Let me, yeah, OK, OK, let me yeah, let me go on paper really quick, um.


It's OK, it's OK


yeah.


Beta.


well.


e kwondo. Hey, man, but there mepicabelo you gonna I want then I think it's vinitomirapevino.


OK, um, so click, all right, click Compass, click compass.


OK


uh, click A.


The good


Uh, draw it like below the line, like right below the line, not, not in the, yeah, uh, no, oh, but like that's above, drop below.


Oh


OK. Yeah, yeah, that sure, that'll work.


I


OK. Now, let me think, use a, OK, cool. So yeah, you do that now, is that you're a little compass circle intersects the line at two points, draw arcs as a as a parts that the compass circle intersects, small, small arcs, small arcs on each side.


Wait


Where do we draws again?


Oh, where the compass circle intersects the black line.


Oh, small circles.


Yeah, small arcs, yeah


This one?


Yeah.


And then as that side too


Yes.


OK, good. After that, you drag, I, I guess you could


OK.


With the ball and not not myseo.


Mm, let me see. Let me do my paper.


they don't you know.


I'm glossy


Don't need to say.


OK. So now, draw, uh, you see the blue circle at A?


Yeah


move that to the arc on the right.


OK


OK, sure, something like that. Now, OK, I think


you let me think, uh, let me do a double check on paper. So after you do that,


OK, I


think


I mean somebody has


too


you draw, you draw an arc.


of


Taparejo wait, sorry, I'm sorry.


No, I'll go, all good. So there's two blue, blue circles, right? One's on the line and one isn't, right?


Yeah, yeah.


Well, yeah, there's like two circus once, yeah, one on the line and one is a yeah.


Wait


So the one that's not on the line. Draw like a big arc to the left of it, to the left of it, but make sure it doesn't intersect the line.


wait over


Yeah, so that blue circle, drawn arc to the oh


oh, don't, don't move it, don't move it.


Let me, uh, wait, shoot. OK, OK, 1 2nd, 1 2nd, I don't know.


Wait, oh my God, I'm sorry.


No, it's not that big of a deal. I think, uh


I'm sorry. Oh my god. I was trying to like make the arc, but.


OK, it's fine, it's fine. I guess the only way to do it is, OK, double click uh Compass, double click compass, it should be fine.


Double click compass


OK


uh click compass, uh, wait, yeah.


Yeah


OK, now click A, click A.


Draw, yeah, click A.


Draw, do the same thing where you draw below the line. Oh.


below the line


All right, sure, something like that. Yeah, OK. Now, draw uh arcs, draw arcs, to where it intersects the lines, small arcs.


Oh


No, yeah, like that


like that


Yup, and on the left side too.


Now, the Blue circle at A move it to the right, uh, to the right arc.


This one.


Yes, good. So after that,


uh draw uh see the blue circle at the bottom?


Draw an arc to the left of it.


like that.


Yeah, not intersecting the line, a bit bigger, a bit bigger. Yes, sure, right there. OK. Right there will work. After that


I uh grabs the blue circle in the middle.


This one


Yeah, and move it all the way to the arc on the left, the arc that's intersecting the line on the left.


Wait, this one.


Yes


OK. After that,


uh, let me think.


You draw? OK, see that big like see below the line, the big arc you drew below the line.


Yes, draw an arc intersecting that on the compass circle.


like this way, this way?


Yeah, oh yeah, yeah, mhm, smaller, uh, small, make it, OK, it's fine, it's fine. That'll work.


OK. OK, yeah, release? OK, good, that'll work. Now, you, I think you draw a line from A to where the arcs intersect. So yeah.


I click line


I, I think you, I think you click on the line.


Yeah, OK, try clicking online.


Yeah, drop


a line from A to where the arcs intersect.


Like that


Yeah


I


doesn't


I think that's it. It should just submit, we'll see.


No, it's


it was


OK, OK


Yeah, oh yeah, it, it, it's purple on the, yeah, cause it's purple on the


right


OK.


I unamal.


wait, I think I have to go to sleep soon.


OK, we'll finish.


Yeah, we have 2 more questions.


Well, it's OK, it's OK. We're almost done, but my mom just telling me that I have to go to sleep.


OK, OK. Uh, all right. I'll do it my, the instructions fast, so try to um


No, it's OK. It's OK.


right.


right, I'll try to go, I'm, I'm gonna go fast, try keeping of the. OK, Compass on uh S do Compass on S.


OK


and draw like um draw, sure, yeah, release it right there. Release it right there.


OK. After that, draw an arc right below the uh draw arcs on where the line intersects at.


Oh, here


on where the circle intersected lot, yeah, yeah, there.


and the other spot


OK, so after that


uh let me uh, OK, OK, that's fine.


Grab the blue circle at S.


This one


It's like, yeah, the one in the middle and drag it to the arc, like to the top right of it.


Yeah. Now,


make the blue circle on the top left.


uh, the top left blue circle.


bigger, just uh move it a bit more, just make it bigger, like top move it top left, yeah, bigger, bigger, good, right there.


Oh no, smaller, smaller, smaller, has to be, no, smaller, smaller.


No, yeah, right there, right there, right there, good. OK. Now, after that, draw an arc uh draw an arc um, can I sketch this? OK, fine. Draw an arc, right above that blue line?


Uh, wait


wait


Right above the blue cir um top left.


OK.


here


No, from, from the right where your mouse is like right there.


Wait.


OK, so see the, see the circle on the top left, blue circle on the top left.


Oh this one.


Yes, right, move your mouse like right above it on the compass circle.


Yeah, from, uh, there.


draw and arc all the way, intersecting the line from there.


Like that


passing the blue circle, passing the blue circle, no other way around, other way around.


Wait, how do I delete that one?


Uh, no, on the above, it says undo. There's an undo bun.


Hopefully that will work. On the um


This one.


yeah.


OK, good. Now.


OK, this, this side


Yes, but it has to pass the blue circle. So, yeah, right above that.


OK, so like this, like that.


OK, uh, no, it's a bit smaller, a bit smaller.


wait


let me undo it


OK.


A bit uh bigger, slightly bigger


bigger


OK


uh slightly bigger, like, slight, yes, right there, right there, that's fine, that's good. Now, right crossing the top left blue circle, now crossing the top left blue circle.


Wait


On the top left, just crossing the blue circle on the top left.


The


wait, wait. What? Like, I, I think it like that too, or?


no, OK, OK. See how the arc you just drew, right?


Oh, wait, I move it.


They, no, no, don't, don't, don't, no, don't do anything. So, OK, you see the blue circle, the blue circle on the top left.


Oh, wait, this one


Yes, draw an arc cross connect the the archi, the big arc you you just drew, and slightly crossed it. Like, yes, from there.


no other way, otherwise.


This, this way or this, this way.


Yeah


things like so connecting like that.


Yes, yes


OK, like that


Yeah, and now do that above, like above, like.


Wait, do I keep doing it, or?


more. No, go, OK, move your mouse up


up.


Yes, the below the stop, stop, stop. Go.


do I do it


OK, no, you're not leave it, leave it, leave it, it's fine. OK.


Now, let me remember. What's the final step? OK, so the, you see the blue circle in the middle.


OK


Drag it, uh, to the arc on the complete bottom. The arc intersecting the line at the complete bottom.


That one.


OK.


Yes, yes, right there.


Uh-huh


Wait


Now, draw last step, draw an arc, crossing, um, draw up OK, draw an arc. Yes, right there. Oh, you had, yes, crossing this, yes, yes, yes.


Like intersecting it.


Yeah.


Like, oh my god, wait


He stopped. 00, more than that, yeah, more than that.


Wait, can I do it?


So I


No, that's fine. You don't need to, you don't need to, uh, yeah.


Yes, mhm


I just continue from here. OK.


Good, stop, stop. OK, stop.


OK


Now, oh, OK, I think we're, OK, now do a line from S


Wait, let me delete what's on my screen. OK, yeah, line from S


do you


Wait, are you using the whiteboard?


No, no, sorry, sorry, sorry, click line. No, I


yeah.


00, wait, wait, blind. OK.


Yeah, because I was drawing something, OK, not nothing. All right, so line on S


click on S, boom.


OK. Oh, wait, like that.


Yes, yes, yes, yes


Like, wait, like that


because it's parapo are clear. Yes, yes, good job.


OK, yeah, hopefully.


Summit, yep


Uh, one more, one more.


With yes. OK, one more.


So what is it, constructing an angle bisector. OK.


OK. So, use a compass to straight at, oh.


OK. Uh, it should be easy. OK, I think I know how to do this. OK, uh, let me just, OK, Draw a, yeah, yeah, draw.


By the way, I have a question. Um, by the way, um, how do you, um, become a, a tutor.


Um, how do you become a tutor? I


Yeah, so


Like, do you need like a degree or do you need to be like a teacher or like


for, for, um, for, for this specific website, you need to pass a test. So let's say, OK, in your case, if you wanted to tutor 6th graders in math, you would need to pass a 10th grade math test and earn a degree for, let's say for geometry, I had to pass the test to become a geometry tutor, but yeah, that's how it works. You have to kind


do they have um like chemistry or like anything related to like science.


Yes, they have biology, chemistry, I think physics too. They have a lot of signs.


cause I'm really good at chemistry and I feel like I would like to tutor either chemistry or English.


Yeah, sure, you could, uh, you need to make a tutoring account. You'd need to pass a test in chemistry, and then


you


Well, do you take it in person or how, like how, how does it work? Do you know?


no, you, you take it, you take it online, but some you take a 10 question test and you need to get an AD.


Well, it's only 10 questions.


Yeah, it's like 10 to 14, something like that. But like, uh, the thing is, don't cheat cause that kind of screws up the people you're tutoring, but yeah, it's only like 10 to 14 questions.


Oh, OK, OK.


Yeah, but I


Yeah, no, cause I was talking to this one girl, like, on the um https://www.example.org, and she told me that um it, it also comes for like, um, volunteer hours or something.


it does, it does. It, you know, for every, like you, they call, if you pass chemistry, you get a degree for chemistry. Uh, every degree you get, you also get you.


Wait, for, for this website or like?


no for this website, for this website. For every like certification you get, they count at one hour volunteering, for some reason. So I have, um, I have like 7 certifications. Most of them are in math. And so since I have 7 certifications. They give me 7 volunteer hours plus the amount I tutor, so yeah.


Yeah


Oh wow. No cause when the girl told me all they give 3 hours. That was really interesting cause I, I really want tutoring, like I want a volunteer hours.


Yeah, OK. Yeah, you could, you could definitely do.


But like how, like, uh, do you know like how to sign up or where to sign up. It's like in the website or is it like here?


yeah, no, I, uh, on Google, I mean, I, I, I think on Google, I searched up UP Chief tutoring account sign up, and then I click the first option. So that's how you do it.


But OK


Oh, OK, OK, thank you.


It's OK


OK. Oh wait, yeah, of course. So, uh, sorry, my, I backtracked. So, OK, for, yeah, for the question, click Compass.


click V


OK.


or I can't, yeah, that's a V. Um just draw one like slightly, like it's in the middle of the line.


