse of


of this, so


Can we do it by Pythagorean theorem?


Yeah, petalgra theorem, so do that.


Oh, OK, I know that


It would


square plus


1 square.


equals the hypotenuse squared.


So


OK, for my hypotenus I got um 29.


That


this right here is 29.


This whole thing, AB is 29, the length.


mm, why is it 2.9 x over 29. Isn't it just 29?


No, no, no, it's, uh, it's not. I'm sorry. I just, I just wrote it under it. It's, it's


s yeah, yeah.


But


Oh, OK. Uh, oh no, my bad. I was like.


it's good


So that means.


this


hotness.


right


But let's just go back


like kind of ratio we have right here


So


let me just um


OK, so


21, OK, since we already know that it's 29, we don't need this 2.9X anymore because we know it's 29, so it's 21/29. So sine is 21/29.


and that is going to be equal to


is equal to sine D


Do you understand?


They


I can go back. Let me just go, let me explain this one thing that


corresponding angles in similar triangles are equal.


So just because


Oh


the sides are equal.


The they what I was saying how the ratio. So time A is the price.


OK


So 21/29 is our answer.


yeah, that's what


um


But um, I have a question. So, like, then why do they say it's 2.9 times the length of DE.


right?


yes


That's like so confusing


it, it adds that, but honestly, you don't really even need it. I, I mean, you could like if you wanted to, you could find out what X is.


Oh yeah, cause it was confusing me because it was basically like


yeah, but


just to focus on the sign.


right


Yeah, that's like the postpartum part.


Cause like this is sign these's answer, right?


Yeah.


So like, to get this right, I think like.


what was I gonna say


You need to like do this one.


And like if you try and go to this one, you'll get it wrong.


Yeah, cause you don't really have a lot of information of that one, of that triangle, um, so it's the best thing for you to do


your sense are similar, you wanna make sure you know everything about one triangle at least.


Uh, all right.


So that's why you'll, you'll so for the hypotenuse, you figure out the hypoiss, and since you know that the ratios are equal. You can just find


I'm sorry, I'm back. OK. So, since you know that the hypois right here is


29. You just, you know that the ratios are equal so fine a plan.


Yeah, and then, OK, ABC is in like the same


or as DES


got you


have to make sure


So you could just use this, and that's why it's equal.


Yeah


yeah, you have to make sure that the order's right. It's honestly kind of weird. Usually I'm used to using the right angle


about it.


but they say that a corresponds to D A and B, I think, and yeah, after the wedding.


Yeah, so that's why you don't have to solve for this one cause they're in the same angle, meaning they're the same thing and equal.


OK. Do you wanna do another one?


Um, how many do you have left


Ah.


I have like a few left, like it doesn't really matter


cause like I do like them


every day.


Um, we can do one more.


OK


I uploaded it.


OK, so first we can just grasp it.


or grapple we know


By the way, like the background noise is like, I can hear it.


OK, is it fixed


Uh, yeah, it's better now.


It was like, it's like sounded like really like.


loud, like loud static.


I apologize, my microphone isn't the best.


Oh, no, no, no, you're fine, you're fine.


Oh, so we graphed this one.


kind of. So it said that the center is at -1.


and it says that line T is tangent to the circle.


That's so confusing


I, I know. So basically,


here, let me


let me try to


Oh, this is a really weird problem.


Have you, have you learned this in your class yet or no?


No, but do you want like um the uh explanation.


Ah


No, I, I understand, I understand it, but I'm, it's, it's it's a little bit difficult. I don't


OK, no, I haven't learned it before.


you haven't learned it


No


OK, so


pretend you have this er this right here is the


the um


Centerpoint


yeah, that's the center point of the circle.


So because the, the, the, the line or the line is tangi, that means that it's like


it's kind of like


like that


and this is really bad.


Oh, should I use a graphing calculator.


you know, it's, it's, it's OK. Like just like


here, I'll draw it a little bit.


A tangent just means circle


Now tangi tangent means


tangent means that it's on the circle at


this point, but it's like, it's only on this circle right here. It's just right here.


Like it's the circle only touches it on the edge of it.


Yeah, right, like right there, yeah


OK.


OK. So first is you need to find this slope.


You need to find the slope between these two points, cause that will give you


that, that will give you the slope of the radius. Do you see?


And how do we find the soul of the two points.


You haven't done slope yet


in your life?


Oh yeah, I know how to do the slope, but um


You just, yeah


oh, OK, yeah, I know this. It's k 0 no y2 minus y1 over x2 minus x1.


Yeah.


OK


So


hold on


OK, is that right


Yeah


And


OK. And then when it says which of the following points also line on line T. Line T is this line right here.


It's since it's tangent, like, I mean, you haven't learned about perpendicular lines yet, but that's how you'll know. It goes through this one point on the circle and it's tangi right here.


um, what math are you in?


Calculus


Oh


do you see how these two lines right here are perpendicular.


yeah


and says it's perpendicular, the slope of this line T right here is, do you know that like that rule that slope of lines that are perpendicular is the negative reciprocal.


Oh yeah, I know. So it's -1 over that slope.


So I do -1 over 56, right?


Wait, why are we doing the perpendicular slope again?


because it basically, when it says which of the following points also lies on line T. It wants you to find line T. That's like the, the best. It wants you to find the equation of line t.


So you need to find the slope of this line.


and said


So I literally got 6/5.


So is that lime tea


That's, that's, that's the slope.


Yeah, no, I did the perpendicular slope.


Yeah, yeah, yeah. So, um, do you know about Point slope formula?


Yeah


Yeah, Y minus Y1 equals the slope


times X minus X1.


So you know that the line is changed to the05-4. So that's gonna be your point, and then you already know the slope


which is 6/5.


So now


They asked us for the perpendicular slope, right?


yeah


Well, it basically


no um


it


when you draw this out and it says that it has a center at -11, and it's tangent at 54.


You know that this like radius right here is this line right here, right?


You are kind of I'm pointing to


Mhm


And then it says that it's tangent. So the best way for you to think about tangent is is like


draw the point that's on the circle.


and then just like pretend that there's a line going through that point along the circle.


Um


Yeah, and then you can just see right here that this line, this line right here, and this line right here, it's they're perpendicular to each other. So since you know the slope of this line, you want to find the slope of this line and you know that it's this, the slope of T


is the negative reciprocal of the slope of this of the radius of the circle.


OK


So you know that the radius, I mean, you know that the slope is 6/5.


You have the 0.5 -4, which is on t.


and you're now you have to find the equation of INT. So, do you know how to do that?


Yeah, I would just plug it in, right?


Yeah


so


um


what points would I use again to plug it in?


54, cause that's on the


line of teeth


Yeah, but no, we need, so this is one, and like I also need


You go


another cod in it, right? Because there are like two whites here.


you don't


you don't need another coordinate to find the equation.


Wait, so it would be just Y minus Y phosphor.


equals 6.


over 5


That's 5


Is that right


Well, is that -1


No


Yeah, it's 5 minus 1.


No, no, you leave X


Um


OK


Oh sorry, I wrote that wrong. My, um, I'm sorry, here, right here, it's X minus y1.


Sorry, now, um.


so


what is it called? So Y1 is just negative 4 right here and next one is this. So let me just


that means that the equation


Y + 4 is equals to 6/5 times


y + 4 = 6/5(x-5)


X minus 5. That's the equation.


I text, I typed it in the chat.


Do you understand


yeah, kind of. Oh wait, let me just recap. So first what we did was, um, we marked the center point and then the um


54, which is our tangent. So then we drew a circle right around that.


and


then


we drew a line


from the slope formula and we got um


Yeah, this is a rate which is.


-5/6. And then for some reason, I forgot why we did the


made it perpendica. Why did we make it perpendicular again?


OK, so


the, the 5/6


Yeah.


is the slope of the radius of this circle.


right


Yeah


So you see how the radius is -11, and we know that 54 is also a point in the circle, and it's a point on the line, like this is the point of this uh on the circle, and the line is going through just that one point on the circle.


if, if that makes sense


So, we found the slope of the radius, which is -5/6.


right?


Yeah, wait, so how is that the slope of the radius, though, like, isn't it just like we were solving this look. Is it radius because like we did it with these two coordinates, and those two coordinates are half of the circle.


OK, so that's why it's the slope. So we found the slope of the radius and then


And then in order to find the slope of this line, because the question is asking which of the following points also lies on line T. So you could literally, so it, you know, your question is probably giving you a bunch of answer choices, right?


And it's like coordinates


yeah


So it basically says like line T


does it have any of these other points?


So in order to find that out, you need to know the equation of line t.


So we're finding the slope of Late.


The slope of IT and then using that slope of line T, then we're finding the equation of life.


So the sofa of line T is 6/5, so it's over 5.


Yes, cause you could see that they're it's perpendicular to the slope of the radius.


Oh, OK


What does perpendicular mean again?


Um, so like say you have a straight line.


Yeah.


Perpendicular is like the opposite direction. So like it's a horizontal line.


Oh, so they intersect with each other.


kind of, yeah. So like, look down here. So say I have this line right here. This is like a line.


And then the another line that would be perpendicular to this line, it would just cross it like


it would be


like


it would be going the opposite direction kind, you know what I mean.


Yeah


Like it's like a cross, so like he have a they will they'll end up making a cross.


OK, so we found the perpendicular line and then we use slow point formula.


