1) Keep the horizontal line fixed

2) place your protractor's horizontal base line on the  above pencil drawn horizontal line.

3) Make sure your protractor's center coincides with the circle's center dot.


are you there?


Yea


Next is the 22 percent one


Which is 79 degrees


ok - go ahead and try


can you poste again? Seems like the whiteboard is not working for me


Is that good ?


yes - looks good - nice work!


I also I may have to go in 20 minutes since it’s past my bed time for school tmrw ….


but again - seems like the degrees are looking greater to me.


Idk I’m js trying to put it where it said 79 on the protractor


Because I still need 26 percent and 9 percent


After 22 percent


you will need to plot 94 dgerees and 32 degrees, right?


Ben and where do I put 79 degrees at too


you marked 79 on the chart, right - label it with the corresponding superpower


Where I put the black question mark


I did not understand?


The black question mark is 79 degrees, right?


Then it is fine.


Yeah where I put the black question mark on the white board picture I uploaded


I saw the question mark - but what is the issue there? that ? should be labeled with the corresponding superpower


Okay got it


Now 94 degrees


yes, repeat the same process and mark it


Right there ?


No, it is incorrect. Do you see the problem?
Your 79 degrees for time travel looks more that 94 degrees


79 < 94 , so the pie for time travel should be smaller than the pie for 94 degrees.
Does this make sense?


Yes , but can you show me where I should put the dots at


1) Keep the horizontal line fixed

2) place your protractor's horizontal base line on the above pencil drawn horizontal line.

3) Make sure your protractor's center coincides with the circle's center dot.

Did you try following this?


Sorry it’s just that I have 2 hours doing this and I just want to be done and go to sleep now honestly  🫠


check the whiteboard


did you understand?


Yes so which line do I erase now


you might have to try doing it again for all - if not do for 79 degrees atleast


It still does not look right. And why do we have 6 pies now?

0 will not be necessary.


Unless it has a video, it is difficult for me also to explain by demonstration.


Oh okay , thank you for all your help tho


no worries! Happy to help


If you liked my explanation, mark me as your favorite!
Thank you!


Okay, I need help with proofs today


Ok


Hello!


Yep, it's me!


So, I need help with proofs in geometry today


I got this homework assignment and I don’t understand it that well


Fire away


How do I know the process of proving something? Like how is it structured


Because I feel like I just want to go straight from what is given to what needs to be proved


Well, whats the problem?


Can I send photos?


Leo


How?


I think you gotta upload them


I added it to the whiteboard, can you see it?


Yes


So how would I solve #11?


And the X's indicate homework problems?


The X’s indicate ones I shouldn’t do


Oh


So just 11 and 13


How would I start #11?


Let me see


I hope you don't mind, but the answer I have doesn't have use any  theorems or anything


Any updates?


Since Y is the midpoint of ZX, that means that ZY is congruent to YX. Since V is the midpoint of TW, that means that TV is congruent to VW.


And since is says that XY is congruent to VW, that means that YZ is congruent to VW. Basically, XY, YZ, TV, and VW are all congruent


SX=SZ+ZY+YX

and since YX is congruent to VW,

given that SW=ST+TV+VW,

we can say that SX is congruent to SW


As for the other problem


Given that angles 1 and 2 are congruent, it is safe to say that their supplements (ABF and DCF) are congruent as well


And since rays BG and CE bisect ABF and DCF, that means that ABG, angle CBG (aka angle 3), FCE (aka 4), and ECD are congruent to each other


Therefore, angles 3 and 4 are congruent


Would there be any postulates and theorems that would have to be mentioned?


Like TV could be congruent to ZY because of reflective postulate or something?


Sure, I suppose


Or maybe the definition of midpoint


Ayyyyy we’re eating this uppppp


hi


do you need help with math?


Yes I do.


ok


ok thanks


I see it


are you working on #19?


Yes I am


ok, this is a tough one!


I see some 90 degrees angles


that should help


do you have an idea where to start?


Not really


ok I think I got it


first thing to do is look at triangle HDF


I outlined it, do you see?


Yes sir


ok great


so we know 2 of the angles of this triangle


the 90 and the 19 right?


Right


so the third angle will 180 - (90 +19) ok?


Ok


how much is that?


90+19 = 109


so the 3rd angle 180 - 109


Oh sorry I typically


= 71


does that make sense?


Sorry I typed it in my calculator wrong*


that's ok


Yes it does


so we can write in the missing angle at F = 71 - 27


44 ok?


ok so now look at triangle EIF I'll draw it in green


see it?