Uh, OK, no, you see your cursor, put it in the middle of the line, each line.


Oh, wait


wait.


Like that.


Yeah, a bit, a bit higher, a bit higher.


Yeah, sure, that'll work


OK. Now, draw an arc on each point while where it's intersecting.


Like


huh?


Yes, mhm


And yes, there.


Uh, then you drag the blue circle on the V.


The wait, oh.


wait, this one


Wait.


uh is uh one on the bottom, the one that's V, yeah, and you drag it up, up, up, yes, right there.


OK, so after that,


after that, you draw and yeah, you draw an arc


to the right of the middle of the, OK, she's a blue circle in the middle.


Yeah


Draw an arc to the right, yes, right there.


Yes, yes


OK, good


Oh


More, actually a bit more, like, yes.


Uh-huh, yes, good. OK, that'll work. Now, draw, drag, sorry, drag the middle blue circle.


to the other arc intersecting.


wait, this, this one


Yes


Now, uh, I think all you do, you just draw, OK, see the uh the other blue circles, the, the one that's intersecting an arc.


Don't drag it, don't drag it, don't drag it. Draw an arc intersecting that basically. So draw an arc, yes.


Oh, like, like that.


Mhm.


Like that.


Yeah, like that, and then all you do, I think you do a click array. I I hope it was, yeah, bisector. So yeah, you click uh array from V.


to where the two arcs are intersected.


OK


That's yeah


And that should be it. All right, then.


Oh, thank you. Thank you so much.


Yeah, all right, no problem. So, yeah, for the tutoring though, uh, before you end, for signing up, just one thing to keep in mind, there's other websites other than UP Chief for chemistry, you know, I can see which uh students are available and for which subjects. I don't have a chemistry degree, but


But you also tutor chemistry too?


No, I don't. I don't have a chemistry degree, but it still shows me when somebody needs chemistry, and chemistry, it is, it shows up, but it is kind of rare. But chemistry and bio, they do kind of show up, but yeah, keep that in mind. So for you.


For up for upchi or what other website.


I, I don't, for you, for up to you specifically, there's like occasionally there's chemistry, but it's not too often, so, yeah.


Wait, what's the most common one for UpT? And then like geometry or math.


Wait, what did you say?


was like, um, like what's so often one, the students.


The


I, I, I think the most often one is, it's just called for some reason, it's called Reading, uh, yeah, it's just called reading.


Oh, so it's mostly for like reading or language arts.


Yeah, no, it for UPG for online, it's reading and and 7th to 12th grade, um, 7th to 12th grade math, and some algebra levels, like algebra, 7th to 11th grade math and reading.


Oh, OK, OK.


Wait, by the way, um, can you also tutor, do you know https://www.study.com?


Uh, https://www.study.com. I've heard of it. Yeah, wait, let me, I, uh, there's a lot of websites, yeah, https://www.study.com, yeah, I've I've seen this.


Do I


Can you, can you, um, like sign up for that too? Do you know or this is the only one that you're signed up for.


um, for tutoring, oh, this is all right now, this is the


uh only website I I signed up on because I, I, it's actually, it's very easy, like this, this website is easy to sign up for. It's really easy, but I think in like, I think soon I'm gonna sign up for more extensive websites other than.


Yeah, cause I've been like trying to like find how to sign up for like up to or like more like um volunteer hours or tutoring and stuff like that.


OK, I, I, I can try.


Uh, I will try to find, ah, I, I find, I found the, where you can sign up for UP Chief, or yeah.


Wait, how can you, like, how can you sign up?


OK


What you do, you search up on Google, on, on, I use Google. I searched up, um, up, I searched up UP Chief volunteer as a coach. You search up UP Chief volunteer as a coach, and first options that er


yeah, clicks, OK, you know.


Wait, can you see my screen


Oh yeah, uh, can I, let me see.


Wait, I, I'm gonna share it. Wait, let me, let me share my screen.


Sure.


Can you see my screen?


see


Oh, I see your, yeah, scroll down.


Uh, I, I, yeah, I think it's the second one, volunteer as a tutor.


Start your journey


He clicks start your journey.


I did


Oh, your screen is frozen. Oh wait, is it not doing anything?


No, wait


wait, let me, let me see again.


Yeah, bring it to me here. I don't know why.


Oh, let's


I don't, I don't think I can sign up for it, but cause it keeps bringing me to like,


Wait, where is it bringing you? It doesn't tell me. Where is it bringing you?


oh it's not, oh, it's telling me to like, um, you know where like you want to achieve and they say, oh, hello, Jane, and like,


the subjects I


Oh, you know why? I'm guessing since you, it's trying to auto log in, uh, I get it, because you're a student, it doesn't let you. So I guess you'd have to click the sign up button. So go back to the start your journey instead of clicking that, click sign up.


Oh, OK. Can you see my screen?


Yeah, I still see it, sign up.


Oh, no, it still keeps ringing me here. I don't know why.


Huh. Yes, cause it's trying to automatically log into your student account.


Yeah, uh, it's OK.


Uh, you're doing the same for me, OK, yeah, I for so just you, how you do this, if you don't have Jane's account on a different device, next time, go to a different device and sign a go to a different device where you don't have Jane logged in on, and then you click sign up and then it won't automatically log you in.


Oh, OK, OK. So I have to do it from another device?


Yeah. Yeah, you know why? Because when you click sign up, it's just automatically logging into your student account. If you were to do it on a different device, it doesn't know your, like, it doesn't know you're Jane. It has no idea, so it thinks you're a different tutor. So yeah, go on a different device.


Oh, yeah. I mean, I don't have my phone right now. My mom has it, so


yeah, I mean, I'm gonna try maybe tomorrow.


Oh, OK. All right.


But thank you


Yeah, all right, no problem


Also, I have one question. I'm sorry. Um, do they also have like um volunteer for like, um, like driver's ed or anything like that cause I've been having trouble with that.


Oh, driver's edd for, for UP for for UP Chief specifically?


Um, well, yeah, well, not to be a tutor because I've, I've been having like trouble like.


You mean to, to be tutored, to be tutored.


Yeah


Yeah, to be tutored, yeah, to be tutored.


for, for up she is not, no, no, no, definitely not.


No


Uh


Oh, let me check. No, it's not in my pen. I can, I can sign up. I can train for degrees, but it's no, it's not here, it's in none of the options.


uh, OK, it's OK.


right


Thank you.


Yeah, no problem


All right


Have a nice day


Yeah, you too. Bye


Bye


Hello!


hello!!


I will share my screen and this is homework, not a test


Okay! It seems you have the correct answer what is it that you need help with?


oops i meant to tell you that i alreday did the first one and if you could check it, my bad


Oh sorry! That's okay.


no you're fine, you have nothing to be sorry for


Thank you. For this question since it's asking for non-linear it needs to have a non-straight path. Meaning that it needs to go up and down or down and up. If it were asking for linear it would only go up or down.


So let's start with the first one


oki


it goes down first, then up the next two times


You can also find this by taking two of the points and using slope intercept form to see if the slopes are consistent.


Yes, good point. It seems that all of these follow a rigid line of being positive or negative so there is likely a differentiation between slopes.


Do you remember the formula to find slope?


Great! Now we can apply that to our numbers in answer choice A.


Can you see outside of the screenshare?


could I do the positive ones?


yes


You could but it's best to compare two points so you can see the difference between slopes if there is one. If there is a difference it would mean it's nonlinear


So what would the slope be here?


umm


can you help me?


Sure!


Since there is two negatives we could add them as positives.


what is 1+9


and 4 minus two is 2


and 10/2 would be?


Okay so we have that slope between two points


now we can take another two points and compare them


Yes exactly!


by the first one?


Yes as long as you don't use the same two points it will work.


so what would this be equal to?


And for the other slope we got 5 as well, that means that it can't be A since both the slopes are the same.


Does that concept make sense to you?


yes


It would be similar throughout the rest of the answer choices you would go through and do the same until they have differing slopes which would make it non-linear and you would have your answer.


Do you want to go over the rest or do you think you understand?


go over the rest


Okay! Of course.


Let's move to answer choice B.


What two points do you want to use here?


i already wrote it on the board


Oh sorry. I was zoomed into the wrong portion


Yes great work! Now you can take another two points as long as they are not exactly the same and find the slope for that as well.


not this one either


Good work!


Now we can move to answer choice C.


is that right?


Try double checking your math on it what would be 6/2?


Exactly so it should be 3


Great now you can grab another two points and do the same thing


Okay and since the slopes are different what would that mean for the question?


this is my answer


Yes good work.


Did doing that make sense?


yes


but this one i am stuck on just by reading it


Okay so do you remember the formula for a linear function?


no


Okay it is y=mx + b


where m is the slope


and b is the y intercept


All linear functions


Are capable of being arranged into this formula


Your answer should be whichever one is NOT capable of being arranged into this formula.


Does that make sense so far?


right, it does


Great So we can start with answer choice A and attempt to get it into y=mx + b


What should we do first?


isolate the y


now we have to determine if this works as a line


does this follow the format of y = mx + b?


yes?....


Yes great! Glad that you noticed that, I know that it can be a little confusing at times but I want you to understand that with an equation like this the slope would actually be 0


I could rewrite it like this if it makes more sense


oh okki


So now that we know that A is linear we can move to answer choice B.


oki


how would we start?


isolating just like last time


Now we have to question does this follow linear solution format


What do you think?


it is also linear


Great!


Now we can move on to answer choice C.


now we isolate the y again


The y is already isolated here, now this is just the concept of truly understanding the linear function.


What do you think? Linear or non-linear?


linear


It would actually be non-linear.


ohh


With the equation y=mx + b


you cannot have an exponent associated with your x


the x should not be changed at all realistically


Sorry, have to tend to something I'll be right back.


Hello I am back now


hello


i went to the next one


Okay that's fine! Seems to be a similar question so we will handle it in a similar fashion


Let's start with answer choice A.


this one is nonlinear


Great! How are you able to tell?


it has a exponet on the x


Good noticing!


so is b, because we look for isolating the y, not the x


Awesome great work. Yes the answer is B as it's the only answer without an exponent on the x.


This one is purely visual as it does not give us points to use.


Based off of what you can see what do you think the one that increased the slowest would be?


Keep in mind that the flatter they look the slower they increased


e


then b


Yes great.


Great work!


Thank you


YES!!!!!


Good job!


I appreciate your help


Of course no problem glad you were able to understand more.


yep. I f do not talk to you again soon, then have a great new year and merry christmas


if if


You as well, wish you the best. Bye bye and good luck!


you too!


hello!


Hi Emily.


How can I help.


so i need help with inequalities, mostly wor problems


word*


So do you mean these <>


yes


So think of these symbols as mouthed pacman.


This is one example


7 would be eaten because it is bigger


So 7>


Apart from 6


You can see it this way.


And if it is underlined


Remember that is less than more than or equal


sorry i am on >= and <=


Right


It means either more than or equal to


So do you have ques about those?


These are straightforward


i do


i know how to o them its just the wor problems


Hey Maria! How are you?


Hello, can you hear me?