Be point formula, yes, to find the equation of line c. And we found the equation of IT, which is why + 4.


is equal to the slope, and which is 6/5.


times X minus X1, which is 5.


because you know that if it's tangent at 5 comma -4. That means it's touching that point. It has that point on its line.


So now that you have this point, um, or you have this, you could simplify it a little bit more.


So like do you know how to simplify this equation right here?


To make it into like Y equals MX + B, you can do that.


to make it more simple


OK


Hello


I'm trying to solve


the um


thing right now, this one.


So like I'm just distributing 65 now.


I can write it out


Oh, it's fine. I'll just do it and


OK, I solved it


Um


OK, I'll just say it because it's going to take me a while to write it. So Y equals 6/5 x minus 10.


Yeah, that's right


OK.


OK. And then is that the answer?


So -10


Well, that's the equation. And then um your, your problem says we should the following points also lies on line T, and it's probably give you a list.


It's probably giving you a list of coordinates, and do you, do you now, you just have to see which one follows that equation.


So it has to match my why.


and my


I mean, it has to match my slope and my X intercept.


Yeah, can you, can you upload a photo of the answer choices?


Yeah, can you feel the board a little bit? There's like a lot of stuff on there.


I'm not, I can't make my eraser bigger. So I'm just gonna clar some pages.


Oh, OK, I'll just


hold on.


Oh, actually, no, wait, I can't, I got this


There you go.


bro, there's so much stuff on this board.


Yeah I'm just gonna erase everything.


OK


he said so


How do you erase everything


I, I have an option that allows me to erase it. I'm not sure why if you have it too.


OK, so hold on.


OK, it's Y equals


6/5 x minus 10.


And of course, now it's not uploading.


I'm just gonna write it out because


it's not working


The answer choices


Yeah, it's not uploading, so I'm just going to take them.


OK.


0, 6/5 b. 4,7 c. 10,2 d. 11,1


OK, those are the answer choices.


Yeah


OK, so you're just gonna


Oh, I can't hear you. Your mic is muting.


uh, I know, I know. Uh, I'm, I'm just thinking.


You can just type it


Are you sure those are the points


Yeah, I'm sure


Here, I'll read them out.


10, 2, and 11,1.


Is it 4/7 or 47?


Oh wait, yeah, it's 47.


OK, OK


So for, for what I would do if I got this, I would just plug in all those X values, and then see if it gets the right Y value cause, you know, you're trying to find which of these points matches up.


R R Y value is -10, right?


That's the Y intercept.


Oh, what's our Y value? Is it the, um,


No, no, like you see how these, these, these are all write them out.


is there Y value -4?


No, we don't it when you graph this line, there's an infinite amount of Y values.


You're just trying to find which of these points that the question is giving you is also on this line.


Oh, OK. So it has to match. So if I plugged in 4/7, the Y would have to um be 7.


equals 7, yes


Yeah


So you can let's just go through all of them.


So that means the answer would have to equal 7.


So, I'm gonna try it now.


You can try all of them until you get the, the right one.


Yup.


OK, it's this one, cause I got um 2 for the answer, and then 2 is the why.


That's correct


OK, well, you have to go now, right?


Yes, I do


OK, well, thank you so much.


Have a good day


You too.


Hlo


hii


Could you upload the problem again? Sorry for that


Do you need to just draw it?


no


i js need to anwser the component


and magnitude


R you familiar with the graphing system


and direction of v


i already graphed it


Do you know the formula of magnitude?


radical a^2 +b^2


It's actually


well thats what we learned


(x2-x1)^2 + (y2-y1)^2


Then the root of this value


(2,4), (-4,5)


thats for vector


Not only for vectors


Its the same formula for any two points


(-4-2)^2+ (5-4)^2


so is our compenent form not -6, 1?


Yes the component is <-6,1>


and our direction of v is what?


170.5° approximately


it says wrong


What says wrong


the problem?


you gave me


idk what exactly is wrong


The magnitude


i put 37


U wrote 35


radical 37


Its 37


yeah i changed it


but the direction of v in s nearest negree


degree


so no .5


but i already tried


Try


that


are u sure


this is my last try


before it marks it wrong


Give it a try


Mark it worked thank uu


Hi


Hello! Im confused on one of my math problems. I understand this topic, but since this topic comes in so many different formats, I always get confused, and it results me in not doing so well at all.


k


let's take it one step at a time


we know that BD is parallel to AE


let's mark that dpwn


BF bisects ABD


yes,


so that means the two parts around it are equal


right?


yes!


we need to find angle E


to find this angle, we need the other two angles of the biggest triangle


make sense?


because they add 180


yes, I think so.


ok


so we can 180-160?


not yet


lets jot down the numbers we know for sure right now


okay


we know that angle C is 85 degrees


we know only need angle A, right?


so we can subtract both 180


to get E


angle A is inside of a smaller triangle as well, and we know that one of the angles 180-116


what is that?


yep


so A is also 64, since 2 sides are the same?


I would look at it this way; since BD and AE are parallel, we know that the alternate interior angle of BF is also 64


exactly


and since we know BF bisects, we know that angle at B is also 64


so we can find A


right, 180-64-64


now we have all we need


to find E


so now we 180-85-52


yup


yeah


Thanks, I understand it.


these problems take a bit of time


you need to go one step at a time


or you might mix up values


but I can tell that you're starting to get the hang of it


Thanks! I have one more, can we try it?


sure


try to go through the steps in chat and I can correct you along the way


okay!


So we know that


start with instructions above


B is congruent to BAD which is also congruent to ADC. Which Im pretty sure is marked already


We also know that D is 80


you sure?


And we need to solve for C. Im pretty sure that this shape 360 degrees


ADE I meant


why is D 80 degrees?


ADE = 80


yep


what does this tells you about D though


That 180 degrees


Its straight


almost


because it's a line


right?


yes


remember that


So we can say that ADC is 100


Since their congruent would that mean that they are the same values?


awesome job


Thanks! :)


any other questions?


No, Thats all the problems I have left to solve. But thanks! You helped a lot!


it was great working with you, have a good one!


You too, goodbye


Hi, how can I help you today?


Hi!


Is there anything you need help with today?


I have one question on parrellograms that requires a written answer. But I am not allowed to get help on the specific question so can I please put up the quesition and you make an example just like my question and help me solve the example


Sure, sounds good!


Thank  you, I will put it up


Just to let you know I am kind of in a rush


Ok! I'll go as fast as I can!


Let me know when you need to go


Thank you!


Can you see it?


Yes!


Ok, let's start by annotating what we know


Can you label angles TUV and TVU with their angle measures?


ok


wait where do I put each one


These are the two angles!


thank you


The middle letter tells you where the angle will be (so TVU has a center at V, for example)


Ok, perfect!


Now, let's identify angle SRV. can you label that one in a different color, please?


yeah


is that right


Do you have any ideas about how we could find SRV?


well we know that v has to be the same distance from R and T and the same distance from S and U so we could maybe use that knowledge


That's true! But those are side lengths, and we want to focus more on the angles


One important part of this problem is that RS and RU are parallel, because RSTU is a parallelogram!


oh yeah


Does that help with an idea of how to start?


well is side TU 78 degrees?


Side TU? A side can't be in degrees!


Angle TUV is 78 degrees


yeah sorry that's what I meant but I still don't now how to start, sorry


That's fine!


I'll walk you through it!


RS and RU are parallel


Do you remember the opposite and same side angle theorems?


no


Ok, let me draw a diagram!


ok


Do you see how that kind of looks like our parallelogram, with RT as the line going down the middle?


When two lines are parallel like that and they have a line (called a transversal) going through them, their angles have special properties


yeah


For example, when their angles are on opposite sides of the interior (like the green ones I drew), those angles have the same measure!


So those two green angles would have the same measure!


Do you remember doing this in class?


yeah now i do


Ok!


So back to our parallelogram


We have two sets of parallel lines


wqat would angle r be equal to angle v?


Close!


It would be equal to angle UTV!


oh cause they are both on the end


Do you see how they're on opposite sides of RT, and they both touch the parallel lines RS and RU?


Yes, exactly!


So now, we need to find the measure of angle UTV, because we know it's equal to SRV!


Do you see how we got there?


would angle UTV be 78 degrees


Can you tell me how you got 78?


well if point U is 78 degrees and TU are part of the same side and point T touches side ST and point U touches side RU and those sides are parallel


TU and RS aren't parallel! ST and UR are parallel, and RS and UT are parallel, but those are two different pairs of lines


In order to find the measure of angle UTV, we need to realize that UTV is a triangle, so the sum of all its angles = 180


This means that 54+78+UTV=180


Does that make sense?


oh yeah


Can you try to solve that?


so UTV is 48


Perfect!


So what is the measure of angle SRV?


Do you have any other questions about this problem?


well I do't really know how to explain my work of show my steps


Do you want me to walk you through it, but faster?


yes please


I get what we did just not how to explain t


Sure!


Ok, so we said that RS and UT are parallel, and so are ST and RU


(stop me if you have any questions)


ok i get it so far


Good to hear! Because RS and UT are parallel, angle SRV = angle VTR


ok


To find VTR, we know that all the angles in the triangle it's in add up 180


Which means that 54 + 78 + angle UTV = 180


Which means angle UTV = 48


And since SRV = UTV, SRV also = 48


thank you


No problem!


have a great day!