Yes sir


ok, so the angle at I is a right angle


ok?


Ok


so now we can write an equation that will allow us to find x


we have 2 angles of the green triangle 90 and 71


so together they add up to 161


what will the 3rd angle of the green triangle be then?


yes! excellent!


so what will our equation to find x be?


can you write it on the board?


or you can write it here if you like


almost


the angle in green is 17x - 7 and that is equal to 19


so it's just 17x-7 = 19


make sense?


Yes


so add 7 to both sides


and we get 17x = ?


right!


so x = ?


yes! exactly


it's a strange fraction, but that's the answer


I hope!


Ok


Is this homework?


It is


I'm pretty sure 26/17 is correct


do you want to do the next one?


Yes please


hhm wait I think there is a problem with that last one sorry'


Oh ok


I didn't see the "incenter" part on the question


do you know what that means?


Not really


here's a definition


The incenter of a triangle is the intersection point of the three angle bisectors. It is unique because it is the center of the triangle's incircle, a circle inscribed to touch all three sides. This point is always located inside the triangle and is equidistant from the three sides.


let me erase and start again


Did you see the definition?


I did


ok and do you know what angle bisector means?


Not off the top of my head.


it means a line that cuts the angle in half


Ohh ok


so for example in corner D there will be two 19 degree angles


ok?


Ok


and at corner F two 27 degree angles


so if we ADD up these 4 angles what do we get?


ok great!


and what do all three angles of a triangle add up to?


right! so angle E will 180 - 92 right?


Right


so 88


and the angle we are interested in (17x -7) will equal half of that


what is half of 88?


can you find x now?


yes! excellent job!


that's a lot better than the weird fraction we got last time


Yeah


I thought it would be strange to get a fraction for the answer


ready for the next one?


Yes


ok so we have to use the properties of an incenter again


here's a new property ...


Equidistant from Sides: The incenter is equidistant from all three sides of the triangle. These equal distances represent the radius of the incircle, also known as the inradius.


do you see it?


great!


it means we can draw a circle at K and it touches the sides of the triangle


I'll try to draw it


see it?


now the lines in green are the radius of the circle


and they are both the same OK?


Ok


so we can use that to write an equation to find x


I'll do it in red


I thought we were finding GK


we are but first we must find x


Oh ok


do you think you can use the equation in red and find x ?


I can help if you like


you got it! well done!


but we want GK not x


so we put x=12 in one of the other radius


which one shall we use?


Go?


Gk*


ok, so 3x + 17 with x=12,


what does that give us?


exactly!


and if you want to check 7x-31 should also give 53 (with x=12)


Right


ok cool so that is KI because all the radius (or radii) are the same


ok, want to do the last one?


Yes


ok, so they give us the radius


18 right?


and we have 2 other sides


DI and DG


these will be equal to each other too, ok?


Ok


so we write 9x-16 = 4x+9


and find x from that


can you do it?


great!


but we have to find DK


4x+9 = 29 ok?


so to find DK we need to use Pythagorean theorem


do you know that one?


yes that's it


where a


a=18 and b=29


and c is the hypothenuse DK


so c = sq rt of 18^2 + 29^2


tell me what you get for 18^2 + 29^2


do you have a calculator?


ok great that's what I get


so DK is the sq rt of 1165


it's a decimal


right! exactly


great work!


Thank you so very much for your help!


you're welcome


have a nice evening


You too!


thanks, bye!


hello


Hi, I'm here.


How are you?


im good how about yourself?


good thanks


i’m having difficulty grasping this topic


which topic?


oh ok


yes


In general, we're saying, where specifically in the graph is y>0


okay


So, it's most of the graph actually.  Just not the part between x=-8 to x=-3


would one of them be -3<x<1?


yes that too


Are all these answer choices?


no


we have to type them in


ok I'm a little unsure what you have to type in exactly, sorry


here is an exay


example


okay, so I think there's just two answers


it can be as many


in other questions there was i believe up to 4


it just depends on the graph


hmm.  To me, there's just -3<x<infinity and x<-8


I don't think you need to break it up into more intervals than that for this question.


could you type that in different terms like -3<x<1 im not really sure how  -3<x<infinity works


yeah.


In words, it would be, 'x goes from -3 to positive infinity'


Does that make sense?


its says its wrong


hm, don't know why it would be wrong


maybe it's the less than or equal sign. ?


yeah i had placed that


oh


i believe its more than one answer


well, yes, there's still the other side of the graph


ah okay


Can you try this one, this time?


what do you mean?