Hello


Hey, yes I can


Hello, I need help with some problems that my teacher provided prior to our test that will be taking place tomorrow and the teacher said that the questions on these then the sheet that he provided will be very similar to the ones on our test. So I need help understanding and deepening my knowledge on this topics and different scenarios and how different equations would apply to these. So I can do well on my test. Would you please be able to explain this throughout your mic because I tend to understand it better. Thank you so much.


Sure yeah we can do that


Great.


just to clarify, have you already solved these or you want to solve them now with my help if needed?


No, I haven't solved any of the problems. I don't know how to do them and I need help learning how to do them.


I'm actually can we start from problem 5 because I already did number, I mean, can we start from number 6.


Ok got it, no worries


Yeah we can start from 6


so first, it's a good idea to define the variables here


Would you be able to use your mic throughout the the explanation cause I tend to understand a better daily.


Yeah one second


Hey, can you hear me?


Yeah, I can hear you


OK, awesome. Um, so,


for the, for problem 6.


uh, first, it's a good idea, like the way you solve it is to


uh define the variables, so like you determine what variable is like your cost of slice of pizza, which variables like uh cost of one drink. That's a good way to start.


OK


So you can have like uh P, variable P equal to like the cost of one slice of pizza. And then like D is the cost of one drink. And then you can use that to like make an equation.


Does that make kind of make sense


So like that


Yeah, so, so you got the equations correctly.


Um, now, what do, what do you think the next step is here?


Um, do we solve them?


Yeah.


And what, do you know which method you're gonna use for solving it?


No, I'm not sure


Mm.


OK, no worries


Um


do you have an idea? Maybe you wanna do like uh substitution or like elimination.


Do you, um,


illumination.


Yeah, elimination is the right choice.


OK


OK, so we can do that.


Yeah


Feel free to write it down and we'll see.


I actually went there that


I'm sorry, could you just write that because I'm not really sure how I would do that.


Yeah, so you'd want, uh, one of your like variables to be uh the same.


together with the term. So you want both of these to become like uh 12%. That's how like elimination works. You want them to be the same and then you can like kind of cross them out. So basically, the way you would do it is like


uh you'd multiply this first equation by 3.


and you'd multiply the second one by 2.


and then that way 3 times 4p is going to be 12p and then 2 times 6p is gonna be also 12p. and then you can kind of like cancel them out. And you would multiply 3 by 60 and 33 as well and do the same for the second equation. Does that make sense?


Yeah, it's kind of making sense.


OK. Well, that's good.


That would be nice


Do you think you'll be able to uh write it down here, what you would get.


bro.


Um, yeah, I'm gonna try it on my paper first and then I'll write the process down. Would that be OK?


Yeah.


Or you, or you can just tell me what you wrote down, uh, we can work that way. If you don't wanna like copy it to the whiteboard.


Oh yeah, OK, that would be good.


OK, I feel like I'm doing something wrong because I multiplied it by a ne so since we want to eliminate the pee. I multiply it by negative to for the bottom equation to get negative 12 of P so it would cancel each other out and then I for the other ones I got um 12. I got 8 Y equals -74 and then for the top equation, I got 18 equals 9099. And when um


I, I subtracted the negative 88Y from 18Y I received a 10 y which equals to 25 after subtracting the 74 from 99 and the 10 and 25 wouldn't go together, so I feel like I'm doing something wrong because for these kinds of problems, I'm pretty sure you're not meant to get a decimal.


Oh, I think you actually got it right here because um


it was supposed to be 10 equals 25.


So I think you got that right


So what about the decimal?


Yeah, so you have 10 equals 25.


and you just want to like have the DB alone. So what you would do is just like divide both sides by 10 to get rid of that 10 on the left side.


But instead of a decimal, you can just write it as a fraction. Typically, that's what they want you to do in those tests.


Mm


Yeah, OK. Since we're talking about money so it can be 2.5, you're right.


Yeah, I mean, I mean, it is 2.5 just most of the time they want you to just like simplify the fraction, not write as, as a decimal. So.


Mm.


what, what, how would you simplify a 25 or 10? What, what would you get?


Let me just.


you would get 2 and then 1 over 2.


Mm, not exactly 1 or 2 because, uh, what are you gonna divide both sides by.


Yeah, by 5. So 25 divided above 5, what would that be?


Yeah, so, uh, it will be 5/2, no, 1/2.


Uh-huh, OK


OK.


1/2. Let me just write it down.


So that would be your D


um


and now, how do you think we get the P.


Um, do we, um, put the D


for the place of the pea. Oh wait, no, wait, wait, sorry, let me just do my calculations.


Yeah, I mean, you're right, actually, you just uh plug in the D into any of these equations and then uh you can solve for P.


OK, let me just see


Sure


Sorry, could you guide me through this one cause I'm confused.


Yeah, no worries. So, uh, like I said, so you, you, you determined that D is equal to 1/2, right?


Right.


Yeah, so


now you, now that you know what D is equal to, you can just plug it into uh whichever equation, oh, sorry, uh whichever equation, and then, uh, the only unknown variable that you have is P. So you can just solve for P and you'll get the answer.


Does that make sense, kind of


If not, then uh I can explain again. No worries.


Yeah, I'm not getting it. Sorry. Could you


You want me to, to explain again


Yeah, sorry. I thought my mic was on and I was sucking. Yeah, I'm confused. I'm not getting it.


OK. So


you know, uh, the value of D right now, you know, it's 1/2. And then you have your two equations that are uh 4P plus 6D equals 33, and then you have the 6P plus uh 4D equals 37. So, you can just plug it, now that you know the D, you can just plug it in into any of these equations.


And then uh you just have to solve for P, and that's how you'd find out the value for P.


Then you have two of your uh variables.


Oh


which will help you get to the answer.


OK, I'm gonna try doing that and see what I get and then


you can like see if I'm right or wrong.


Yeah, sure. That sounds good.


But you don't necessarily uh have to use like the version that you made after multiplying. You can just use like the original one. That way you don't like work with bigger numbers if that makes sense.


Yeah, OK


OK, let me know once you're done.


I got 7.5.


OK, so I don't think it's gonna be um 7.5, but can you walk me through, uh, well, uh, actually 7.5 for what? Is that what you got for P?


Yeah, I got


I got 4 P equal I got 4. Yeah, for P, I got 7.5 because what I


so I um did what you said. I put the 1/2 in.


Gosh, I put it um instead of the D and then I did the thing on my calculator, so I got 4 X and then 6 times 1/2, I got a 3 and then so 4 x + 3 equals 33 and subtracted the three on both sides which give me 4 x equals 30 and then when I divide it by 4 on both sides it it gave me 7.5.


Mm, OK


Um


but you said you did 6 times, 1 or 2, OK.


Uh, wait one sec, let me double check.


something here


Oh, I, I'm sorry. I, I wrote it as one or two, but it's uh 5 or 2. We determined that we, my bad, um, so you're gonna have to do it again, unfortunately.


That was my fault. Sorry about that.


OK, I'll just redo it.


Yeah.


OK, so this time for the final answer I got um a 4.5.


Yeah, that, that would be correct.


Or you can also uh write it down as 9/2 if you just want like a fraction.


OK.


So now that you know, uh, the values for D, and you know the value for P, uh, what do you think the next step here is?


I don't know. I.


No worries. So, you know that pes like the price of uh one slice of pizza. So, and it has, it's asking you the price of 3 slices of pizza. So what do you think you can do here?


to


Um, doing we multiply by 3?


Yeah, you just multiply by 3 and then multiply the D by 5.


And then you get like the total cost.


Uh, OK, I'm gonna do that real quick.


Of course


OK, so for a while, I mean for


for, um, D, I got 3 equals 7.5, and then for pizzas, I got equals 13.5.


Mhm. OK. So


uh, for D, you said you got uh 3


7.5 forbid you. So for the pizzas, it would be 13.5, so, uh, good job on that, but I think you need to double check, um, what you got out for the drinks. Can, can you tell me what, uh, we did for the drinks.


Um for the drinks, I got 7.5.


Mhm. So that's, so it doesn't seem to be exactly right. What did you multiply, uh, to get, to get 7.5.


I multiplied 2.5 x 3.


So it wouldn't be x 3 because for the drinks, uh, it's, it wants you to do 5 drinks here.


not 3


So you got the pizzas, uh, correct.


on tricks.


000, OK, OK, OK, OK, OK.


Yup.


So


OK, I got it.


Yeah, that, that's uh correct value.


Um, so now, uh, I'm, I guess you need to just add them to get the final cost.


What would that mean


Yup, that's right


It's.


So yeah, the uh final answer would be 26, so good job on that.


OK. OK, I got that. Um, we can go to question 7.


Yeah, sure. Um, do you think you know what the first step here is?


The first step would be um


let me just read it first


Oh, elimination method, I think, yeah, 00, are we him? Yeah.


Mm, so kind of, so usually you wants to have the equation in a form of like Y equals mx + B.


uh, and, and you can notice here that


um


you have two next to the Y, and you can actually divide all these terms by 2.


and uh then you can get an equation.


And also you'd have to move the ax to the other side of the equal sign, and that's kind of how you can uh solve it or like simplify it. Maybe that's the correct uh term.


Sorry, why are we dividing it by 2?


Yeah, we can, we can divide it by 2. It's just like a shortcut because you see that the 2 is next to the Y.


Mhm


Um, so


uh, basically, it's gonna be the same exact equation if you divide by the two, but that way if you do that, um, then you just have that you you can just have the equation in the form of like Y equals MX + B.


So if on the test, I get like another problem, I can just divide it by 2.


Yeah, as, I mean, uh, not always by 2. It's because here the coefficient of the wise too because it's too wide here and all the terms divide by 2. So yeah, you can do that if uh


if that works for a particular scenario.


OK. OK, so how would we solve it in another way if we're not dividing it by 2.


Uh, if you're not dividing my two, you can just um


move the 4 X to the other side, so then you have like two Y equals -4 x + 10.


And then I mean, then you would still have to divide by 2 because you want to isolate the Y, so, uh, either way, you're gonna have to divide by 2 because that's the coefficient.


of uh Y


and you want to isolate the why


So you want to leave it alone, basically.


OK, so I did that and I got, so I got Y equals -2 x + 5, and then under it I got 2y equals 4x plus. So do we um add the wise or do we like leave it alone?


OK, you got, you said you go for the second one, to Y equals equals what?


-4 x + 10.


Yeah, that's correct. So now, uh, now that you have that form, you want to go from 2Y to just uh Y So that means you're still going to have to divide both sides by two.


OK


because you want the equation to be in the form of just like y equals to something.


OK, OK.


and have like go fishing next to it.


So


So I got um Y equals -2 x + 5.


Yeah, that's the correct answer. So as you can see, like either way you'd have to divide by 2 just whichever one you want to do first. Uh, but if you can notice something odd here is that it's, you got the same exact equation as the first one.


Um


you know, uh, what that means.


that means I might


Well, yeah, uh, yeah, but also, um, since, since you got the second equation the same as the first one.


Uh, it means that this uh system is gonna have infinitely many solutions because, uh, two equations that are the same.


because they have the same slope, same wide intercepts, so just gonna be like the same line.


OK, OK, OK.