You too, hope you ace your homework!


hi


I am glad you signed on.


How can I help?


Hello


Can you hear me


yes


How can I help, Emily?


Oh, good evening, sir. This is Emily's, uh, dad.


Pardon


This is Emily's job


Oh yes


to


Yes, that's fine.


Yes. So, we just signed up.


so


Good, yes


for subject areas that she has issues that she needs help, so we just signed up, so


she said uh geometry is one of the areas, so


you can continue to.


OK, I can do this. Yes.


You're welcome


Thank you very much. I'm leaving you with Emily now.


All right, well.


Hello


Hi


We can do this, can't we?


Yeah.


Well, I have 2 problems. The one is uh


with the types of triangles.


where


Types of triangles, OK.


yeah where there's.


the Ioli


um


the natural and the scaling triangle.


OK. Can you draw me, are there two triangles?


No, that's the, there's a collateral isosceles and sing.


Bilateral, asociles, and scale.


Yeah


And do you know the differences?


a collateral half the congruent sites.


Right


and isosceles has you and, and then scalene has 0.


Right, right.


I


So if I drew something like that, it would be assosceles.


You know, with these two are marked equal.


Ah.


like that


would be scaling probably.


Uh, so what if, what if it has like uh


like something like this at the, at the bottom, at the top.


I'm sorry, curvy like that?


What if she has, yeah.


I wouldn't be a triangle.


OK.


No, like, OK, let me do your, so you can see.


I have to give my dog a treat, OK, I see it.


Is it hurt like this on it?


And then, yeah.


And that's a saucily.


Oh, OK. OK.


Two sides are equal


um


If they mark the angle.


if they mark the angle, that means this side is equal.


to this side


Yeah.


So


so


Can you, um, do like one problem.


so I can like try do it.


So?


Just because it was normal. That's why you did.


the whole


that.


OK


So.


Oh, it's


you


So sometimes you're gonna have information about the angles that help you about the size.


I had to take her.


But if you can draw it


what


we can look at it


OK. So you want me to give like a problem?


Yes


OK, got you.


even if they don't use it almost a thing because I like you said, well I have to do more. I stay close to me. I'm OK.


I just.


I I don't wanna go outside, you know.


With a heart OK.


Hey.


Mhm


We actually did this in school today, and


it was it was kinda confusing.


think.


Oh


no


Oh, you got numbers. OK.


Yeah.


So this is 54.


Yeah


And that's too sorry. Uh, it, it's hard to.


just


How much is this one


Yeah, that's supposed to be 2 like you.


OK.


62 or 52?


No, that's just 2


angle 2


Yeah, and he has a number, um, has X +61 here.


Is that 61 how X plus 6, how long this is?


Um, it has had the volume of X.


OK. Do they have any information about this angle at the top?


Um, it's this


OK


And this is what it says at the top


This, oh sorry.


I've seen that the measure of ankle, I think the measure of angle 2 is X + 6.


or X + 621.


Yeah, X 61.


are they telling us


that this angle


and this angle are the same.


Um,


I, I, I, I, uh


It has to with the placeholders.


and I'll, I'll get that.


I'm trying, OK, X was 61 is angle 2.


What is the question


That's it. That's the whole thing.


No, no, did they ask what kind of?


Oh, find the volume of X.


find the value of eggs.


So, yeah, the body effects.


OK


Now, you drew the arrows.


Wrong. That's a that's.


Are the arrows there to help us?


I think


OK. I'm gonna draw what I think is happening.


that this angle is 54 degrees.


and this angle is X


Now, am I missing anything that they put on the picture.


Yeah, the 2, which is the placeholder.


What's a placeholder


I I don't know. She, my teacher just put it there. And so


it's


So how do you get it to how's the place over there?


Did they put, did they put any marks like this, the green marks.


Yes. Yes.


Then you have to share that with me.


Of course


So, the green mark says this is an assosceles triangle.


Well I do, it means to come.


in an assosceles triangle.


If these two sides are equal.


then these two angles are equal.


I see, yes


OK


Which means X +61 equals 54.


Can you write that equation?


Yeah


Good. How do we solve for X?


Good


We subtract like6 to 1


The, yeah, they make it sound.


Do you want me to continue?


Sure


OK.


All right


um


they don't have a calculator on this thing.


OK, we can do it here. 61.


tract 54.


Um, that


oh, I thought we do 54 minus 61.


Well, you have to put the larger number on top, even though it's negative.


Um


my teacher, um, she put it like that, and we got a negative. I don't know.


Right, you're gonna get negative.


I'll be a -7.


7, yes, X equals -7. Good.


That's right


Because we had information saying this is an assosceles triangle.


I.


Yeah.


with slides are equal, that means the angles.


opposite those sides are equal.


So let me get this is only, um, isosceles triangles have like the same diagram.


Right, now


So what will


times, sometimes they might draw it like this.


And this is marked equal.


Do you know which angles are equal if I turn the triangle a little bit wacky.


Yeah


Which angles are equal


So


it's, this hurts.


Yes, and, and this mean taking it up.


If this


OK


This one and this.


go opposite


let me see.


These are the two angles they're equal.


Hm


So it might not always be sitting like this.


Sometimes the triangle can be sideways.


Mhm.


What if it's a uh


equilateral triangle, like with the same example, would it be something like this


and


um


All the sides are equal, and guess what, all the angles are equal.


Now, would there be something like this?


Oh.


Now


wait a minute


You drew a triangle.


Yeah


and you put two marks here or 3 marks?


See.


And you put 3 marks here.


Yeah.


Yeah, would you have like the uh


Which angles are gonna be equal.


OK. I, I don't know. I just made that up.


Oh, you made it up, watch.


this angle


and that angle


I


Oh, so the opposite side is gonna be equal.


Yes, that's right.


OK


So it's not gonna always be like this one.


It can be like this.


And it'll be like the same solution.


Mhm. That's right.


Now, sometimes


they're gonna tell you this angle.


and ask you to find this angle.


Can you help me with that


Here's the deal


OK.


and this angle are equal, aren't they?


Yeah


That makes this angle X because it's supposed to be the same as that one.


Mhm


And then my equation would be all three ankles.


all three angles add up


to what? Hmm.


Oh


No, what did the angles in one triangle add up to?


There you go. I've added all three angles.


angle 1, angle 2, angle 3.


So will that be 2 eggs plus 40 equals.


Hm, mhm.


That would be 2x + 40 = 180.


OK, so you're just gonna OK. That'll be too ex40.


Oh, we have to put this scriber. It starts at 4:10, but We did this, um,


I don't know my teacher said you can also use that like where you put the eggs.


um


OK, that's square root. We're not working with that right now, but did you have some of those?


yeah


Like the square root is 16 is 4.


Mhm.


We you


you working with


a


I had that in a.


were you working with a right triangle when you did that?


Yeah.


You're probably using Pythagorean which says leg squared.


just


like


It's must be a.


equals a hot mood squared, and the hypotenuse is the side opposite


the right angle


But how do you know, how do you know, um, what led to the exes, or you can just put any letter for it.


Right, um


let me erase that for a minute. Um,


OK. So if we have a triangle.


Oops, terrible


I.


This 3 and this is 4, and I want you to find X. You're really looking for the sea, aren't you?


X and C is the same thing.


OK.


Does it matter if I do 3 squad or do I have to start with 4 squared.


Uh, I think it doesn't matter.


It doesn't matter, right?


No


The legs are the part that


make the right angle.


OK


Oh, you get this one to go.


OK. What is 3 squad?


Tabina


and 42.


Um, 8, I


not today, not today. Of course times 4.


plus 9 + 16.


Mhm


You have 25. Do you do this?


That's right


OK. So that'll be 5 acres.


Am I change the numbers, OK?


OK. She gave us um one example where this, uh, where the X was like


A so, can I go like grab it quick?


Sure


I


I think she didn't get it yet. So I didn't get it back, but it was like this.


It was something like this and then it had the numbers.


but


oh, what did I do?


And then the sea wasn't um the, the number, the X was a C. It was like A.


That's what it was like.


The X wasn't The X wasn't, it wasn't um see it was A


The capital letters named the vertex.


So are you saying


this was an A right here?


Yeah


So it's, it could be a


it could be X, it could be C.


You're still gonna write.


flag squared.


All right.


plus legs squared.


equals


hypotenuse squared.


No.


Would you like to try one?


Yes, please


OK


Ito is having it.


Oh you can


OK.


I'm gonna put different numbers.


Oh.


I can call it A. I can call it X. It's what you're solving for, right?


Yes.


Well


But um what would be the A no number.


So just


I


you're so, you're solving that.


um, some, OK.


Oh, I'm kind of confused.


because there's no number for the A, so I, I, there's nothing for me to put for the.


OK. The, the formula says


if I don't say A, B, C, I could say leg squared.


OK


plus leg square equals hypotenuse squared, right?


Mhm


So


this is a leg


Where's the other leg


Yeah


And then this one.


This is the leg


This is a leg


no.


thing about this and you say So the family will be a^2 + b^2 to c^2.


Oh, OK. That's how soon she is.


And what


I thought I'll have to go that way.


and what is 6 squad?


What is 82.


um 64.


We still keep our equation.


36 + 64.


That would be 100.


OK.


equals C^2.


Good.


And so when we have that little square thing.


We draw the square root.