Can you answer it


ah.. ??


..wrong?


it's wrong


what should i be looking for specifically


It's the part of the graph that's to the left of the red part.  Y is positive there again.


when do i know where to stop it


like okay i start at -3 and then go to the top of a peak?


That's the part we already did.


Now we have to do the left hand side.


but thats below the y


x*


yes- but then it comes up again at x=-8 and left of that.


does our next one start at -5?


No, that's still in the negative y axis interval.


You have to start the interval where it crosses 0


-3 or -2


I'm talking about left of the red line.


starting from -8 and going left.  yes


infinity


yes- but since it's to the left- it's negative infinity


okay


I hope it's making sense.


im still a bit confused why we went from -3 infinity to then -infinity -8


Do you mean, you're confused about the order or how you write it?


or something else?


like specifically where we are supposed to start to go about the problem


when you first look at the graph


where do you begin


Ok so for this question they want you to identify where in the graph f(x)>0


So that's anywhere above the x-axis.


got it


ok good


i understand that part


So, then you have to think of the graph in parts, and you have to name the parts that are above the x-axis


hence why we got what we did correct?


yes


so for our next one


where do i begin to look at the graph


because my eyes goes to -3 but thats where the last one ended


umm.  Is this the full problem?


It doesn't make sense to me.


me neither


lol oh boy


Are you maybe supposed to just type those in as the answer?


yeah this is what they give us to type in


Isn't what you just put up the previous question?


oh i thought we were working on the same one


the one i sent was just an example the app gives us to see what we needa find


Have you pressed submit yet?


no


should i


yes please


it wad right lol im sorry


lol. It's alright.


mind doing one more with me and if that okay? its a lil different concept


sure!


okay, where the graph is increasing is simply where it's going up


do i count it if its already up?


like - infinity <x<4


yes that part would count.


You're asking if it's above the x axis


but this concept doesn't have to do with that.


so it wouldn’t be?


I'm not sure what you're asking.  But anywhere on the graph where it's going more up, is called increasing.


ah so like -2<x<2


yes


but does the previous one i said be one of the answers as well?


yes, that is going up


5<x< infinity


Not quite.


is it 6 or 8


6 because its at the bottom of the peak? but at 8 its directly going up


All the blue parts I colored are increasing.


i see okay


ok cool


So just remember that these are two different concepts.


i will continue to complete more on my own for practice thank you


Alright


good job


thank you


yw!


Jamie, how can I help you?


hii I need help with 35-37


OK.


also I cant talk or turn my volume up at the moment


sorry


Some of the angles for triangle ABC degrees, right? Do you know that?


So 35


yes


So then you have


two parallel lines, that is STNYZ.


The angles 2 and 3 are equal.


and the angle W


which are opposite angles are also equal.


from the given


1 and 3 are supposed to be equal.


So that means all angles between the two triangles.


are equal


so they both are eququilateral triangles.


Does that help with problem 35?


yes sort of


1=2
1= 3
2=3
1=2=3


Mhm


Mm.


OK


Mm


sorry I have to go now but thank you for the help


hello


Sam


Hi


i need help on a few questions i put on the whiteboard


Hold on let me get on my computer


Ok


here


what do you mean


so number 2,5 and 7


yes


for number 2
step 1
1) root 32= root 16x2
= 4 root 2


2) root 50 = root 25 x 2
= 5 root 2


3) root 200 = root 100 x 2
= 10 root 2


step 2
1) 2/3 x 4 root 2 + 1/3 x 5 root 2 + 1/4 x 10 root 2


8/3 root 2 + 5/3 root 2 + 10/4 root 2


are you getting it


step 3 add first 2 terms that means 8/3 + 5/3 = 13/3
 and for the other on just divide by a common divisor for this is 2 so 10/4 =5/2


now add the 2 13/3 + 5/2


but you cant add fractions unless a common denominator so you find it


the common denominator for 2 and 3 is 6


multiply both top and bottom by 2


Hello


How are you doing


Hi!


I'm well, and yourself?


Hey, doing great


Good to see you again and achieves.


What do you have an algebra today?