Yeah.


You wanna go to uh


#8 now


Yeah, yeah, yeah


OK.


Let me read it first now


So I read the question, so point Q represents that she has to pay for it if she goes there for 35 days, right?


Uh, yes, that's uh correct.


OK, so was that all for this question, right?


Uh hm. Wait, let me double check actually, one second.


OK


Oh.


Yeah, so, uh, the way it's worded here is, um, kind of odd, but uh yeah, it does look like the, like you said


um, that she has to pay $175 if she goes to the gym 35 times.


uh, under the


$5 per month plan of under 5 for the $5 per visit plan. I mean,


with no annual fee


So


So that's it for that problem then?


Yeah, it's gonna all that they


did such a long problem description for a relatively simple question, but that seems to be it, I think.


OK, so we can move on to number 9.


Yeah.


OK, so I read the question and we can start working on it.


OK. So, um, what do you think the first step can be here?


Um, the first step is to identify the problems.


Mhm


Yeah, well, um


I guess you identify


uh and write down the equations for Maya and Ethan the linear equations


Could you go ahead and do that


sorry would you excuse me for a few minutes there is some disturbance


yeah, no worries


let me know when you are back


OK, sorry about that. Um,


we can continue.


All right, yeah. So, um, could you please write the equations for my and for Ethan.


OK, so let's close, but it, it would not be


um


it would not be


12 X


and it wouldn't be 4 X.


because those are fixed costs.


So


so they would just be 12 and 4?


Yeah.


And uh that's because you, you're just calculating the monthly cost. So, uh, it's always gonna be for one month. So there's nothing that you're gonna have to plug in here if uh that makes sense. If it was yearly, then, uh, yeah, but you just have to plug in for this one, just the number of devices, not the number of ones.


So that's why, uh, there's no variable there.


OK


So how would we solve this?


Yeah, so, uh, as you can see here, it's saying that Maya streamed on 4 devices.


So, uh, now that we know she used 4 devices. Do you think there is something that we can do with this number.


Can we multiply it? Like, can we put


can we put the 4 like plug it in in the Y part.


Yeah, but actually, I, I'd suggest this replacing the Y with the X here. That way it's like simpler. And then this would be like Y equals 2.


Uh


but I mean, in this particular scenario, it doesn't really matter, but yeah, you would plug in the 4 into here.


and then you would uh get the


number


for Maya


OK, I'm gonna do that.


Oh, what I mean is just you can do like, uh, just the next year. So it'd be like here 4 + 7X for example.


And here will be 12+, uh.


So it'll be like this


and then you can label it here like this is for my uh oh well.


I don't know how to mark it, but like that, I guess.


Ethan


or something


Sorry, I'm just so confused cause I don't know what we're doing at this point.


Yeah, no, no worries, no worries at all. So,


uh, for this, you don't really need the Y equals urge, it's kind of just like there as a reminder.


But, um, pretty much, you just plug in the 4.


uh into for your ex, basically, and that would give you uh the cost for Maya that she pays uh monthly per 4 devices.


Does that make sense


So you just have 12 + 5 times 4.


Then you get like a number here.


OK, yeah, that makes sense.


Awesome. So you got that right. That would be 32.


Um


and now


you can, uh, set this equation for Ethan, uh, 2:32 as well.


okay i got 30?


So it, it would not be 30.


um, because here you would just set


the basically 32.


equal to this equation.


So here you're just right, 32.


Uh, and that's because it is asking you, it's saying last month Maya streamed on 4 devices. So now you got the amount that she paid, which is $32.


And then it's asking you what is the number of streaming devices that Ethan could stream, uh, for their monthly cost to be the same.


So what that would mean is, uh, you take the 32, and then you set it equal to Chloe's equation, and that would allow you to get the X, which would be the number of streaming devices that he could use, uh, for that same amount of money, if that makes sense.


And then here you would sold for X just like uh the regular equations.


Yeah, that's right


Yup. That's exactly what we're gonna do.


Awesome. So, uh, yeah, the ax would be equals 4. that's the correct answer. So, um, that would be the number of streaming devices that Ethan could, um, stream


for their costs to be the same


OK


OK, I'm gonna upload my next image.


Sure


I hope that um clear up some things up for you.


practice.


Oh yeah, I'm, I'm getting it.


That's good


OK, can you see the image


Yeah, you know


Thanks for rotating it.


Mhm


So for the first one, it, it doesn't have any, any shadings, right?


All right, here it's kind of dark, like right over here.


Yeah, I kinda saw it, but it's not super clear in the picture.


Yeah, that would be helpful


Yeah.


So I'll just shade it a little bit for myself because I don't get confused.


Yeah


OK, so we know that that area is shaded.


Um.


so what do, what do you think the first step would be here for this one.


OK, I'm gonna read this question.


Sure.


So we will find like two points on this.


Uh, so not exactly two points, but you're on the right track. We'd have to find that to.


ways.


and the equations for them


00, OK.


and that will help us, um,


Smoking up


figure out the system. Yup, the intercept is the right, uh.


way to start it


You can start uh identifying them.


OK


and maybe write it, write it down if that's what you want.


Hi.


Yeah.


So the Y intercept is 4, and then the slope intercept is


yeah, you did the rise overrun.


Mhm


OK, good job. Yeah. So, um


but you wouldn't call it slope intercept. It would just be slope.


slow


Uh, slope intercept is what you call the form of like Y equals x + b.


Oh, OK


Uh, but yeah, OK, you got that right. Now, so now you can use that to write the equation, then you'd already have the equation for the first line.


But you also need to figure out what the sign is.


for your inequality.


Is it um


um, more or more than, right?


Yeah, it's gonna be more because uh this is above your line. And then this is below your line. So you know it's more than because uh the shaded areas above this line.


So yeah, that's correct


OK.


So like this kind of.


Yeah.


OK


But um


uh, keep in mind you still need the X here.


Oh


because you want it and uh MX + B form. Yeah.


And then, uh, 3/1, uh, you can just simplify it to 3.


So it's divided by 1, it's just uh gonna give you the same number.


Hey.


If you want, I can move it for you.


Should be fine


OK. Uh, so that would be your


your first equation.


a first inequality, sorry


And then


I do the second one.


The same principle


OK, so for the second equation I got Y is less than or equal to 1/2 x + 8.


Mm, OK, yeah, I think that's good. But are you sure uh that it's 8?


here?


Let's look at the wine Intercept.


Is it not 8?


You know, because I think, I think it's 7 because 8 is right here, 6 is right here, and this is in between.


Oh yeah, OK, yeah.


So I think it would be a 7


I think because you had that line and it, it might have confused you a little bit.


OK, so just


It it confused me a bit as well, so it's OK.


OK, yeah, it's good if there's 7.


OK


Awesome. So those would be your, uh, two inequalities. And then


So


the last step that you can do is like format them.


uh, like this.


and just move this one


away


How can I do it?


So do we need to solve this or like we we were just supposed to like find equations, right?


quickly.


Yeah, we just find the system, um, but the last thing you can do is um to make sure that it's correct. It's just to plug in a number, uh, like anything inside the shaded region and test whether your equation is like true or not.


So you can plug in something easy like 00, and then see if it's uh false or if it's true.


OK, since, OK. OK, we can move on to the next problem.


Sure


Um


we're following


OK, so,


OK, let me just try it in my mind because it


sick.


OK, so I received um


6, I mean,


yeah, so I received why is more than or equal to 2 to


to 2 plus um.


one


over 2 eggs.


Uh, why is more than or equal to


2 + 1/2 X.


That's what you got


Oh, no, not more than or equality. I just got is.


and why is


yeah, why is more than than 2


and then plus 1/2 X.


Mhm, OK. So, um, you're correct about the


uh 2


but double check, so the B is correct, but double check the sign and then double check your


uh slope


Is the sign? How is like, how like, wait, what about for the design over here, it doesn't have like an


a underlying under.


Yeah, the underline just means that um


I, uh, it just means that, uh, whether something is equal to or not, so it's either like the solid line or the dashed line, so, um, the underline just basically means it's gonna be equal to or not. But what I meant by checking the sign is, it's not gonna be uh why is more than, uh, and that's because, uh, why, uh, because of the less than is facing the Y basically.


So it's gonna be why is less than, not wise is more than.


Does that make sense


So could you explain to me how you did the problem?


Yeah, sure. So


um, you would


divide both sides by 6.


and so


you would get


here you would get 2 +


over 6.


X


Is that what you got or you got something else?


Like in your intermediate stuff.


Yeah, cause they did a whole another different way.


That's why I mixed them up. So let me just copy this.


No worries


Yeah, so typically when solving this, your main goal is usually just like isolating the Y. So if you have something like X uh sorry, like 6 Y.


You want it to just be Y and you, you, you do anything in your power to like get rid of anything else that's like next to the Y and that's how you sold those types of problems, usually.


OK


Yeah.


So if you keep this in mind for like the future.


uh it'll be like super helpful for you.


just like a tip


OK, I'll keep that one in mind.


OK, we can move on to problem number 12.


Way, but for this one, you're not uh fully done yet.


00, my back


Because uh you still need to graph it and also you can um simplify the 9/6.


So 90 6.


And also you can rewrite it where like Y is on the left side.


So it's uh easier.


So that's in, and that's why it's in the traditional like sult interce form.


OK.


So what I think, uh, no over sexual simplified too.


Can it simplify one?


Uh, what do you mean simplified to one?


Cause


9 can be divided by 39 divided by 3 would be


Yup.


and then


and then we got 6, and then we can multiply 6 by 2, and then if we multiply, and if we divide, I mean, if we divide 6 by 2, we get 3 and then 3/3 is 1.


Yeah, but, uh, you wouldn't divide 6 by 2, you divide 6 by 3.


Oh


Because, uh, because you divided the 9 by 3, so you divide the 6 by 3 as well.


Mm, OK.


So 2


I think while you're confused is because um 6 divided by 3 is 2, so maybe that's why you got, uh.


thrown off there but


Oh, OK. So 3/2?


like that


Yeah, it would be 3/2


X


Uh


I


OK, so like that.


Yeah, and then which area would you be shading?


The area that I will be shading


Over here?


No, it would, it would not be over there because you need to look at where uh the sign is pointing.


Morning


It is pointing more than to this portion of the equation, but you need to look at uh the, how it looks like from the Y side.


Oh, so last time like you.


You see that Y is less than.


Yup, yeah, it would be like that


So if you wanted to, you could just like rewrite it as uh


this so that you wouldn't get confused for like next time.


And uh original like uh sloping yourself for.


Cause you look at where like the beak is pointing to.


the greater or less sign.


OK


And yeah it would be the dash line. So good job on that.


OK, sir, would you give me


some water? I'll be right back.


Sure.


OK, sorry about that. We can continue.


Yeah, OK. Sounds good. Um, so here we need to graft the system of equations so


uh


you can go ahead


What do you think the first step here is


Just uh for this one, to get the, sorry, to get um


so we would


subtract eggs to get over here, I think.


Mhm. Yeah, that's right


Yeah, so that's uh


correct. Now I just need to isolate the Y.


Yeah, that's right


Um, you can also ride the 2.5 as uh 5 or 2.