What's the square root of 100?


OK


So the whole partners is 10.


So 10 res A. So it's based on what the


what this is. That's how it had this, we have to set the uh the formula.


Yes


Now, sometimes you're not gonna be asked.


to find


Oh, that's terrible. I gotta draw that in.


Then.


the


This is the hypotenuse, isn't it?


Mhm


And the other two parts are the leg.


Yeah, that's true.


So what would be our equation this time.


yeah


Which parts of the triangle.


are legs.


Mhm.


But wait a minute. All right, hold on.


This is C


If you're doing ABC


side opposite the right angle is always C.


Oh


I thought it, it didn't matter. I can just put a.


Doesn't matter about the A and the B.


OK


You still would have A and B, OK?


I.


Um


Yeah.


It's kind of confusing for me when I put the eggs before the other numbers.


Is it


And I can, yeah, this can be egg or B or whatever variable they're drawing on the board.


So if I do it like this? If I uh do the formula like this.


You just can't put C here.


C is always the hypotenuse.


Just.


and it's gonna be by itself.


over here


Good


That's right


I


12 x 12.


12 times 12.


It's 144.


I keep added that my phone.


That's 169.


OK


Oh, the


Do I have to do like this?


Subtract 144


Yeah


And I will tell you, you usually will put


the line


underneath


the negative. You're not going to put um


the line here


One


That would work if you were dividing, OK?


OK, wait a minute. Wait a minute, wait a minute.


I got to draw a line in the middle.


I got to draw a line down the middle.


We're doing the same thing to the left side that we're doing to the right side.


I.


I know what you did. It's not illegal, OK? I just wanted you to realize


Mhm


if I'm following the format


Mm.


the right-hand side is 25, isn't it?


Mhm. Oh, thanks.


I


Do I still have to put the XO, OK.


To be X Aro.


I'm sure you're lucky to be around a forest.


There we go


That's correct


that


Despite still confused me, though.


Like despot.


OK. Let me throw another one and you just write the equation.


just


with


improvement


What would be the equation.


probably


You know, some people


some people


I


OK, that's a.


I say.


That's B


Mm


and that's C


Let's see.


um


hm


and you see that


and


uh


OK.


you


I.


I feel like I did something right.


I got him the


Yeah, to is it's supposed to have this.


Hm.


OK


I


Oh


I changed the numbers. What would you be putting in the blue spots?


the


Good


Right


That's how you do it


So


Yeah, the square root of 676 is 26. That was the previous one.


Mhm


So, yes.


The parts that make up


the legs are A and B.


and the part over there across from the right angle is always safe.


I can't take it out.


I. It can take forever.


and


I


Mhm.


Oh


I think I gave you one that doesn't come out right.


You might have some of those.


Yeah.


Yeah. It's gonna be the square root of 189.


So sometimes they want it to the nearest tent.


So like 13.7.


So it's OK to have a decimal.


Yes, and some say leave it like that. So,


Is it wrong if I don't like round it up?


you, you have to follow the instructions on the


Yes


paper


What if it doesn't say Rounded up not, I just leave it like that.


Then you could do 13.4 or whatever I said, 13.4, 13.7.


189, 13.7, that's 13.7.


Yeah, I, that's what happens when I make things up. I don't always get them perfect.


That's OK


Now, so if we have


triangle like this,


what kind of triangle is that?


Yeah


That would be a sausage. No, no, no, no, no. That'll be um e collateral.


Right


Do you know how much the angles are?


in equilateral triangle.


Um


How much is all three angles in any triangle.


Isn't it gonna be 60-60 and 60.


Yes, yes, because


all three angles


tangles have to be the same.


It's a whole angles 180, and if you divide by 3, that'll be.


And then, so 2x equals 60, doesn't it?


How about that


Or somebody else might say, oh, it's 2 X 2 X 2 X, and they would add it all up at 6 X equals 180.


There are two ways to do that.


How did you get the 30


I, I, it's an equilateral triangle.


Oh, you divide by 2.


Yes, with two X is 60.


and X is


OK


In the right triangle.


if I tell you this one is 20 degrees. How much is this one?


Mm


I think.


Where did I get 90 from?


Huh


Where did I get 90 from


From this the I think you.


And if, if a triangle has 180 degrees and I use 90 right here, that leaves 90 for the other two ankles.


So 90 minus 20.


would be 70


Mm.


These two angles in a right triangle add up to 90.


OK.


Yeah.


Is it possible for the 20 to be here and I have to find this.


Mhm, mhm.


Typically, the smallest angle has the smallest side.


you know, so if I drew something like this


the 20 would be here.


Mhm


and the 70 would be here.


I


It's 70.


So this is


my side in the twenties left with the little short side.


What do you think happens if I draw in assosceles right triangle.


That means this and this are equal.


So if this is 4


this is 4


and then I could find C.


OK.


Um


IBX + 4 + 4.


Mm.


I'll be 6 to 16.


I 32 equals to say square.


That's gonna have a decimal.


right


gonna be 5.6.


Yeah


Mhm


You know, some teachers


will work with the square root of 32 and break it factor it down. So I'm not sure if you work with that.


You know


So they'll probably go with decimals.


I


OK


Put some numbers on my, on the right triangle and let me write an equation.


I need 2 numbers and I need a variable, right?


Oh.


So you're asking me to find the hypotenuse, so I'm squaring the other numbers, the legs are getting squared.


and that's gonna equal X^2.


and this kind of numbers easy too.


square


That's a big number.


times


Almost forgot the X on it.


Um.


squari of that might not be an even number.


No


It's the best.


Yeah


I hope it's 62.2.


Good


So even though it's big numbers


this is a


this is B, and I'm looking for C, but you know, you could have made it a K.


I would still know


the K goes over here by itself.


Mm


And sometimes you're looking through the leg.


So it can be any letter, it just has to be opposite with the B.


So


I could say this is X.


and this is 3, and this is 7.


I


The 7 is the hypotenuse, the 7 is the.


and the other two parts.


are the legs


OK.


Now, I never would have atriangle that would say this is 3 and this is 7. Do you know why?


Why? No, I don't.


Because the hypotenuse is always the longest leg.


You can't have the leg longer than the hypotenuse.


So if somebody puts a 3 there.


this number has to be 89, 10. It can't be 6 or 5 or 3 or 2.


I.


The longest side is the hypotus.


Lots of information.


Are there any other questions in your homework or paperwork or school work?


Mhm


No, that's basically it.


But I'm uh


I don't know if it's, if it's gonna be you again tomorrow, but we, I think we're gonna be doing something like that tomorrow.


And then


Well, one of the other questions is


if you're given


3 numbers, you might be asked, Is this a right triangle.


OK


And so I'm gonna do a^2 + b^2.


Does it equal


really.


and the largest number is always what's going to be over here, isn't it?


I


OK.


So 4 square + 5 squad. Does it equal


no


7 squared.


yeah.


I said this. Mhm.


My, my, my.


blood pressure blood pressure.


It doesn't equal, does it?


So this is not a right triangle.


41 doesn't equal 49. It will make a triangle, but it won't make a right triangle.


Mhm


Mm


So you might be using that, you might not.


So if somebody gives you 3 numbers, the biggest number is the C part, and the other two numbers can go for the A and the B.


If it doesn't equal, then it's not a right triangle.


OK


It is equal, then it is the right triangle.


but


I see.


And you might not get me, you might get someone else, but there's lots of


Sure


I have a question.


What if all the numbers are equal, like what if you had numbers 5, 5, 5 and all the sides.


Then, then it's an equilateral triangle.


OK.


If all the sides have the same number, it's equilateral, isn't it? It's not a right triangle.


Same thing if you had 10, 10, 10, 10.


All the sides are equal


So I just have to list can be a right angle, a scale can be a rectangle also, OK.


So if you give me 5, 5, 5, it's equilateral, and it cannot be a right triangle.


No, I'm talking about isosceles and


excuse me, that have color.


Well, 555 is automatically collateral, but if he gave me 4, 4, 6


that would be assosceles.


Mhm


And you had 4


6. That's associles.


So which is


You, but if you had 5, 5, 5


it's equilateral.


What if you have 14, 6, and 12.


That would be scale like.


not a triangle, but it might be a right triangle.


But it's also scaly triangle.


Right, it's a scaling triangle.


So the, so they built like share.


All the sides are different? Yes, it's scaling.


OK


The site is open 24/7.


So some people I know at midnight or 2:00 a.m.


or 5 a.m.


cause there, there may be less people to answer the questions at that time.


But it's not possible to have the same patient every day.


Right, right


OK.


Yeah.


Because some people like myself, uh, I was getting ready to watch some TV and I said, let me go see if there's someone who needs a math help.


That's very nice


I enjoy it because I don't want you to struggle and get


frustrated or think you're not smart. Geometry.


is a different math


That's true. I'll find it hard.


and it uses, yeah, it uses some algebra, you know, when we have X


+44 equals 61.


Yeah


We're using geometry algebra.


and then you've been introduced to the X squad.


um, but geometry is about the shapes


and the relationships.


It will not be easy


but you have a tool. You have up achieved to sign on whether it's one question or 3 questions.


Do you, at this subject to its geometry.


Say again


Do you do other subjects?


OK


Yes


uh


Oh yes, I do the algebra and uh algebra 2. There's um there'high school math.


Um, I can do SAT math.