Can you hear me well


Looks like go away


Yes


OK


So I want to practice a bit on some problems just to ensure that I still understand it. Can you create some problems in order from the first pdf linked and then when we finish that can you do the same for the second pdf. I want problems with different numbers but the same concept, so I won't be practicing the same ones I did in class. I am currently working on page 2 problem 23. I want two questions each just so I can ensure I am familiar and remember how to solve it! PDF LINK 1: https://example.com/math_problems.pdf


Do you want me to open that link


OK, it's difficult to copy any


link here


Its on the whiteboard


Yeah, we can try that


OK, which one you're currently working on page 2 problem 23.


page 2


mhm


Can you write the problem on the whiteboard


Yeah, sure, but I'm not clear on page 23, so I've opened that PDF


Page 2


and I'm looking at


Problem 23


page one is fine.


Oh, OK


OK, I see your problem 23


Yes so basically I need two problems that are like that problem but diff numbers of course


So do you wanna put me, do you want, uh, yes.


OK


Give me a second


ok


I'm still here. I'm trying to find a really complex problem for you.


ok!


OK, I'm fine. I think I found something. Let's try them.


All right, I'll put something on the board, see if we can solve it. Uh, let me just arrange it appropriately.


Just give me a second. Don't get started on it yet.


this isnt like the problem


Like I want one just like the problem, only difference is the numbers


Oh, OK. So, I thought you wanted a more challenging problem. That's fine.


Uh


Basically what I'm saying is the same problem but different numbers.


Yes, I'm on it


All right. You're gonna give a shot.


thanks


can you actually solve this one and then ill do the next one you rewrite


Oh this is exactly like the one year solid on paper.


Yeah I know but I'm not good with this one I kinda don't know how to solve it


OK, can I just solve the one which you already have on the paper?


and you can try this one


sure


OK, I'll explain the one about the ones on the paper.


is sold, uh.


can you show the work on the whiteboard as well


OK, do we, do we know the basic concepts of this already, or do we need to go through that?


yes kinda


So let me walk you through that. So fire to the minus 1 basically means that it is one


upon 5


2 square, you know, 2 multiplied by 2.


22 is 4


And 5 by 3, you're saying essentially is that we need to the reciprocal of that, so that's 3 x 5.


Any questions so far


Maybe I'll talk you through the concept here a little bit. So,


any number raised to 0 is 1.


Holdon


1 upon A is equal to A raise to 1.


1 upon a square.


You go to


give you this 2-2.


OK


Hi


Hi Sarah! How are you?


I'm good


Awesome :) How can I help you today?


I have some questions I want to go over


Great! Would you like to put one on the board?


It's 56x+45=188


Okay! Do you have an idea how to start?


No can you help with it please


Sure! So our goal is to find out what x must equal


Okay


To do this, we apply valid algebraic operations to both sides of the equation, making sure to keep the equation balanced, until we've transformed 56x + 45 = 188 into x = something


Can I put the question on the board


sure!


very good! Nice first step


Is that right?


That's correct! Nice work :)


Ok the next question is 45x-56=265


okay! Can you give this one a shot too on the board?


Yes can you write it for me my writing is messy


sure :)


Is this right


Yes!


Any other questions? :)


Hi


Yes I'm sorry


Hi Liam! How are you?


hi again, sorry about before I lost internet I'm back now


awesome :)


this is the last one I had to check


okay! Give me a minute to work through it


ok


That looks correct!


thanks!


that's all i had


Awesome! Have a nice day :D


you too! bye!


Maya


what do you need help with?


Could you give me some practice problems that are similar to these?


sure :)


Given Points: A, B, C, D, E (with B as the vertex for all)

1) Write another name for ∠ABC

2) Name a right angle.

3) Identify a pair of congruent angles and find their measures.

4) What type of angle is ∠DBC? (acute, right, obtuse, or straight)

5) Which angle is larger: ∠ABE or
∠EBD? Explain how you got this


Is there an image to go off of?


okay there


Perfect! is number one CBA?


yes :)


And then DBE for the second?


yes!


and then CBA and CBD for the third?


yeppp good jobb'


and then acute for fourth?


yup


anddd ABE for the fifth?


I got that because ABE 70 degrees and DBE is 90


yayyy good job!


Thank you!! I think I a got a better understanding on this now, thank you for your time! I appreciate it so much!


you're sp welcome!! you're doing great :) have a good dayyy


you too !


unit 1.5 ap precalc


polynomails


Hello!


Hi


How is your day going?


Great! yours?


It is good!


What do you need help with today?


polynomial equations practically, I kinda forgot my alegbra 2 skills


finding zeros and mulitplicty


Do you want to give me a problem and we can work it out together?


Yeah! in my copy it is already solved but I still dont get the concept, is that ok?


Yes!


those are the ones


Ok, lets start with 1


Ok


The first apart is difference of squares!


yeah!