But yeah, whichever uh works.


So now it's time to plot


We'll actually do the second one as well.


Uh, and then you can plot it.


You can make it a bit smaller so you got more space.


something like that


OK


Um


why it's more than


Mhm. So it would not be, uh, exactly that.


Uh, and I think in this case, it's gonna be simpler to just like, uh, subtract the two eggs from this side, and that would be it.


Um.


so, uh, from both sides.


to Y like that.


And then you would just have the Y and the left and


the rest would be on the right


Oh, OK, cool


So,


God.


I


Hm.


Yeah, so it will be uh wise more than


-2 x + 3.


So I could start uh graphing it now.


Is that the first line that you graphing right now?


Sorry if my lines were not straight, but yeah, that was supposed to be the first line going going through these points.


Mhm. But I think you


I think you got the wine Intercept, not graphed correctly here, though.


Oh


Because, uh, double check it's


But your slope does look correct. It's just that you have to shift the line.


OK. How do I


like that?


Oh, I don't think I see it yet.


Um


Uh


It still looks like, uh, that it is where it was before for me.


Like, I'm, I'm talking about this slide that you have here.


Oh, I'm, I'm trying to like erase this line, but then if I erase it, it's gonna erase the whole thing.


Oh, OK. Yeah, no worries. I mean, there's a tool here. I don't know if you have it or not. Uh, it's like the 3rd 1 from the left is like a square and um mouse.


OK.


and you can use that to like pick it up and move it. But let me know where you wanna move it to, and I can do it for you.


OK, so


OK, it looks like you already got rid of it. No worries.


Oh no, it's.


OK, almost there. So you got the Y intercept, right? Um, but the second dot would have to be a little bit more to the right um


you're going one up and then 2 to the right, but you went a one up and one to the right.


OK


Do you need to, need to move this second dot a bit, uh, to the right, so that it's on X equals 2.


So be somewhere around here.


I know


I believe.


long.


have people


is pretty


wrong about you


and I have


living room area. It's a studio apartment.


OK, yeah, it does look uh correct.


Now you can graft the second equation.


So something like this.


Uh, one sec, I'm checking. OK. Yeah, that, that is, uh, that looks correct.


You have the slope and uh well, the Y intercept in the slope correct, so that's good.


Uh, so now all you have to do is just to shade uh the right area, so.


But also think whether this line um is gonna be solid or dashed.


Yup.


this one


Well, the other one is not gonna be dashed because uh this one has the equal.


uh or equal to sine as the underline.


So, uh, it's only the 2nd 1 that's gonna be uh the dashed, yeah.


And then the first song is going to be solid.


So this part is gonna be like the


point like where they both crossover shades.


withdraw a little bit


later.


And so, um, not exactly because I think you might have


I think you might have confused them.


Wait, actually, 11 sec.


Yeah because


this is your 2nd equation.


and then


this is your first.


So


uh


the first equation, what sign does it have?


It has a, it has a, um, more than or equal to?


Yeah, and since this is the first equation.


uh, it means it can only be above. It can only be this one, or it can be this area. So everything above, so.


everything here. And now we need to check for the 2nd equation. Uh, what sign does it have?


Um, more than.


Yeah, it has the more then, so, uh, think which er it's gonna be. It's either this one or this one.


More area, uh sorry, more than, doesn't mean it's above the line or below the line?


Above the line


Yeah, above the line. So now think which area for the second equation is above the line. It's both above the first line and above the second line. Which one would it be?


Above the first line.


Oh


Yeah, but, uh, figure out which, which of these areas is going to be the one that's above both of them.


OK, so,


OK, it's just a little bit messy. I'm just gonna try to clean it out.


Yeah, I can.


try to help you, maybe


OK.


Mhm.


right


Yeah, that was closed, but remember, yeah, yeah, that's correct.


CA it's gonna be above this line, above this line.


Because if you had it like this, it would only be above the first line but not above the second line. So yeah, you got that right.


You'll be that region


So yeah, I think you are done with this page.


Yup, OK. I still got a


few more sections.


I don't know if you would have time because I'm pretty sure my teacher said there's gonna be like let me check how much more problems I have.


OK, so I have 16 more problems.


Hm.


I don't know if you have time or not.


Yeah I'm not sure if I'm gonna be able to do all of them. Um, I'm probably gonna, I have like around 30 more minutes.


and then you might have to try and connect with somebody else after that.


OK, yeah.


Yeah, that works right


Mm.


Great


It's like a


that


before we graduate you to a remov


partial denture which is like the one with metal.


So OK, so we can start with question one to an IPD.


So this is my first


All right, yeah


week ever


not watch it


Let's read it


Be good contains


pain.


OK, so this looks like we just need to make, well, you just need to um


right uh linear equation for this, so.


um


if you want, you can go ahead and let me know your thoughts.


OK, I'm gonna attempt the problem.


Good morning


So.


in the morning I look for a state station so


I'm comfortable I worried about how.


I


a.


the


finding


you


line, so


the area we see that line


is where


um how he was going. So how


would be.


we need to.


so we're gonna


do


uh pre binding and I'll


also take


I feel like


so


or.


Is that correct?


4 months


OK


OK.


Right.


yeah


that.


So, um, that is super close, but remember that you need the X.


since it's a linear equation, you need to


variable.


So think where you need to play sax. Yup, that's right.


Well, actually, in this case, instead of X, I think they want you to use an H.


Um, so


no


you can write down


I


watch TV


And then here instead of the 4,


it's just gonna be H because you're writing the FOH function.


all.


OK.


hm.


and and uh


So


know


because you're not plugging for, you're just writing the function for H and then the person can uh plug in whatever number they want.


OK, so like this.


The OF of H equals to 4 minus 0.5H.


So you're done with the first part now.


Mhm


Uh, now, I just find them out after 2 hours.


Mm


So, uh here it would not be


uh this, it would be something else.


So, how do we get the


do we multiply something by 2 or


Uh, not multiply because you already figured out the function FOH equals 4 minus 0.5H. So that means you can plug in whatever number of hours that you want.


and you would get the


uh amount of paint left over. So this is asking you to uh find the amount of paint after 2 hours, so you would just plug in the 2 and you would calculate f of 2.


Yeah, so it would be uh 3 L, that would be your answer. But I think one small suggestion I'll make is um instead of formatting it like this with like parentheses, um, cause it looks a bit uh confusing here. Uh, I, I would just write it down as just F of


Sorry something just came up! I might need to leave early today, but thank you so much for your help today! Have a good night/day!


equals


let me just write your original equation 4 minus


and then it would be


times 2.


Oh, it, it doesn't fit, but I think you get my point.


Uh, it will be times


2 here.


I just need to move it


Oh


OK


Yeah, I think, I think you know what I mean. So just put like uh times 2, but that would be.


uh up here because I'm running out of space.


So I'll write it in the chat


hello


Hello! How can I help?


will you help me with this


Sure!


This requires implicit differentiation


ohh what i did so far is find dy/dx


what did you get ?


e^x+y -1/(1-e^x+y)


yaa so i have a final soon for calc bc (basically all ab review) for frqs


I see


idk how to study for it i feel lost


Its all good


You got the right expression


What did you get when you plugged in the point 1/2 , 1/2


oh so i didnt know what to do after i did that lol


all good lol


you just plug it in?


the point is just the x, y coords


yes!


yay i got that too!!!


its just i didnt really know how to get about this problem


my foundation is not very good...


For every problem


If it says dy/dx or f'(x), you wont be far off the solution if you just take a derivative if you go from there


dy/dx will need a point because your statement will likely have x and y in it


ohhh okay


f'(x) or dy/dx in terms of x will only need x


As far as I'm aware, Taking Derivatives, Basic Limits, Second Derivatives, Optimization, Abs Min and Absolute Maximum, Local Min and Local Maximum will be the majority of the test for AB especially in your case if you haven't learned integrals


yet


i seeeee


can we work on this one now


I can give some tricky problems from my tests years ago if you like!


sure


sure! but i want to work on porblems from my study guide first


Do you want to do it here and me check it or do you want me to continue doing it


got it!


uhhh can you work on it and explain each step?


sure!


ohhh that was easy


yep!


uhhh i want to work on 3 more and then can we do an actual ap frq?


hate this problem lol


lollll yeah i dont get this one


will you explain what you did


i dont get what the problem is asking


ofc


1 sec


trying to skip out on algebra here I apologize


ahh i made a mistake sorry


ohhh its okay


I kind of skipped out on the algebra part bc I keep making mistakes somewhere but Ill restart explaining each step


Based on the question, we have acceleration and position change


yes


we know that the integral of v = x so int of v from 2 to 6 should equal x(6) - x(2) based on the fundamental theorem of calculus


If I find v by integrating a, I am not given an initial velocity for the plus C


regardless, I can still integrate it because I am given the evaluated integral to equal 10


I can use that to find C


In the exam, this is too lengthy for me so I'd rather look at the options


Based on the options its either A or B, for the v(t)


ohhhh


because they only differ by the initial velocity


this is a tricky one


yeah


What i'd do is right here, bc im between 2 options


I would integrate A)


from 2 to 6


if that gives me 10


its A


if not it has to be B


ohhh so its like testing


yup


you can integrate with the plus C and FIND c


to get 7/6


but its too long and prone to mistakes


wait what do you mean by that


because we don't know the initial velocity we cant just plug in C


but we can still integrate V(t) with C in it to see what value of C would give 10


Ill show the other way as well 1 sec


lOl i think the other way of testing is easier


Yeah


but this method is ncie to see


There


c = 7/6


Oh


thank you


No problem!


you do everything so cleanly!!


Appreciate it!


wait can you just sum up how to approach this problem>


Sure!


i thin kwhat i have the trouble most is jus reading what the probelm wants


We are given a(t) and x(6) - x(2)


btw i have been copying down things


Great! its good to refer to


based on the question we need to find v(t)


its easy to find v(t) if we are given an initial condition, because we can use it to find C


mmmhm


what does initial condition mean?


in this case however, we aren't given a simple v(1) = 0 or a point for v


initial condition is any point for v(t)


we can use it to solve for C


like if v(1)) = 0, C = 0


if they said v(1) = 1, then we would do 1 = 1^2 - 4(1) + C


ohhhh


C = 4


i see isee


without that we can't say what C can be


Got it


in this case we are given the integral of v(t) from 2 to 6 through x(6) - x(2)


recognizing this is the most important parat


part*


yaeahhh


based on integrating with the plus C alone, you should be eliminating C D and E


how did you know?


Because the integral we found WITH the C was x^2 - 4t + C


C can be anything


but the other terms have to be exact


for A. C would be 0, for B. C would be 7/6


For everything else, you NEED to have a t^2 -4t the same


i meant t^2 not x^2 my apologies


ohhhhh


and so basically b already gives it away


b and a


yeah


you still dont know for sure between them unless you find plus C OR you do the integral assuming C = 0 for A


and see if that equals 10


if it does then its A, if not its B


okay so you do the integral of a


and make it equal to 10-


can you do the integral of b and it would equal 10? then


absolutely!


wanna try it out here?


i can try doing it


Go for it!


wait is that right


close


what is the derivative of t^2/4


errrrr


its just slight algebra mistakes


if it makes it easier, for such integral evaluation things


do each term separately


hmmm where did i do it wrong


like instead of plugging in 6 everywhere and then subtracting the 2 plugged in everywhere


lol....


did you multiply the minus sign??


oops


yeah


and 7/6 should be +


simplify as you go!