OK.


Uh, some people do history and environmental science.


Mhm.


or uh reading comprehension and things like that, and there'other applications as so many, many.


subjects that are covered.


right


OK, thanks for your help.


You're welcome, and the, the microphone is new before that we typed everything, but it's hard to type sometimes, isn't it?


Mhm


Yeah


But again, you can sign on right before a quiz and go over some review questions. Again, it might be, you only need help for 5 minutes.


or


20 minutes


whatever you need. Now, some people


like I signed on tonight.


and I might have said, oh, it's almost past my bedtime, so some people might have to stop after 20 minutes.


You were way too.


Then you get to sign on again and get another coach.


OK


So I can just like end the session or you have to end it.


Yeah, we usually say thank you and have a nice day


Thank you


And you're welcome.


Have a good night.


And it was uh a pleasure talking with you and working with you.


You too


So sign on again. Don't hesitate.


It's a very, very safe site.


and the rest of us are volunteers. all age, and so there's different ages helping.


OK. Thank you again. It's nice.


You, you're welcome. It's good to meet you.


Have a good night


Good night


hi


Hi, tell me what you need help with today


Sarah needs to shade 1/5 of the 20 small squares in the grid what should Sarah do to correct her work?


Do you want me to do the exercise on the board, or is there something specific you don't understand?


board


Do you understand the reason for the exercise I'm doing on the board?


I think.


Okay, let me explain. Since we have 20 squares and we need to know how many there are in 1/5, we have to multiply them first so we can then divide.


is it 5


The answer no, but we can divide it by 5


Aw man


I got it. I got the right answer.


Can you tell what is it so i can confirm it


Correct, good job


Thank you.


you are welcome


Do you need help with anything else?


David needs to shade 1/4 of the 24 small squares in the grid. David's work is shown. what should David do to correct his work?


This exercise is very similar to the previous one; do you want to do it or should I


you


sorry


It's Okay don't worry


I was trying to write the line there.


Don't worry, it's fine; in fact, it only shows that you understand the topic that is very good


So, what would the answer be based on that procedure?


fast


Hi.  How are you?


Mr. Maya, can you please turn on your mic so I can talk to you. I'm Amy.


Give m a minute.


So I, I'm here to review, um, a chapter in statistics. It's called Making Sense of the statistical significance.


I would exam tomorrow.


Can you hear me?


Yes, sir


OK


Can you hear me


Yes, I hear you


No, I wanted to ask, are you familiar with um like um what determines the power of a study and


stuff like that


Um, how I've, I'm, I'm not intimately familiar with it.


Is that, that's one of the statistics that to determine how


good the the test is, right?


Yeah, like, um, it has like several, what did, what determines the study's power.


Yeah. Um


I can try to work with it, uh


through with you, um, it's been some time since I've, I know it has to do with the


type uh er the error types, right?


Yes, sir. So I also have a question about that.


OK. Um, let me see what I, give me a minute to see if I have some notes here


that I could look at. Um, to be honest, I'm not that good at it if, you know, there's somebody else that might be


um


better at that, more familiar with it.


Yeah.


You know what? No, sir. So I have been looking at different tutors, and I can barely find a tutor who knows of anything about this topic, like, at least you know type 1 and type 2 errors, right?


Yeah, I, I, I definitely understand type one of


yeah, if I, if I have it in front of me, to be honest, let me go see if I


have a little material here that I could look at


Yeah


Hold on please


OK


OK, so kinda trying to help myself review a little bit.


Let's see


see


There are two types of important types of mistakes that can be made when reaching a decision on the basis of a hypothesis test.


Rejecting the null hypothesis when it is true, is called a type one error.


not rejecting the no hypothesis hypothesis when the alternative hypothesis is true, it's called a type 2 error.


No, no, no. For me, I see it as so the type one error is when I reject the non hypothesis when it's true, and the type 2, it's failing to reject the all hypothesis when it's false.


Correct


I'm a, I'm a copy a table.


Yeah.


Yeah, this stuff is rather, rather hard to get in your brain, my brain anyhow.


So are you getting something


are you loading something?


Yes


OK.


I'm trying my best to cop it. I hope it comes up, but it's not coming up. So my table that I have um and I do


for, so I was doing some practice problems and stuff.


Mhm.


So


um


the, um,


you want me to tell you the, the statements.


OK, I guess, um


yeah, you can, you can do that.


I'm gonna read it from the textbook because my publisher doesn't allow me to paste and copy or whatever, so I won't be able to do that.


All righty


So, the problem is saying, um.


so


And are you familiar with meta-analysis and stuff too.


Meta-analysis? No, I'm sorry. That doesn't ring a bell at all.


I hate to say


OK. OK, so the, um, so it says, um, a study of whether colorbrine individuals can distinguish gray shades better than the population at large.


Hello


David.


I scream out David.


Mm, OK


Uh, hi.


sir.


W


The


Vanillano


fleon.


strawberry strawberry, strawberry only. No.


Yes, my age.


vanilla do But Ramanandabiche Are they all around you?


Ah, what, just a second, sir. I'm on a phone.


That's fine. Don't worry. You're fine.


I'm still here


Yes, yes, yes. So the question, um, so the core is saying that


a study of whether color blind individuals can distinguish gray shades better than the the population at large.


OK.


and what I thought, so for my type one, where I'm rejecting the no hypothesis when the known hypothesis is true. I put color blind individuals can distinguish gray shades better than the population at large, which is not true, like it's incorrect.


OK, so the null hypothesis is always basically the status quo, which says the null hypothesis would say, I'm just saying this to get my understanding correct. The null hypothesis would say that colorblind individuals


aren't any better than


the normal population at distinguishing grade, right? That would be


the null hypothesis


Repeat your statement again what you said.


for


I said color blind individuals can distinguish gray shades better than population at large, which is not true.


um


when you say which is not true, what do you, what are you saying with that last little statement?


No, I put, so I put like color blind individuals can


Oh.


distinguish gray shades better than the population at large, and then I put a not true like that's not a true statement.


yeah


So again, I, in that way I would say it is


um,


there is no difference between color blind people's ability to distinguish gray color.


between them and the norm and the overall population, so.


um, or the


There will be, that would be in my correct decisions, right? Where I said no difference.


right, there is no difference between the two is the null hypothesis.


There is no difference between color blind people


and non-color blind people.


with respect to distinguishing gray


colors, gray shades.


There is no difference. That would be the no hypothesis.


No, that would be my correct decision though.


So,


um


Cause I thought so for the type one, I just put like um the color blind individuals can distinguish gray shades better than the population at large, which is a which is an incorrect statement. That's my type *****.


right, so if um


if we


if we performed it, I'm just doing this for my own benefit more than anything. If we


we do the calculation and we find the P value


to be, we would find the p-value to be


a small number, and it would put it in the range


where we would


we


it, it would be smaller than our significance level.


and we would um


but we would go ahead and um reject


the null hypothesis will be rejected in that point.


even though that would be a mistake.


Yeah. So what I said for my type one error is correct, right?


Say it one more time for me, please.


I said color blind individuals can distinguish gray shades better than the population at large, which is not true. It's an incorrect statement.


OK. So, it sounds


that sounds right to me, to what you said.


And then my correct decisions would be that there is no difference between color blind individuals and the population and non non color blind individuals, um


So


and that


no, no, no. Let me, let me, let me rephrase it.


that, that is the, that is the no, that is the no hypothesis is what you just said.


No, I was saying my correct decision. I told you my type one error, which is that color blind individuals can distinguish gray shades better than population at large, which is an incorrect statement, but then my correct decision in the next box is saying um there is no difference between color blind individuals, and the population at large at distinguishing


gray shades


OK. I'm, I'm, yeah, I, I know you're trying to fill out a paper and I


So I, I, I agree with what you're saying.


best as I can determine.


So you're, you're filling out a like uh


these are correct


I'm, I'm doing like a practice thing.


OK


All right


Sounds, sounds good to me


All I could say for my correct decision, like there is no difference between color blind individuals, um, being able to distinguish gray shades better than the population at large.


Mhm


And then my type 2 error, I said color blind individuals can distinguish gray shades better than the population at large, and this is also an incorrect statement.


Right


Sounds, sounds correct


OK. So my correct decision would be when I retain the no hypothesis when the no hypothesis is true that there is a difference between color blind individuals and


Yeah, the, um


there's a difference between color blind individuals and the um who can distinguish gray shades better than the population at large.


right, that would be


right, the essentially the alternative


uh


the alternative hypothesis is true.


Yeah.


Do you want me to tell you the next one. I have one more.


OK


OK, so it says a study comparing individuals who have never been in psychotherapy to the general public to see if there are more talented of other people's to save their more tolerant of other people's upsets, then is the general population.


Read it to me one more time, please. I'm sorry.


A study comparing individuals who have ever been in psychotherapy to the general public to see if there are more tolerant of other people's upset, then is the general population.


Psychotherapy, was that what


you said?


Yes


Who, who, who have been in psychotherapy to see if they're more tolerant, OK.


So my type one error I wrote individuals who have been in psychotherapy or more tolerant of other people's upsets than the general population, which is an incorrect statement.


So you're type one error, say again one more time, please.


I said, Individuals who have been in psychotherapy are more tolerant of other people's upsets than the general population.


and it's an incorrect statement.


Right.