And then for the second part, they found the 2 numbers that multiplied of give you 4, and added to -4


yes


Then since that is the same thing twice, it can be squared!


so you practically just factor it out?


Oh!


Do you want to review how to graph it too?


So we first find our zeros. That is all of what x would equal if you set them to 0.


In this case, they would be 3,-3 and 2


Ohh


And then, you cross at any of the factors are to a degree of 1. When they are squared, you bounce instead of crossing.


In this case, it bounces at the 2


Yeah! that makes sense


Do you want to do the second one?


So first, we can take out a GCF of x, since all of the terms have at least one x in them


And then they factored it out from there!


that makes sense I honestly didnt notice it at first


And then to graph it we find the roots!


Yeah!


What are the zeros at here?


and 0 because of the x


Yes!


yeah!


And then you graph them, and it bounces at the -5!


Yeah because when you factor it  both are positive


nice!


Could you go over4? on the other page


So first, we put the roots into the equation


yes


The from there we can combine the last 2 terms


how so?


Do you understand how I got to here?


yeah you factored out the 2i?


and the 4


I distributed everything out.


why is it 4i squared


oh nevemrind


Do you notice how the middle 2 terms can cancel each other out?


and i is equal to the square root of -1


so it would cancel out


Then lets square the square root


yes!


That is how to combine those two terms!


got it!


Then from there we need to find the a value!


We do that using the other information they gave us!


Put 5 in for all the x


and it equals -145!


Yes!


Do you want help solving for A?


I think its understandable for the most part


Sounds good :)


yeah I got it you plug in the 5 multiply them and than divide wthe result from the a


yeah!


I have to go now, but I hope our time together helped!


Thank you! that helped a ton!


Your welcome!


have a great day! :)


You too :)


hello


How may I help you this afternoon?


you sound like a bot


but I need help with math


That's funny.


Can you show me your problem?


its like really hard


can you upload an image of the problem, by any chance


I can try


I am not sure what you are drawing


5+2 does not =20


I know it is 15t


k=mx+20 is the austion


question


that is the equation of a line


what is it that they want you to figure out?


so its 2 piggy banks


15 in each


15 pennies in each?


15 dollars in each


yes


and one piggy bank get 20 dollars


k=mx+20 is what they put


k=mx k=5 wast the first one


what do you mean that one piggy bank gets 20 dollars.  I thought they both had 15 dollars


Sorry, but I don't really understand the problem


hello?


are you there?


hi


waht do you need help with


hi can i  get help with this because i need to relearn algebra because i forgot how to do it


okay


what are you stuck on


anything in specific


yes this questions


what are you thinking about it


i need a general thought of where you are


i only know that a number with no exponent is 1 degree


okay i see


do you know how to complete the square


no


we need to elarn that first


ok


first things first


i have a google doc for this i can paste it into the board and you can understand what it says


read this and make sur eyou understand it


ok i see them


so first we have to make your function into the form of (x-h)^2+k


does that make sense


tell me what you get


whta would be h)^2?


okay


so


you are supposed to condense the original equation and make sure that when you square it, it goes back to what the original formula is


so would it be2+k?


it could become ((x-3)^2


that is what (x-h)^2 is


how did you get 3


bc when you simplify the equation it goes back to 6


its a perfect square


how do you simplify the equation?


when there is no 3 in the first equation they gave


look at this


you should know this information


this is how you complete the square


does this make sense or no


ok kinda


now try it yourself


ok i get everything else but how fif you get 9+14 at the end?


that comes from completing the square


like you have to put it


it comes with completing the square


so i have to do x^2-(6x+9)?


what you said does not make any sense sorry please say it in other terms


ok so i have to do x^2


its on the board


yes


that is what you are supposed to do


like this is how you complete the square


does that make any sense


do you want another example


are you still tutoring?


hi! how are you today


Hi Alex I am doing well. How are you doing and what can I help you with?


I'm good :)


I was wondering if you could check my algebra answers?


I can do that show me your work and your answers so we can get started.