Aha!


thank you!


can we work on these two


yes!


same process as eariler!


Do you know how to bound integrals?


I personally hate +c if you want me to do it that way I will if not Ill bound it so we don't have to deal with it


LOL whatever method is easiest\


Indeed!


yaaa i was confused why that is a 1


Dumb mistake :(


Ill write it out a little bit better sorry


There are other ways to do this, but in my opinion bounding just makes it easier


if you didn't bound you can do the same thing except put + C, plug in 1 for x and e for y


and find C


and then plug in 2 for x to solve y(2)


or just bound it here to find y(2) directly


ahhhh okay


i see i see


will you explain each step and what the probelm is asking for


sure!


the problem gave a random function y's derivative in form of dy/dx


we need to find y(2) given y(1) =  e


y' = dy/dx so asking anything about y means we have to 'integrate'


based on the point y(1) = e, x = 1 and y = e


we can make that the lower bound for both integrals


upper bound will be what we NEED to find in this case y(2)


ooooh okay


so integrate and then plug in


before that you can multiply dx to the other side and put all x terms on one side and y terms on the other


yep!


at the end just exponentiate to get rid of ln


let me know when I should start with 5


yes! sorry im reviewing it rn


no worries go ahead take your time


how did you know to pick the boundfs?


If they EVER give you an initial conditions I always make bounds


It doesn't matter if they ask you find y(2) or y(x) even


+c is generally more annoying


for instance if the question asked you to find y or y(x)


instead of plugging in the top bound as y(2) just plug in y


ahhh okay how did you know its not just 1 anD 2


and for x just plug in x


but its y(1)


im sorry if im asking stupid questions LOL


wdym?


oh nvm you transitioned it


to 2 and 1


yep


yayya okay we good for 5 now


Great!


will you explain this one too?


sure!


we are given velocity as a function of time


and are asked to find a position at a time


given a singular value of position at a time


what you could do is integrate to find x(t), put a plus C, plug in t = 0 to get a value for C. this would give you x(t)


and then you can plug in t = -3


in this bounded way


you can bound v(t) from t = 0 to t = 2


the bottom value should be the value you KNOW for x


the top value should be the value you WANT to find


what do you mean?


or the time of the value you need to find


t = 0, we know x = -3


thats my lower bound for v(t)


using FTC we would get x(top bound) - x(0)


ahhhh okay


x(0) = -3 so x(top bound) - (-3) = x(top bound) + 3


the top bound will be the value we need to find


here we are asked to find x at t = 2


yessss okay


so -3 at the bottom


nono


-3 is the value of x


we need to bound the t


Sorry im just a bit confiuesd


at t = 0 x = -3


allg!


why is b 2?


because b is the time we want to find


a should be the time value you know


b should be the time value for whose x position we need to find


ohhh


and we only know t-0


you can do b = 0, and a = 2


if you want


that would give you x(0) - x(2)


same thing but a little weird


okay so we are trying to find t=2


so that goes atthe to[


yep!


and t=0 is what we know


exactly


use FTC


if you are confused by bounds let me know


Ill do it the other way


lil longer but may be easier to follow


nono i like this method more but there are so mnay little things


that i need to understand


yeah


wait but what was the sign for you to know you had to integrate


good question


if you are given x and we need to find v


you need to take the derivate


derivative


if you are given v and you need to find x, you need to do the opposite so integrate


x -> v -> a (derivative) for every step


a -> v -> x for every step integrate


ahhh okay


a few mins to write notes


go ahead


I do need to leave soon so I might not be able to do another problem unfortunately


ohhhh do you think i can contact you through the chat?


i really learned a lot through this session


Im not sure


Im glad you learned though!


I can help you tomorrow if I do see you requesting again at a similar time


okay!!!


do you have any final tips


for my exam....


also on particle motion


wait what are these letters


Bounding is key to solve problems fast, knowing when to take a derivative or integrating should be second nature based on the a -> I sent above. If you do that, bound correctly, go step by step on the algebra similar to how I bounded here instead of bounding a number for all of it then subtracting it would be easier on you for simplifying


its just a curvy x lol


I do have to leave so If you can please take a screenshot


I apologize for the inconvenience


thank you so much for helpinh me today i really appreciate it


have a goodnight


you 2!


Hi!


Hello!


How can I help you today?


I have this geometric sequence problem that I got stuck on, I have an idea of what to do it's just I don't know how to set the knowledge in motion


I was wondering if you could guide me through the question


yeah of course


whats the question


I'll type it on here


Let gn be a geometric sequence where g_1=-5 and g_3=-45. Which of the following could be r?


I. r=-3  II. r=3  III. r=9


Answer options are


(a) I only  (b)  II only  (c) III only  (d)  I and II


ok so for a geometric sequence do you know the formula?


There are 2 but idk which one to use


gn=g0r^n or gn=gkr^(n-k)


It looks weird typed out let me kinda draw it for a better view-


ok so for this problem you would use the second formula


now you are given two values, g_1 and g_3


so do you have an idea of how to plug these into the formula to solve for r?


Yes I do!


Would I have to use g_n or g_k tho


so what you want to do here is to think of each of them as a different one, so gn should be one of them and gk should be the other


try to get rid of all the variables in the formula other than r


OHH


So soul it be this (drawing it out)


would*


yes!


you got it


YAY


now you can plug in the values for g_1 and g_3 to solve for r


Aight let me solve it on paper


ok


Ok I got r=3


Do I have to do anything else?-


ok so I think you missed one part when solving


let me do it on the board


k!


I'll write my steps on here-


oh wait nvm (First time using this-)


I think when you did the square root, you missed the negative answer for it


Ohhh, I forgot about that answer


but basically since both 3 and -3 squared equals nine, they are both a possible answer for r


So the answer is (d) I and II


yep!


good job


Thank youuuu!


of course!


is there anything else you needed help on or was that it


Well already the Next problem is scaring me so yes-


ok lol


"Let an and gn be an arithmetic and geometric sequence with a_1 = g_1 = -1 and a_4 = g_4 = 8. What is the value of a_5-g_5?"


ok so what you want to do is figure out the formula for each one separately first


lets start with an


since you are given two values you can use the same technique as last time


So we use the 2nd arith formula?


yeah


Do we worry about d?


yeah so you want to solve for d here


so you can get your equation for the arithmetic sequence


great so now plug d into your formula along with ak to get the formula for an


use a_1, its easier


almost


make sure you keep the n as a variable here


Woops


ok so that is your equation for the arith sequence


now do the same thing basically for the geometric one


Aight


ok so now same thing plug in the r value and g_1 into the formula to get your equation for gn


wait you went too far


Er


thats the equation


you can multiply them since one has the exponent


ok so now since you have both the equations


solve each of them for the terms


almost but make sure you do the exponent first before multiplying  here


so do (-2)^4 before you multiply that by -1


yes


so now just subtract a_5-g_5 for your answer


yes!


you got it


Thank you ever so for helping me!


no problem!


is there anything else?


Nope, I'm set!


great


have a good day!


You too!!


hi


i have a geometry test tomorrow and nedded some help on some questions


ok


im still pasting in more questions hold on


okay done


can u turn on ur mic, i feel like it would be easier and help me better that way


is that ok


Q' is the mirror image


are u able to turn on your mic???


Hello, can you hear me?


Uh, yeah, I could hear you.


OK, cool


The Q is 1.5.


R


Are you able to plot this already?


Um


no, those are already like there for like the question for number 4.


Yeah


I'm just confused on like how I'm supposed to find the answer with RY equals -2. Like, is there like a um


it's like equation I have to use. Like, I don't know.


Um, so it's basically


telling that


that uh


that the TT is minus, sorry, I'm just plotting here as well. Uh, minus 2.3.


minus 2 X.


must be


and


-2 this year.


Yeah, so if you plot this, essentially it shows you like a


quadrilateral


figure


and then what you need to do is are Y equal to minus 2 essentially is telling you that you want to find a reflection of this


OK, so how would I use Y equals -2 to find my answer.


Yeah, so you'll have


basically why to -2 is anchored.


at the point T. If you see T, T has X


Sorry, uh, Y is equal to -2, right? So Y is equal to -2.


will be


on the Y-axis.


at -2


We need to find the reflections of each of these.


Have you, have you studied reflection, dilation, translation.


Like a little, yeah, but like I don't usually plot it like we have to, like, I'm pretty sure we have to just like


use um


an equation to find the answer like without plotting it.


Hello


sorry we got disconnected


for e.g. Q's y coordinate is at 5 and is  7 points away from -2 | so he reflection would be -2 -7 = -9 for Q' i.e. Q'(1,-9) | R ( 3, -3), S (0,-4) , T(-2, -7). That is the answer. I will be online if you can rejoin


Hello How are you?


I’m good


How can I help?


I was hoping if you could help me revise for my exam that’s tomorrow


OK


do u mean review?


Yeah


Could we use voice chat because it helps me understand better


OK pls wait


Okay


OK, I'm talking now. Can you hear me?


Yeah, I can hear you


OK, I'm gonna just turn down the volume. Is my volume OK?


All right, I'm gonna turn down the uh you're a little loud. Don't, don't, don't change any. I, I'll change the volume here.


All right, so how can I help now?


Um, so


I was hoping if we could like review this.


Uh, do you have specific questions or should we go over what's on this sheet or what would you like to do?


Um


I was like


if we, if I could like solve it.


OK


check if it's like cracked.


OK, yeah, yeah, OK. I'm, I'm going to uh just give me a minute. I'm gonna look, uh, I'm gonna move this picture to another screen here so it'll be a little bit bigger.


and then we can go from


there.


All right


So OK, so we're looking at example number one, is that right?


Yeah, so, should I try to explain it to you?


Yes, yes, that's a good idea, yes.


So, we're gonna talk about the coordinate plane now, and it's a


Yeah


um


when one is drawn horizontally and the other is like vertically.


Yes


The horizontal is like daxaxis and the vertical line is the y axis and


it, um


And, and what about where they cross? What do we call that?


oh, the origin?


That's right. That's right. Yes.


and then


the pear X and Y, it's like the ordered pair.


That's right


and then the first number is the horizon to vault.


x-axis


Yes, or X value, yeah.


and then the vertical is like the


Y value


OK


Um, should I do example one now or?


Yeah, if you'd like to, yeah.


So first, I'll draw a coordinate plan.


So now you're gonna draw this on the whiteboard.


Um, I don't think I can cause I'm using my phone right now.


OK, OK. Uh, so


you're gonna just draw it on paper and then tell me what you did. Is that the plan?


Yeah.


OK.


Oh.


Do you have some graph paper?


What? Sorry. Um


I do.


I, I mean, you can draw the grid, you know, but I mean if if you have graph paper, you know, it already has a grid on it, as I just don't know if you have that.


oh, I don't have that


OK, OK


I'm using my whiteboard right now.