So then it would be like there is no difference between individuals who have been in psychotherapy that are more tolerant


of other people's upsets than the population at, um, then the general population, correct?


That's the type 2.


No, no, no, I'm talking about my correct decision.


Oh, OK


What would it be? Would it be something like there is no difference between individuals who have been in psychotherapy that are more tolerant of other people's upsets, then the population in general.


Yes, I agree. There, there would be no difference.


if, if, yeah, that's saying that the no hypothesis weren't, was in fact true.


that there is no difference. Yeah, I agree with what you said. That's a rather


cumbersome thing to


put on a problem.


They're really


a lot of words there, but um, yes, I agree with what you just said.


And then my type 2 error. Are you ready?


Mhm.


Individuals who have been in psychotherapy are more tolerant of other people's upsets, then the general population is incorrect.


Mhm


So my correct decision, I would say there's a difference between individuals who have been in psychotherapy that they are, they are more tolerant of other people's upsets, then the general population.


Yes


that would be the true statement, right?


Yeah, am I correct decision?


Yes.


So, the way I'm just um I have to try to


keep this in my mind


kind of with the tests that are performed. I'm just talking here for my own benefit.


So the way you get a type one error


is you have a certain significance level


like 5%


significance level. So you've got a little area on your normal curve


and you find out that your p-value is less than that number


Well, in that case, you're, you're rejecting the null hypothesis, even though it was true.


That, that's how you make that type one error. Yeah, I'm just thinking about


calculation here, which helps me understand it. So if I look at the normal curve and I'm all, let's just say


I'm looking at one side where there's a 5%


um


area there, and I, I do a test and I get a a P value that's 0.02, let's say. So I'm in that critical region and therefore, I think there's a difference that, that the no hydro hypothesis is, is not true, but in fact it is true. That's how I make a type one error. That's the way I think of it.


Did you?


OK


so


Mhm mhm


This confusing for me. I just think of it as like, um, I just write down the whole statement, kind of, and then I just put a knot through like that's not a true statement.


OK. Yeah, I, I, I get it. OK.


Right


Yeah, because I look at it as rejecting the no hypothesis when the no hypothesis is in fact true and then type 2, I look at it as failing to reject the no hypothesis. In fact, when it's false.


Failing to reject the null hypothesis when it is false.


Um, the, the first one you the type one error you defined exactly right.


Um.


the type 2 error, say, say your definition of the type 2 error again.


It's for failing to reject the no hypothesis when the nuhapothesis is false.


Correct. I get it. Yup. That sounds, yeah. I like your definitions there and you've tried to adhere to them.


in these problems that we discussed.


Yeah


Mm


So, you have a test on this tomorrow. Is that correct?


Yes, and, um, yeah.


OK.


And it doesn't, is it involving more just stating this stuff, or do you actually get


will you actually be getting


That's, that's, this is all I had to do. I had to use like a teeth teacher like, yeah, and I to why the things in 4 boxes.


OK. Well


it sounds like you've got it to me, got it down, and they must be taking things very slowly here, just trying to get you to work with the null hypothesis and the alternative hypothesis and understand


what these errors are


by stating them in, in verbiage, right?


Yes


Yeah.


Mhm


And I wanted to ask you one more question, if you don't mind.


I'll try


Yeah


So are you are you familiar with the empirical rule like the, the normal curve, like 34%, 14%, and 2%, it's divided like that on both sides.


right


Yes, I am familiar with


that.


Familiar with it, right


I have a question like a part of a question that you, I want you to explain it to me.


OK.


It's, it's from a test.


OK


Let me get it


Sure.


It's saying um


So, the problem says a business uses a 7 point scale about satisfaction with services it provides to clients. The ratings are normally distributed with a mean of 4.8, and a standard deviation of 0.5. What percentage.


Hold on a 2nd. 448, 4.8 is the mean.


Yes.


and the standard deviation is what?


0.5. OK


What percentage of clients weighed their satisfaction above a 5, above a 6, above a 4, and below 4.


OK, so you're supposed to use the empirical rule to solve this.


OK, so


Yes, um, it says use the normal code table and include a sketch for each.


OK, is it the empirical rule or the normal?


curve? Did it say empirical rule or did it say?


It says bolt.


OK.


So


um


It says one of them, but I have to use both.


OK


Um, so, I, you gave me the mean and the standard deviation and ask me the first question again. What is, what is the question, first question that I'm supposed to.


we're supposed to


Like, first part is above a 5.


Above a 5. OK, so I'm going to draw myself a little picture here.


And then I, I actually solve the first part of it, and I got a Z equals 0.4.


what we're gonna do is we're gonna take 5


minus


0 minus 4.8.


Yes.


and divided by 0.5.


And let me do that on my calculator here.


So that's 0.2


divided by 0.5, right?


So


Yeah.


are we supposed to find above or below that value.


Above a 5


OK.


So the Z value is 0.4.


So I'm gonna go into my calculator, which has the normal


um


distribution


I just want you to like do one or two with me so I can understand what you do.


OK, hold on, please


OK, so


just taking the uh the amount above 5, it's about


if I use the exact values.


it comes out to 0.3446.


OK


Yes. How did you, but how did you get that value from the normal co table. That's what I'm trying to figure out. How is it?


OK, do you actually, do you actually have to use a paper table or do you get to use a calculator.


I had to use a paper table, like it's on.


they all have a little bit of different instructions. I don't, I always use a calculator now.


but um you have to look at whatever instructions that are on your


some of them, let me


I'm, I'm asking like um how did you get the 34.46%.


OK. So what I did


was I used the calculator


and


But do you know how to look it up on the paper table?


well, the, do you have


some they're, they're, they're very


some of them.


I do have a paper table.


So when, when you answer these que questions.


how are you supposed to do it if you don't have a table.


Oh, OK. Can, can you, can't show that on the screen, can you?


OK


Um


No, my textbook wouldn't, it doesn't allow me to copy, but I can tell you the heading of the table.


OK, go ahead


Mhm


The table is um normal cold areas, percentage of the normal curve between the mean and the Z scores shown and percentage of scores in the tail for disease scores shown.


OK. So in this case


So when I go to


so just, let's just stop there. We, we computed the Z score, which you agree is 0.4, right?


Yes


So I, I think what I'm hearing is you have an entry for the tail of that.


for the tail, right


So if you look up, the Z score of 0.4 in your paper table.


Oh


Do you see an uh a tail


value?


Yeah, person intel. Oh, I see how, how, how that person came.


Good. So that, that explains that problem anyhow. So what you're doing is you're, your Z score normalizes it to a


a, a mean of zero


and a standard deviation of one.


And then you're just looking at the area


since they asked for the percent above the Z value, above the


um


5 in this case


Um


we, we looked at that tail


above the Z value, and you see your 0.344


So that explains


Yeah. Let me, cause for now B says Part B


mhm


it says above 6, and I have a Z value of positive 2.4.


OK, so we would just take 6 minus 4.8, which would be 1.2.


and divide it by


and you would get


2.4, right


Yes


So you look in your tail end again.


and what you get for 2.4.


which I can do on my calculator. Let me go ahead and do that.


All right.


One second


Distribution


Oh, I see.


Hold on, please


So we're gonna look for


what was the Z value? I said, I'm sorry, I forgotten. 2.4?


The Z value is 2.4.


And anything above that


So what did you get


I got 0.82.


OK, it should be 0.0082.


No, I actually, I actually, well, 0.82%.


Well, that doesn't make sense because it's very far in the tail.


So you're 6


6 and above, right? That's what we're looking for.


Um


so


Above a 6


yeah, 6 minus 4.8 is 1.2


1.2 divided by 0.5 gives us a value of 2.4.


Now, if you take the area in the tail above 2.4, it's only 0.0082.


It's very small


Yeah, that's what I got.


Oh, I thought you said 0.82. You mean 0.0082.


Mm, but my, but my like my thing is saying 0.82.


No, it, it, it's 00.00. Um, so you're looking at a, a paper


you're looking at a paper


Yes, it's because it's a paper table.


Yeah.


So


like was the last one.


we, we know that we got an answer correct on the last one. Now we're even further along


on the tail end of the curve because we're way above


you know, 6 is way above um 5.


So we're, we know that the area is going to be less


And when you say 0.82


you're, you're saying it's more area than the first example, which can't be true.


So, it, it's kind of funny that you're saying it's 0.82 when the answer is 0.0082.


But that's what my paper table says.


Well, there's something funny going, does it have any instructions like divide by two or something like that.


you don't see


No, no, no, we don't divide by two.


I know, I know


Um, that doesn't make sense to me. I'm sorry. I'm just trying to be


So think about this


for a minute


If


if your area was


about 30


5 % before.


and now you're asking just for the amount that's above


uh


6 instead of above 5.


you're gonna have less area than your first answer. There will be less tail on the curve.


Um.


so I don't, I'm not sure what the misunderstanding or problem is here. Um,


just


OK


hm


OK, can you, do we want to move on to the next part, um, next part.


OK, we'll try. Yeah, let's, what's going on.


It says a bottle 4. I get a Z value of -1.6.


It says above 4 now.


Yeah.


OK, so let me


And that is the value of 1.6.


OK, so let's


so what we're gonna do is we're gonna do a Z value of 4 minus 4.8.


divided by 0.5.


we would get


negative


over 0.5


and that would be -1.6


Do you agree with the Z value?