9. 2
10. -2
11. 3
12. -5


I didnt really show any work since it had graphs


could you zoom in on the graphs so I can see the numbers?


do u need another picture or is that one fine


This is fine. Looking at your answers it looks like you got everything correct.


cool thank you so much


glad I could help


I hope u have a good day :)


you as well


Hello!


hello


Ive been waiting forever lol


what do we have here


I am currently working on this, when finished


I will let you know


got it


and then you can check over my answer


yea sure ofc


can you check the red im gonna work on the blue rn


ill be back in 10 okay? ill check over everything as soon as i get back sorry


kk!


i put it in and its correct now im going to work on a new problem


you can check if its right when i finish


alright im back


hows it going so far


Ok this is a new problem that I will need help with I've done the other ones already when I sent that message and theyw ere correct


okay good


take an attempt at it first and we can go from there


Ok


is the prt right


im take an attempt at it let me see


ok


p is correct


r is a monthly rate so it should be 0.028/12


and t is almost there just need to multiply 40 periods which is the total number of payuments


yep i'm doing that rn


itll show when i finish


got it


take a look


thats perfect


just i rounded a little more so mine became 907.83


pl


you round to nearest cent


alright got it


nice work


can you check blue


yes thats correct


now which one for c


well they want you to try both


and see which one has less


k


so the bank would be cheaper


right or wrong


yes exactly


but did you find out by how much more


going to rn


got it


is it right?


hello?


nope c is incorrect


oh maybe bc its i pressed blank instead of savings?


it should be bank


it said it was wrong maybe its my calculation idk


can you check over my math


my answer was by 48009.60


but my rounding is different


i dont round


until the final answer


yea see


yeah your not supposed to


"Do not round intermediate computations"


okay let me do it once more


kk


sorry i didnt see the do not round intermediate computations on the photo you gave me


almost done okay


ok


i gto 48008.88


can u show ur calculations on the whiteboard


working on a new one rn


was i correct?


idk bc i put the original answer i had and it said it was wrong i think its bc i pressed savings idont remember


hmm okay sorry about that


its kk


check my math


okay let me take a look at it


a is correct


part b says 8.1% not 7.8% lets try that one again


ohh right


dont stress it


simple mistake thats why im here


yep!


ok take a look


perfect


thats what i got


now c


you're getting a hang of it nice


is this right


yep its right


next one


can you check my math


nvm its correct next problemm


sorry im back


its ok


working on the blue rn


got it


take a look


okay


everything looks good to me


i got the same answer


and its online lending company for c?


yes


and what is the total amount less than


thank you, its correct!


ofc you got it


i'm gonna head to english now


thank you for your help!


okay thats cool


good luck!


geometry


hi David


Hello, how's it going, sir?


Uh, if you have your mic, just let me know.


Um, I'm sorry, I'm muted.


It's just say though, huh.


No, it's already on.


my wife is sleeping


Do you actually have a mic, sir? Oh.


OK. OK, I see.


so I need to be quiet


Good evening geometer


what will we work on today?


Is this a real person.


What do you think? =))


I don’t know I just need help 🙁 my mom made me sign up


So your goal is to deepen understanding of a topic


What would you like to know deeply about?


well, don't worry, I only work on your need


no matter what, I just serve to help you achieve what you want


no judgment, no complaint, no force


Okay. So far.. my teacher doesn’t give notes particularly but


I have questions talking about midpoints


oh


And I guess I don’t understand the word problems


I’ll give an example of one of the questions:


I'm all ears


“Find the coordinate of J if K(-5,10) is the midpoint of JL and L has coordinates of (-8,6)”


just to make clear, you just have problem understanding the word problem, or you want me to help you understand deeply the midpoint?


I suppose both


alright


I have no notes to review because my teacher doesn’t hand out any. So I have nothing to reference off of


don't worry


let's treat it as an opportunity to understand deeply midpoint


Oh and also to add the JL had a line on top of it


I forgot what that stood for


just thought I’d mention it because I can’t type that out on keyboard.


don't worry, we can draw it out


first, tell me what you already know about coordination of point?


we will start on what you have already understood


Um


As in the coordinates it’s mentioned: (-5,10) (-8,6)….?


yeah, you can identify the coordinate. That's great!


Oh okay. Yay! 😀


so what does (-5,10) and (-8,6)?


what do they mean?


if you are struggle with describe them by word, you can draw it on the board


Oh. I’m still learning this app, okay I see now.


wait, I will draw a bigger cxy plane


alright


what does (-5,10) and (-8,6) mean?


feel comfortable to tell me whatever you think


(-5,10) represent the midpoint of JL or something


that's true, but I mean what do they mean


what do they suggest/ definition?


for now, just focus on coordination. everything else, including mid point , is the later work


For example, if I ask you what does "point A has coordinate (8,3)", what do you think?


The point on a graph..


Or something..


that's trueee


Does this all tie into a formal of some sorts


Regularly, coodinate prefer to something on the graph


Because I think I remember there being a formal. But I honestly not sure if that’s something else..


you know it means something on the graph, it is great


now, what do the first number and the second number mean?