Oh, I see. You, you have a whiteboard where you can uh


write with, with, with, with markers and things.


OK


So I drew the coordinate plan, so now we're gonna locate a


Yeah, OK


so


we have to do 2, which is on the x axis because the first number is always on the x-axis.


Yeah, that's right


So we go to 2.


Right.


We start at 0 and then we go to 2, and then we go up.


to 3


That's right


So it should be like


I don't really know how to explain where it is, but


Well, you could just look at example 3 and, and


yeah


see if you agree with where they put it. You see, they already have it there, so


I got the same thing


OK


All right, so now, uh, how about you do B?


Yeah.


B, you start at 0 and then


you go left.


to -3


OK.


Um


That's right. That's correct. I shouldn't say right because this graph


That's correct


and that


And then


to 3


uh, that's, yes, that's correct.


And then C, we start at 0, go left.


and then go up, no, go down to -3.


and then D


which is you start at 0 and then go to 3 and then go down to -4.


And


That's right


Yeah.


That's good. So what you have should


it looks, look essentially like what they're showing is the solution here, OK?


Yeah


Now, have you heard about the quadrants, you may not learn about those until late.


Oh yeah.


OK


So, so what quadrant is A in?


A is in quadrant 1.


OK, and B


quadrant 2.


yeah, and C


quadrant 3


OK, and D


quadrant 4


Yeah, so we, we go around counter-clockwise. Do you know what that means?


Yeah, OK


With digital clocks, some people don't know what counterclockwise means.


Oh


Oh wait, I have a phone call here. Just give me a second here. It's probably a scam at this point.


Hello


I'm back. It was a scam. Health insurance.


well


just goes on and on


OK, so we've done the example one now.


what should we do next


um, the activity.


OK


OK, did it upload or? OK.


Uh, it's coming up uh


uh


let me see if I can find it. I think it's, uh, I'm gonna move it a little bit cause I think it's under what we already have.


Oh, wait a minute, let me move things around here.


OK, I'm gonna make it a little bigger and then I'm gonna copy it over to my other screen, so.


bear with me here


OK, so I'm going


to select this, select this.


select this


and we'll do that.


OK, so I'm looking at an activity one.


Mm.


and magnified here.


I'll magnify it a little more


OK, so


I see. So this one


uh, it looks like, let me see if I'm correct here.


Yes, it looks like they don't, oh, wait a minute, maybe they do.


I'm a, I'm a little


OK, it looks


oh, I see, it looks like an activity one.


Yeah


Yeah, they, they, they, they don't show them.


Oh yeah, there's no coordinate plan.


Well, I see a coordinate plane, that's the thing.


And then I see a K and an I. I.


Oh no, that's the other.


Oh, OK, OK, I see that's another reason OK, OK. I, I see. Yeah, OK, I got it. So that, that doesn't apply, OK.


All right. So, um


right, here's what I'll tell you what I'm gonna do on the whiteboard, I will draw


and, and you can tell, you, you can tell me where to put the points, OK?


OK, yeah


So I'm gonna draw some axes here. Now,


let me just think about this. One of the problems is


that these um


right


so do you see the uh let me try to make it straighter here. You see that black line? That's the x-axis.


See, it doesn't, doesn't let me move it.


Yeah, yeah, I used to let me move and see, I'm trying to get it, all right, well.


I'll do my best and uh there we go, OK, and now I will put a Y-axis.


OK


Now, let's try this.


um


let me think about this.


OK, that's all right. Each little square is gonna be one. They're, they're kind of close together, but I think we can live with that. So we're going to start with T. So tell me how I should get to pee and I will put a dot there, OK?


Um.


Or I should say I will try to put a dot there. I never know.


P, um, is start at 0 and then go to the left 4 steps.


OK. Can you see my cursor?


What


Do you see my cursor on the screen?


Yeah


OK, so I moved it to the left for I think, but my eyes aren't so good, so it could be 5,


well, it looks like 4, no, well, you count them. Does it look like 4?


but


or is it 5? No, I think it's 5. OK, I'm moving over to 4.


OK, so there's, wait, no, that's 3.


one


OK, something's weird here.


I think it's their way.


OK, OK


wait, should I turn


here?


12, yeah, right there, that's it. OK. And then we go, now what do we do here we go up one.


and then, yeah, go up one step.


OK, so I will put a dot.


OK, well, it's a little bit big, but that pink dot is it, OK?


Yeah.


I'm not very good at putting them, but OK. So that we're taking care of P. Now tell me what to do about cure.


2 OK


and I'll use it, I'll use it to try to use a different color, you know.


start at 0 and then go 3 steps to the right.


OK


So


12, does that look right? 12, feel my cursor is.


123, yeah.


OK, and then what do we do


um


5 steps up.


So that's 3 steps, 4 steps, 5 steps, so I'll put a thing that


and you see that, oh, well.


Yeah


All right, I'll, I'll try. All right, well, yeah, I think you guys pretty close


Uh, OK, let me try one more time, see if I can do a little better.


I think that's blue though. I thought it was supposed to be green. All right, 12.


3, and then I go up.


Right, how does it, well, OK, the top of that, the top of that thing I drew there, that should be the point, OK?


Yeah.


OK. All right. So now we've got R


R


so tell me what, I'm gonna try a different color, but tell me what to do for R


OK, so start at 0 and then


Yeah, OK


6 steps to the


OK


right


Let's do 4


OK. I think I'm at 6 to the right, and then what do we do?


And then um


go


2 steps down.


OK. And I'm gonna put a red mark there, I hope.


Oops, well


OK, so


but let me try again.


I'm trying to make a little mark, but it doesn't let me make little tiny marks.


OK, how's that? Does that look about right?


Yeah.


One time we count


00 yeah


I just wanna be sure that's 6.


OK, I guess it is. Yeah, OK.


Oh


All right. So now we've got one more to go, right? That's 5.


But you see, we've, we've got 4 quadrants taking, I think they put, oh wait a minute, wait a minute.


Oh.


wait a minute.


I'm


a little confused. Oh


Yeah, OK, yeah, the next one's gonna be in quadrant 3. OK. So what should I do for the, for S?


Oh, wait, let me just, OK, so 0 and then go 4 steps, 3 left.


OK


So we go


OK, now that's the same as I mean he was 4 steps to the left, so that'll be there. Then what do I do?


and then


Then I go


4 steps down


34, and this one will be blue.


But while I thought it was gonna be blue. OK, it's red.


So, OK, so, so now we've got all 4 of them, and they seemed to


usually do one in each quadrant, OK?


Yeah.


All right. So now,


we've taken care of that now.


I'm a little con 00, I see, and my eyes aren't so good. OK, so the next thing, should we look at activity 2.


Yeah


OK, let me


all right, wait a minute, wait a minute. Uh OK, draw one.


OK, here's what I'll do


Uh, OK, let's try to use the same coordinate plane, and I'll try to


put dots like maybe we'll use different colors for these. So the first one now, the new P is what P.


So is it all right if I put them on the same plane here?


Wait, let me


Yeah we should.


beros


I'm sorry, I didn't hear you


Should I like raise it or I raised them.


Oh, all right, all right. If you want to erase it, all right. Yeah, I can erase some too. OK, all right. I will, uh


wait a minute, let me fix that. I think I can fix. OK.


All right, yeah, erase that too and I'll try to fix the gap.


OK


Uh, uh, OK, let me, uh


let me try this here.


Let's draw a line here.


Yeah


Yeah.


All right, that's pretty good. OK. Uh, now, we'll just ignore that, that black dot, OK? And I will use


red for now


Oh, OK


All right. So, what's the first one, the new P, what's the value?


So first we start at 0 and then go 5 units to the left.


And then what do we do


And then you can't really go up and down so it is.


That's right. So how about when that red mark is, does that look good?


OK. All right. So now the next one


Mhm.


is Q, so what do we do for that?


We start at 0 and that's


well, that's the thing we get in that.


But that's 1234. OK. So, I'll put a red mark.


there. How's that? Well, OK. I think you get the idea that the red marks a little too big, but OK.


All right. I've got one, another phone call. Just bear with me.


OK, I'm back. That was another scam call. I'm going to mute the phone, just bear with me here. This phone, I have two phones, I can't mute the other one.


OK. All right. So now we've got two red marks. What's the next thing we're gonna do here?


and then um R


Yeah


which is 0 and then go down.


it


OK. So, OK, yeah, so we go down to.


-2 and then


OK, you see the red dot there?


yeah.


Is that good


yeah


OK, so now we have one more, and what's that?


Um, you start at 0 and then go to 4 and then stays there.


OK, so I will


how's that


Yeah.


OK


Now, suppose we wanted to make


make a square


How, how could we change these like, you see, it looks like


Q and S


Mm.


are OK if we wanted to make a square with a side, oh no, that one,


Well, if we wanted to make a square


if we, since Q and S both have 4s, what will we do with the G and the P to make this thing square.


You know, what we could change


Mm


You could


um,


Well, I, I, I'll show you. I'm gonna use, um, let me pick a different, I'm gonna use like a pinkish color. It's uh, I, I think it's called Fuchsia or something, but


I'm gonna put a dot


right.


there


See that? Well, it looks kind of red, but I think it's a different color and then I'm gonna put it that


right there. You see now they're all


they're all poor and now I will draw some lines


and I


will use black


well, I'll use uh blue for the lines.


So


he couldn't you just connect it and make it a square?


that's what I'm doing


Oh


You see, but I move, I moved them so that they all have, they're all a distance for from the um


OK


from the origin. Now we have a square


Hm, that makes sense.


It's actually looks like a diamond, but if we


I didn't draw it very well, but it really is a square, I think.


Yeah, it is


OK. Now, let me just ask you this, this, you may not have had this in your class yet, but


if we wanted to find the length of the side of one of these squares. Do you know how to do that?


Mm


Have you heard of the Pythagorean the?


no


No, OK, well, you'll have that next year.


Have you taken geometry


Yeah, I'm taking geometry right now, but


we haven't.


Oh, you are


So you, so you're taking algebra 2 also, angioometry?


yeah


Wow, that's so you have two math courses


Yep


My goodness, wow


You're a busy, uh, a busy student.


OK, well, using the Pythagorean theorem, we could find the length of the sides of this square, but you'll probably learn that in a few weeks. OK.


Wait, I wanna learn about it, kind of um.


OK


OK. What, what other courses are you taking?


what?


What, uh, you have geometry and algebra 2. What other courses do you, are you taking?


Um, I'm taking physics. Well, it's just like pre like the introductory.


Right, right, right, yes, yes


and


well


You must, uh, do you have an English course?


Yes.


English, English is basically just writing.


Right, he's no, yeah, yeah. OK. And about history or geography or anything like that?


Um, I'm doing history right now about Ancient Greece.


00 OK. Well, that's interesting. OK.


And what grade are you in


Seventh grade


8th? OK.


Yeah.


Uh, you're doing quite well. OK. All right. So what should we do next here?


Would you like me to give you a question?


Wait, but um


wait, you said the Pythagorean theorem.