Yes


So we're looking for anything above that, is that what you said?


or below neck


Yeah, above a 4.


OK


So


let me um let me go ahead and do the cat.


And I got a, I got a value of, um.


Don't tell me, don't tell me yet. Let me come up with my own, so I


don't get


um


influenced hearing them


So we're gonna go above 4


OK, you can tell me what you got now.


OK.


Um, I don't know value of 44.52, but then I add the other side, so 44.52 plus plus 50, it would equal to 94.52%.


That is correct. That's the same answer I'm getting. Yes.


So that one, that one works out.


So for that particular problem, I wasn't supposed to be looking at the person it tail section, right?


Um


well, I mean, it's all to the right


It, um, so again, using your, I think the problem comes down to how you use that table that you're looking at.


Um.


Cause for the previous 3, previous um two problems. We looked at the person in tail. That's how I got my 34.46 and my um


you said that time you said it the way I had it, 0.0082.


Yeah


That's what I, that's what I had. So I agree with that. I thought you were saying 0.8


82 but you're saying 0.0082, right?


Yeah, my, my answer, my table showed me like 0.82, so that's what I put but I guess I have to agree with you.


Yeah, um


the problem, I, why I don't like the tables, I mean, they're, they're fine and for the day, but


it's much more


it's much easier to use a calculator, of course, but you're not you're not allowed to do that, right? And your


No, we don't have it on, on our calculator link.


I see. OK


Yeah, tables are a little bit kind of obsolete nowadays, but that's what you have to deal with in your class. So, um,


so it's really making, do they show like a picture of you, uh, you know, a picture of the normal curve above the table, kind of


telling you how to


how to compute it


Yeah, it does say it's, it says um um percent mean hui and percent in 2.


present, say the first one again.


Percent me, me, and person intel.


Percent in mean


No person mean to Z.


Oh, mean to Z


OK. So that's from the center to Z.


OK.


Yeah


And then the tail. Well, the two of them


um,


two of them together, it seems to me would add up to 5%.


if I understand what you're saying there. The percent


from the mean to Z.


is one piece of it and then the tail was the rest of it.


yeah


So


um


when you had the negative value


we were down, we actually had


a whole, we were actually


had a a whole half of the curve plus some


to the left


So yeah, um


I think you've got the right answers, right? Each time, do you, do you understand


The only one that, the second one seemed like we were, we were having some problems, but you managed to come to the number somehow.


OK


I'm sorry.


below.


And the last one, it says below 4, and I have a Z value of again 1.6.


So, yeah, and then we would, let me, let me go ahead and, and do that and see if I get the same answer that you do.


So I got about


below that was below -1.6, right?


Yeah, yeah, yeah. That's what I got. 5.48%.


5.48% is right, yes.


OK, so that's how I figure out the um the area of, of the once I get my Z scores, right?


Right.


Yeah


I have to look that, look at the thing, like person in the till.


You, you think, you seem to be


OK, because it was confusing for me on the exam.


yeah,


I didn't know


how I got percentages.


I felt lost


Well, you seem to get all the answers this time. I, I guess they


Yeah, yeah, and now I understand.


Well, sometimes that's what happens with tests, right? Unfortunately, we, we make a mistake and then it


the bell, the bell lights up or the light turns on and we understand


So maybe when you were taking it, you were


confused by the table or something like that.


cause I got this Dails correct, but the areas they were hard to find because the first one was 0.4. So I was actually looking at um


the Z score of um


Uh.


Yes, that would do it to you, yes.


Oh, it was tricky. But I understand now it's 0.4.


Mhm


0 got.


Yeah, I think you, you've, you've got all the answers, so whatever you're doing to read the table now and your Z values are fine.


Just keep doing what you just did here tonight and you should be good.


Yeah. This was just from another exam. That's it.


I get, I get it, yeah


Yeah, we all hate to take an exam and then find out.


oh, I understand it, but at the time, you know, something happened, which is


normal to happen. I mean, it, it's


it's


that's sometimes how we learn things.


Yeah


Yeah, yeah, yeah


I understand


This is a, you know, the hypothesis testing, and I've always found, you know, unless I sit down again


cause I'm, I'm


uh


I'graduated for


55 years, so it's, it's been a long time. Um,


but you


No, you were a professor?


excuse me


University professor?


No, no, no, I'd just say I went to


Oh


my undergraduate, like 55 years ago, so.


it's not, and then this was not one of my favorite things, hypothesis testing, so it never really um


you know, it, it doesn't, never sunk in all those years. So every time somebody talks about it, I have to go get out of


uh statistics book and look at it again, trying to understand it for the umpteenth time, you know.


Yeah, yeah, yeah. I, I get it.


The hypothesis that I, you know, the hypothesis testing is kind of mysterious and that, I guess they're, they're making it, they're walking, which is good, they're walking you through it slowly.


and surely, so the concentrate on the statements, which is what you're kind of doing right now and the errors that


you know, the hypothesis, no hypothesis and the alternative hypothesis and the type one error in the type 2 error.


and trying to make sure that you can understand


the definitions of all those so that when you actually


um compute some statistics and


get into the P values.


which I assume you haven't done yet. Uh, when you do, it'll all fall right into place.


Yeah, we do use the critical values, P-values.


Right? You have, we, you, I assume you will be at some point, right?


Yeah


Well, I hope I haven't confused you in any way.


No, no, no, I understand all of it.


OK, good


And um do you understand, um, so do you know, like, are you familiar with what determines a study's power


Well, there's a definition, let me get it out here. Um, again, like I said,


I have the I have the definition of statistical power, which is the probability that um a study will produce a significant result if the research hypothesis is true, like the alternative hypothesis.


the alternative or yeah.


Let me, let me just look up what I have here. Hold on, please.


Again, that's not something that I


remember all that well too


266 power or section.


So it says this is from my


statistics book


The Power of the Test


is defined to be the probability that the null hypothesis


will be rejected


when uh


mean is are the


alternative is true, I guess.


Yeah, something like that. I have it as, it's a, it's a probability that the um study will produce a significant result. If the alternative hypothesis is um true.


Right, the alternative hypothesis is true


um,


probability that the no


alternative hypothesis is true and you're rejecting


80, right


I don't know, but I just go.


The power, the power of the test is the probability that the null hypothesis


will be rejected when


um


the


um boy


Anyhow, I don't wanna confuse you anymore.


Yeah


I, I appreciate this children.


OK, I'm, I'm sorry that there's nobody who really, I'm, I'm sorry to hear there's nobody that really uh has great understanding


Uh, I kind of


certain parts of


probability, I, I do very well at. The statistics part, when we start getting into this


is a bit murky for me, but I, I think we slugged through some stuff. At least you understood um.


the um mistake you had on your test. So that, that's one good thing.


Um


and you're, you sound like you've got these statements down correctly from what I can grasp.


Yeah, yeah, yeah, yeah


My God


OK, thank you.


Bye


You take, take care and good luck tomorrow.


Thank you


Bye-bye.


Hello


hello


Are you there?


yeah


What can I do you for?


Talk to me


ok mb


so there's this question i need you to help me with


Okay, here to help


next round follow the three clues to find a hidden treasure write each answer as a mixed number


thats the question


This isn't a complete question. Is there a picture or something?


wait


If there's a picture, upload it here


clue 1 start at 3 and add 2/5


Come to the board, let me solve there


Are you at the board?


Done on the board


Based on clue 1, answer is 3²/5


hello  there


What did you type?


can you say 67


You know, you shouldn't be saying that. Why do you kids keep saying that? You think it's funny?


ok i am sorry


Hi Chloe!


How are you?


good


I need help with my work on Springfield math


Okay, are there any specific problems you would like help with?


yes


this the first question


Yeah.


It's the first question.


Now is the time to check your


Okay I see it. So in this case, we have a reflection over the line y = -1. This means that the new figure will be above the line, and you get this by changing the sign of the y-coordinate.


Can you do that with the points of the figure?


is there any way u can talk so u can help me with steps and how to due this


Sure!


thanks


Hello, can you hear me?


I can


OK


Um, so you want me to explain just how to get the points.


Yes, and I had to do it like I'm not good at this though.


Mm, OK. Um, yeah, basically just change the sign of the white cornet for every point, so like, um, I'll give you like, I'll show you how to do one of them and then hold on, so.


for example, we have like 8 and 2, so to get the reflected point, we change 2 to 2, so it would be like


right here


currently?


It would be, do you see that, like that point I plotted?


I do.


Oh wait, no, no, not right there. It would be, no, wait. It's actually, sorry, I


Very good


wrong advice. Um, so it's actually not this, it's.


because that's for the Y axis, not, not, um, going on. For Y equals 1 or -1, it's just basically like um


the distance from the point to the the line cause you see it's like one unit, like from 2 to -1.


Yes


It, um, so then you took, so if we go one more unit, we would be at 80, so it'd be


here


You see that


I do


Does that make sense? Like the way I explained it.


Oh yes


OK, do you think you can do that for all the other points?


Um, this is my first time doing this, so.


So like what I suppose.


Uh, like I said, you know, like,


to learn


Oh, OK, OK.


um, so you count like how many units um the pains away, so it's, so it's like 12, for 2 units away, so you just count 3 units again, and then you just, yeah, do you get the gist?


I, I see what you're saying. So basically, he said, 123. And so I just go up there on, on the axis.