K(-5,10 (-8,6)


Oops


Hold up mistype


it's ok. Happens often


I thought you could add a space in lines but I guess not.


Erm. Hold up


you can try using shift + enter to get to a new line


point


Okay yeah something like that


so you have already know that the first number represents x-coordinate of the point, while the second number indicates the y-coordinate of it


Yes


now, can you plot the two points on the xy plan that I have provided?


Yeah, it might not be directly right because I’m on my phone. So, we’ll see


Idk how to zoom in.


I can make it bigger if you want


Is it enough?


Okay. Yeah. I think that’s good


😭 baaalright


the first one is correct


Okay so that’s that one


it's ok


I get it


Okay 😎


can you write the Capitalized letter next to the point for us to distinguish between them?


you can use letter mode


it's good to chat on phone because you can use emoji


Yeah 😎


Anyways


Ok,


Maybe not because I can’t really place the text box


you did it right. What's wrong?


Oh, my end must be different


Because it’s not going where I want it to.. but it’s okay


actually, I did edit it a little :D


Emily


Okay. Idk how to add another box. Soo


I can add it for you


Okay


alright


now, turn to midpoint, what is it's definition


you got everything about coordination perfectly, let's heat it up


The middle of the two lines


which line?


So wouldn’t that be -5,6


Like, the midpoint would be where the two lines cross… or meet..


I think


Educated guess 😢


ah, I see


so what you are thinking of..... is the definition of the intersect point


Oh


Bruh.


oh, I guess looking at the graph make you confuse


let's refresh


ignore the graph


Okay.


Literally, what does midpoint mean?


The center point..


very closeee


what does mid short for?


Middle. Center point of the lines in the middle


Right, right.


yeahhhhh


so midpoint is the poitn in the middle


😎 let’s go.


between C and D, which one is the midpoint of segment AB?


Between c & d…


ah, I forgot to tell you to get backto the graph


sorry, my bad


Like, the number on the graph or something.


Idk 😭


using our definition "midpoint is the point in the middle", what is your guess


i saw you draw a red line, that is a good approach


I’m over thinking- this gotta be easier than it sounds I’m sure. But lowkey idk


no problem


your effort is really good


so, between C and D, which one seem being closer to the middle of AB?


Um


3 & 9


A= 3


actually B=10


So uh


Oh


I did it on purpose


My bad 10


because I just expect you to observe the xy plane


Ok-


so, which one do you think, C or D?


C


Idk


C closer to A so uh


Yeah


oh, that's a point


however, let's check it again


my question is which one is midpoint


Do you want a number


if you prefer number, yes


Idk if I’m even on the right track


it's ok


I usually lost when I first faced geometry too


Yeah, I can’t really keep blaming myself because the teacher I have sucks


So imma guess the middle of C & D if it were a number be 6


Because if that’s not it. Then lowkey idk what else would be the middle


my question may be a little bit hard


let's work on another question


No it’s probably not. I just don’t understand


what do you think is the middle of 3 and 10?
choice A: 5
choice B: 6.5


So 3+10=13


good approach


trueee


Was that it this whole time 😭


by using formula, you figure out the middle number between 3 and 10


Yeah.


Now, if i ask you: "the middle number of 3 and a number x is 7, what is x?" what will be your guess


you can use the board


to create equation


Correct!


how do you get it?


Chris


you get it if it is 1-dimension


I that part now


let's work on 2-dimension


Oh boy


Oh, my phone turns off at 9:50


I’m cookedddd


oh, Let's speed it up


Okay 👍


alright


what is the midpoint of A and B?


hint, work on each dimension


dimension x and dimension y


Hello, are you there


Yeah


I wrote it


that's trueee


brilliant


Welp I gotta go in a minute


But thanks for helping!


you're welcome


you get everything perfect


keep going on


good night


feel free to make request at any time ;)


Hello, What can I help with today?


I have a few worksheets that I need to get done by tomorrow


Sure do you want to start with a specific problem?


Yes please, I can send you a picture


Ok sounds good


Did that go through?


Yes I see I can see it now


So the first step is to try to combine the like terms


Do you know how to do this


Not really


We learned it in class but I have a hard time in math


Ok thats fine ill explain it here for you:


For our problem the two types of terms we have are a number with a variable and just the number


so 2b and -9b are both with b's, and 4 and -18 are both that are just numbers


those are like terms, does that make sense?