Oh Pythagorean theorem, yeah.


OK, well, you want me to show you the theorem there.


Yeah, just like, so I'm preparing so.


OK, well, down below this, I'm gonna draw a triangle, OK?


It's a right triangle. Do you know what that means? It means


yeah, you're right


OK, one of, one of the angles is a right angle, so there's


one side is black


OK, now the next side if I'm, if I do this right, the next side will be red.


OK.


So the next side is red. I need to move that over a little bit.


Oops, well, all right, I'm gonna try to move it again. It's not so easy to move these things.


All right, that's pretty good. And now, the next slide I'll make uh


OK


green.


Well, no, I'll make it sort of this pink color here.


I try this


OK, so that's a right triangle, and do you know what we call the, the long side there, the pink side, do you know what we call that?


We call that the hypotenuse.


But I'm gonna label these sides with letters, I hope.


Let me see if I can pull that off.


OK, so


the bottom side is a, you see the A?


Yeah.


And then


the red side. I'll see if it'll let me do this in red.


maybe.


Red side is B.


and


the hypotenuse will call C.


let me see if I let me do this here. OK.


Oh, OK. Well, the sea came out red. It's supposed to be pink, but


came out red. OK, so now


um,


all right, I, I, I, um, you know, right, I'm gonna type this my, my stylist is not working right now. So here's what the Pythagorean theorem says, it says that a^2.


equals


oops I didn't do that right.


You know what square means for squaring numbers?


OK


Yeah, isn't it like the uh powers and


like the power


or


Right. And I wrote, I, you see that little arrow carrot thing or that means.


Yeah.


OK, so that's the Pythagorean theorem. It says if we have a right triangle,


the square of the hypotenuse, which is c squad, equals a^2 + b^2.


that's.


I'll move it a little bit, OK?


Have you ever seen that before?


oh like the equation.


Yeah


Um, I've seen them with numbers but not letters.


Yeah, yeah. OK, OK.


So, OK, well, let's just


um


OK. I think maybe we'll leave it at that because you haven't really had that yet, but that's yagor. Well, we can try an example, but let's, let me, let's say that um


I will write on here, let's say, let me see if I can go on it. I mean, any, any number will work, but some of them work out nicely. Let me think if I, OK, so let's say that A equals


and B


Let me see if I can do this here.


Maybe it won't let me


Let me try. OK, B


No, it's not being cooperative here. There, there's a bug in this thing.


See, I can move see, but I can't figure out how to move the bee.


Oh, there we go. I, I sort of, all right.


I'm gonna try to edit the.


doesn't seem to like one


All right, wait a minute, wait a minute.


use


I'm gonna do this


get this right


All right, there we go


All right, now I'm gonna give B a value here, don't let me.


uh let's try


this


All right. So B equals 3.


OK


So now


if, if, if A equals 4, what's a squad?


Oh, so 4 squared.


So 4 times 4


And 4 squared is what, 16?


Yeah


OK, so we have


um 16


plus and what's uh 3 squared?


plus 9


9, and what does that equal?


the


square


OK, but what, what is 16 + 9?


Oh.


OK. So that is c^2. I, I'll, I'll try to write that here in the text box.


c^2 is 25.


right?


Right, so what do you, so what do you think C is if c^2 is 25.


Yes, that's right. So that's a sort of famous triangle, 345 right triangle.


That's, that's actually easier than I


thought, I thought that


Well, that's good


it.


kind of hard


Yeah, it's a lot of times, you know, these things have big names, so they seem hard, but they're not, they're not as difficult as you might think.


OK. So what would you like to do next?


Um, the terminology in the four quadrants.


Terminology in the OK. Now, where do I look for, let me see if I can.


is that


The bottom.


Oh, OK, let me make a copy. I apparently, I didn't, did I not copy that?


Oh, I see it. OK. Terminology in the 4th quadrant, OK.


If I explain it in my own ways, so.


Yeah, yeah, go ahead. Yes, yes.


So the first member of like the ordered parrots, the abscessa.


Yeah, that's right


And then the second one is The Ordinate.


Yeah


And both of them, they're referred to as coordinates of the point.


Yes, OK


And


so basically ordered pears, whose abscissae and ordinates, they're both positive cause like in sense why it's in the first quadrant because


it makes sense cause


Right


you can look at the coordinate plane, and they're both positive.


Right. So that's the first quadrant, OK.


And then the second quadrant is the abscesses are negative, while the ordinates are positive because


you look at the corner.


tonight


so


and then the third quadrant, it's one, both of them are negative cause


again you can look at the coordinate plan and it makes sense.


And then the 4th quadrant is when the abscessa is positive and the ordinate is negative.


Yeah, that's right


And then we have the


and why


axis


which are.


oh


yes, that's, that's a good point. The axes don't belong to any of these quadrants. That's right.


There's some name for that in trigonometry, but I can't remember, but yes, because they're on the borderline.


Um


oh, there's an activity on the next page. Let me just send that.


OK


this.


I think I've had you as my tutor before.


um


that's possible, although my records, let me check through, I have a spreadsheet here. I don't, I'll see if I can find your name.


November 18th


dividing numbers with scientific notation.


Yeah.


Yeah, I remember.


that's good


I didn't remember, but you're on my sheet. I've done, I've, I've almost five hundred sessions. I'm getting close.


That's a lot.


Well, I started in the


I started about 6 years ago.


Oh


OK.


When I started, there were hardly anybody on


Sarah actually


Should I try to explain the example?


Uh, yeah, well, let me see if I can find it first with, did you upload it?


yeah, it's


uh


Uh, is this example two?


yes


OK, let me, let me move things around so I can see it, OK.


All right. I'm going to um


I'm gonna take a screenshot and then I put it on my other monitor so it's bigger. So let me just do that.


That way I can magnify it.


OK, so we've got that and I will look at it here.


you see


OK, I've got it I'm just gonna make it bigger so I can read it better.


Let's zoom in.


All right, that's good. OK. So, yes, why don't you explain it and I'll see what you have to say here.


OK. So, what I like to do is I like to make a table because


it's more clear


OK


So I do points and then I write the obsesses


like.


OK.


coordinates


and then the quadrant, it belongs to.


And then


the first


OK, I'll write all the points, 3.


and 2A, which and then


B


and you have 2 and 0.


OK, OK


E


4 and -2


Wait, oh, I think I have to make it smaller.


0 and 3


Excuse


And then the abscess stuff for point A is -3


Yeah


Yep.


for point B is -2.


The obsessive for point C is for the abscessa 4 point D is 0.


OK


And then the ordinate 4. A is


Yeah.


still theorate for


2 and then negative.


OK, now


um


it's not really necessary to write the


coordinate plane


if you know it


it.


So I like to think in my head.


that I have a coordinate plane, so I don't really like waste my time on doing that.


OK, OK.


And then um


so I see that the


negative 3 is to be left.


and then it's going up. So that's the 2nd quadrant.


Yeah, I agree. OK.


And then


we have -2 to the left and then it stays there, so


that's the X-axis.


That's right, yeah


And then, yeah, 4 to the right and then go down.


which is the


um quadrant.


or.


OK


and then


we start at 0 and go down to -3, which is the y-axis.


Yeah, OK


OK. Now, 11 thing you should uh I mean, you did fine. You should just keep in mind that the quadrant names are usually given in


I did


uh Roman numerals. You see them here? So like


you know


knows


I'm sorry, say that again


I, I missed what you said, but, but I think you see that it's just


um,


uh


like.


I guess you could, you could write 4 F O U R T H, but they, they always seem to use Roman numerals for the quadrants.


it kicked me out for some reason.


It does what


It kicked me out for some reason.


It kicked you out? Oh.


Oh, I don't know why. Maybe the battery is low on your computer or something.


I don't know.


Or maybe you, maybe, maybe there's a time limit. I don't know.


Oh really


I, I, no, no, no. Uchie doesn't have one, but maybe the something else does, I don't know.


I think I missed accidentally clicked something.


Oh OK


Oh maybe, maybe. But I, but I have to go pretty soon, so is there some something you'd like to do uh


for a final exercise.


Uh hm


No, I think it's fine. If you have to go like it's.


OK


OK. All right. I have to clean up this room, otherwise my wife will be very upset, so, so I better go. OK.


Yeah.


All right, well


yeah, you have a good day too. It's nice to see you again, maybe, or, you know, see you speaking loosely. Maybe I'll see you again. You seem to be doing very well. I'm quite, uh


I, I would say you're doing fine. uh


and also when you get to the Pythagorean theorem, you'll know that you've already seen it.


Yeah


and I can


It also, you, you could look on the web. I mean, if you search for Pythagorean theorem, I'm sure you'll find many, many examples of it on the internet.


yeah, now I'm gonna like impress my teacher by already knowing it.


Yeah, OK, that's Pythagorean, that's PY T H A G O R E A N, Pythagorean. OK.


Uh, but if you misspell it, um, the, the, the internet will probably fix it anyway.


and yeah


All right. Well, I hope to see you again and, and, and good luck.


Thank you. Have a good day.


You too. Bye-bye


Bye


Well you not letting me know.


hi!


hello??


Hello, what do you need help with today?


this!


Okay, what do you know about the problem first?


um ik the circle standard formula


Thats good, ill write it out


So the problems says that the C can be written as kpi


meaning that we need to find 2(r)


no lets look at the circle and I want you to kind of draw a circle that goes through those points


because we need to find the radius


can we use mic?


I cannot use mic at the moment


I apologize


oh ok can i


Sure


So I don't really understand what we're supposed to do first, so now I know some conferences are, but um, you said that we need to draw a circle that goes to these points.


So.


Yes thats good


Okay so do you know what the radius of a circle is?


Yeah, so a radius is halfway through the circle.


How many units is that?


Let me see some.


8 is the diameter, so the radius is 4.


Yup thats good


So to find this some conference we would just do 2 pie.


There was some conference of the circle is pi.


It's the value of k


OK, is that good?


Yes so now that you have 2pi(4)


U can multiply 2 and 4 together


so itll be 8pi


And we would have 8 pie.


yeah


and that means the value of KS 8.


yup


OK.


Thank you. I have more questions.


Okay send them over


OK, so we has to be the 90 degree one. Since there's 90 degrees, does that mean that this is a right triangle and the hypottenus has to be the longest side.


Yes thats true


Or does this not have to be a right triangle.


If B is a 90 deg angle then yes it is a right triangle


OK, so now I'm confused if A is the hypotenuse or C is.


or like what's a pup for it.


What is the questions asking?


The questions asking what's the value of k, so I have to figure that out, but first we have to put our angle A and angle C somewhere, right? Or no?


Yeah


does it give you angle A or C


Yeah, so Angle A is 54 and Angle C is K over 2.


Ohh I see


Okay so lets say '


Here I made the question beggar.


Okay so remember all triangles


Oh wait, I understand.


their angles have to add up to 180


It doesn't matter because it's sight, not side linked, this angle, so it doesn't matter where we put them.


OK, so this one would be


K


over 2.


So you can make an equation


So then we would have to find the value of K, so couldn't we do 90 + 54 minus 180.


180 minus 54.


So then we can do 36 times 2.


or whatever