Yeah.


uh, 12, so go right here.


All close, it's um that's 4 units from the line, not from the axis.


Oh


So, so it's 4.


No, I meant like what you did was for, but that's not what you're supposed to do cause it, it's 3, so like


from the line Y equals -1, not from like the white actor from the X-axis.


Oh, that's.


So you said


12, so it's 3, right?


Mhm.


3 units


So 12 race right here.


Yeah, right, right here


Oh.


Oh no, not there, cause it's, yeah, it's from the, yeah.


OK


So I, so I can feel like the *****'s not right, they go right.


Mhm, yeah, just


yeah.


I got you


So 12345.


Mhm


sneak it into me every week.


It ain't much good, but it's.


Uh close but not quite.


It's supposed to be on 2


No, I mean, um, like.


it's so you, what you're doing is you're like counting um like


it, uh, so the 8 units don't start from like right here, they start from right here. So you're going from this 0.8 units upwards, so you're at 7


Oh, OK, I got you.


Yeah, so let me just like erase these points.


the point, and it so I just put it right here.


Yeah


Right


Do I do the same way for us all.


through.


Um,


What is wrong on 23, 05, 67.


8, so it's 8 for next, right?


Oh, for this point, yes.


Oh.


It's also a


You said 8?


yes


All right


So 12346, sorry.


No, not quite. Um, make sure, OK, so when you're like counting um


Why


like upward, make sure you're on the same, uh, like X value you.


Yeah


cause you tend to like drift a little further away.


Oh, got you.1, 2, so it should be right here.


Um


yeah, like in this area


Um.


OK.


There you go


Well, yeah, like


yeah.


All right.


Yeah, OK


That's, that's 4 points.


All right. I kind of do get more so is that fun?


That's OK with me


All right


But this is only the first question. I got 4 more.


OK. Uh, uh, excuse me one second.


Uh


see


And uh she said 37.


OK, I'm back


So, um


we moved on to the next problem.


All right, so like how delete the picture?


Oh, I can delete it. Um.


you know, just


This is my first time using this.


oh it's cool, yeah.


All right, here's the signal.


Girl


Hm


I got the same line. OK. So,


yeah, just um


Yeah


same thing


All right


just with a different shape, so.


I got you.


Mhm


Sorry, so for negative 4. I just go up.


Yeah, and then you yeah, you count the units um to negative


Alright


So


to, so it's 3, so it'll be on 2, right?


Um, yeah


All right. Oh, look.


So let's put it right here.


Oh, no, I mean, it's on the negative 2 like.


Oh God, so it's been on one.


for the X axis or from um on the X, but like for why you're still like, you know, going 123 units, um


one more, 2.


All right, 2 of my favorite


Yeah, 123 units and 3 units. So like right.


here


I got you


OK


Mhm


No, so I do the same one for the rest of them, right?


All right, so 12


Mhm.


so it'll be 3 right for the same.


Uh.


so sorry here.


Um, little bit lower.


Right here.


Yeah


All right


I do, oh.


OK. So, 1234 saving.


So I go 3 and they go up 7.


Look


Yeah, and you go up 7, but remember to do it from Y equals -1, not from when Y equals 0 on because you, you see the blue line? Like, that's where the reflection is over. So you start from that line when you count.


Oh, OK, I appreciate.


Mm. Just, yeah, keep that in mind.


Why, 2, sorry.


Mm


I'm a little songs. All righty. Mm.


I'm going to one.


Uh


so it can be 6


Yes.


Um, so.


It's right here


Yeah


Appreciate it. 2345, let's see.


So here for this for last night.


Wait, hold on, let


me verify


Wait a minute. Oh, yeah, yeah, that's right.


All right, so I do a thing with mouth real quick. But I think I understand it now too.


So appreciate it too.


Um


I'm happy to help


Oh, you too. Thank you.


Bye.


hi


hello!


What do you need help with today?


I need help with this question


Okay! Give me a minute to read the question


ok


I can't see the full question. Could you move the screen a little to the right?


thank you!


First, do you know the formula for continuous exponential decay?


Yes


In the formula, you will plug a as the initial population which is a


and t = time taken which is 12 minutes


question a is just asking you to write the formula


For question b, you need to find r


Did you get 53 for r?


yes


r is not 53.


First you have to plug in your numbers in the formula, a=400, y=140, t=12 minutes in the formula y=ae^rt


did you plug in your values?


can you show me your equation?


Do you need help building your equation Maya?


Okay. For y, we will substitute the value 140. Can you write y equal 140?


We do the same with a =400, and t = 12. Don't focus on question b yet. We are trying to find r


Great job Maya! That's the first step


The next step is to divide both sides by 400. Can you do that for me?


Great! So what will our equation look like now?


Let's write it on the graph


So we can have more space!


This is what our equation looks like now. Can you see it on your screen Maya?


good! You can reqrite 140/400 as 7/20


rewrite*


Now we take the natural log on both sides.


Did you do that Maya?


yes


So do you know what the equation will look like now?


no


That's totally fine!


Once we take the natural log on both sides the equation will look like this


Did you get that?


What would you do next?


If you are not sure that is fine! Just let me know


not sure


Thats okay!


Since we are finding r, we need r by itself.


So we divide both sides by 12 to get r by itself


We found r! Great job!


So now we have all the values we need for question b


we need a=400 and r=(ln(7/20))/12


Question be asks us how many bacteria there are 23 minutes after the beginning of the study. So we would substitute t with 23.


Do you know how to write the equation?


thats okay.


I will write the new equation in pink.


ok


this is what our new equation will look like


then we simplify our esponent


exponent*


You can rewrite this as


and since e^ln(a)= a, we can rewrite that as 7/20


Do you know what to do next?


plug in 23


we've already plugged in 23!


oh


We now compute!


7/20 as a decimal is 0.35


so we will write it like this


since we rewrote it, we have to compute the exponent.


23/12 as a decimal is 1.9167


that will get us this


So now we can get our final answer!


multiply


yes! tell me what you get as the answer


Yes, now round your answer to the nearest whole number


Correct! That is your final answe!


Is that all Maya?


I have another problem


Okay!


will you show me your problem?


ok


Give me a minute to look over the problem


So first we write the formula


We plug in the numbers. the initial amount 5800 kg. So we plug in a =5800, y =1856, and t=9


Can you write the equation for me?


Yes! Perfect! Let's write on the graph!


What do you do next?


Great job! Keep going Maya!


Lets go down to the graph


after dividing both sides by 5800, we will get an euation that looks like this


when simplifying the fraction, you can 464/1460


We take the natural log on both sides


To find r, we need to get r by itself.


So now we plug it back into the model!


that is part a in blue!


Now shall we move onto part b?


yes


Okay we will move on to part b


Maya, I will end the session at 5:05!


ok


We substitute t with 15


Part b will be in pink


we are simplifying the expoinent


Now we will compute


you can write 1856/5800 as 0.32


15./9 as 1.


ln (0.32) = -1.1394


And 1.6667 x (-1.1394)=-1.899


Multiplying 5800 x 0.150 gives you approximately 870.


870 will be the answer!


I hope this session helped you Maya!


thank you


You're absolutely welcome! Have a great day!


Chloe


oh hi Chloe its you again haha


hey


haha


what do you need help withhh?


this


okay you need to multiply 3/4 with 6/5


because when you divide by a fraction, you multiply by its reciprocal.


yupppp


simplify that


nope, not quitee


ok


try again


uhh ok


remember to find the GCF first


what's the GCF?


of what


3 and 6


of 18 and 20


nope its 2


so divide 18 and 20 by 2, then you get the simplified form


what's the simplified form?


idk


here let me write it down


answer that


9 and 10


yes


so the simplified version of 18/20 is 9/10


ok


yaa


do you need anything else?


okay sure


show me


wait can you show that again


I couldn't see properly sorry


yea


okay so the first step is to make the mixed number an improper fraction


do you know how to do that?


I'm lagging


its okay take your time


here


there


no


do you know what a mixed number is?


yea when it's a whole number next to a fraction


okay good


how about improper?


A improper is when the bigger number is on top and the smaller number is on the bottom


yes thats right!!


so to start with this question


we need to make 1 1/2 an improper fraction


W


ill show you how on the whiteboard


soo


to get it, we multiply 2 by the whole number, then we add the numerator


nope, its not 11/2


L


yes


then you add 1


what do you get?


yaa


nope .-.


no


its not done yet Chloe


ok


there are more steps


so what's 2 x 1 + 1?


its okay its easy


okay so


the numerator of the improper fraction will be 3, while the denominator will stay as 2


so the improper fraction is 3/2


can you show me the whole problem again?


yea


okay so now it is 1/4 divided by 3/2


the first step is to make it a multiplication expression


do you remember how to do that?


what does 3/2 become?


idk


you just flip the numbers


what does it become when you flip 3/2?


yes


so now u multiply


1/4 x 2/3


what's the answer?


yess that's right!!!


now you need to simplify once again


what's the GCF of 2 and 12?


uhhh


greatest common factor


nope


yes!


its


ok


so you divide both numbers by 2


2 divided by 2 and 12 divided by 2


what's the answer for both?


Ifg (I forgot)


okay


what's 2 divided by 2?


okay so that's our numerator


what's 12 divided by 2?


okay good, that's our denominator


so the final answer is..?


nope, what's 2 divided by 2 again?


its not 2