Yeah


Ok so to combine those terms we have to get all the numbers with b's on one side of the equation and all the normal numbers on the other side


So based off of this how do you think we can move one of the b's on the other side?


I’m not sure


Ok I can help


Do you add something?


Yes you can start with that


So we could add 9b to the other side of the equation to 2b


to combine those like terms


Do you want me to draw these steps as we go?


Yes please


Ok sounds good


So the lines i drew are saying that those terms are like terms and we can combine them


You can do it in any order because its addition in subtraction, but I will start with adding 9b to 2b


Do you understand why we do that?


So now we have 11b + 4 = -18


What do you think we can combine next?


Add the 18 or minus 4?


Yes I would minus 4 so we can have all the b's on one side of the = and the normal constants on the other side


Because at the end we have to solve for b, by getting it by itself


now its 11b = -22


How can we get b by itself?


Add 11b and -22?


Think about it this way: right now 11 is being multiplied by b.


how do you undo multiplication?


Divide?


Yes so what would the equation look like now?


11b divided by 22


If we did it that way the equation would be 11b/-22, but remember we want to get b by itself


So we could divide 11b by 11 so 11b/11 = b and -22/11


Does that make sense?


I think so


Do you have another one we can go over like this?


So this time you can go through the steps and I can help where you get stuck


Ok


Do you want to draw too so i can see your steps?


Sure


Ok great, let me know if you get stuck somewhere and ill let you know if i see something too


Ok for this first step I noticed that you are trying to subtract by 9 right?


Yeah


There is one problem with this, (3+B) is inside a parenthesis. Meaning that you cannot move anything until you solve for the parenthesis


Do you know the phrase PEMDAS?


Yes


Ok that is the order of steps to solve for


so P is first, parenthesis


So we have (3+b) and it is simplified, so we look outside the parenthesis


do you see something that is being multiplied with the parenthesis


So do that first?


Yes do you see what Im talking about that is being multiplied by the (3+b)?


if not i can show it by drawing


Can you show me?


That part i underlined is the first step. the - is actually just a -1(3+b)


Do you understand how that can multiply


Is it the -1 instead of the b”


Yes because we cant do anything with the b and the parenthesis because its on the other side of the equation


But we can multiply -1 with (3+b) because they are touching


Do you want to write out what the equation will be after this step?


Is it -3?


We still have the 8 and the other b from inside the parenthesis too


Are you stuck on a part?


Yeah I just don’t know what to write out next


Ok so after we multiplied the -1(3+b) what does this become


well it was 3+b at first right?


so multiplying both by -1


it just switches from + to -


does that make sense


3 x -1 = -3, and b x -1 = -b


I’m sorry, I have to go, thank you for your help today!


ASAP


I had a tutor but he left bc I wasn't answering him


Please give me 2 mins


Hi can you clear the whiteboard and post the question again? It is messed up at my end


can u see the board


the whiteboard is clear. have you posted the question again?


ok I see it but I need to zoom in


ok this is perfect thanks


no need to make it bigger


which question do you need help with?


ok so the ball is on the ground and y=0 on 2 occasions. 1) when it is kicked and 2) when it hits the ground


so in that case you need to solve for 0 = -6*t^2+11t+3


can you solve this quadratic equation?


for a. it is 6 feet


and b. it is 0.9167


how did you solve for a?


I plug in 1.5 for t


that is the correct approach


so yes the answer is right


how did you solve for b/?


0.9167 is right but I am curious how you got to it


perfct


ok no on to (c) as I said solve the quadratic for y =0


what do you  get as the two values of t


I don't know to do this one


for a standard equation ax² + bx + c = 0, have you seen this formula before?


x = [−b ± √(b² − 4ac)] / 2a


how to do that


can you see my scribbles on the whiteboard?


let me know if you are following


yes


this is a lot of work I have a test tues


so far so good?


so we plugin for a and b and c


that's a lot of work


r we plugging in the number yet


thats the final equation for a quadratic


which I typed 15 minutes ago but you had no clue about. so I took 15 minutes to explain how we get to that equation


ok


if you now plug in a b and c, you will get two values of t


one negative one positive


that is a lot


the difference between the two times is when how long the ball is in the air


hey if it had been that easy, you wouldnt be here asking me about it


yeah


the equation I have derived is the most generic quadratic equation applicable for all equations of the type ax^2 = bx +c =0


ax^2+bx+c =0


-1.18+ or sqrt^2-4(0.01x^2) (2)


like that


you might want to double check the calculation


no that the calculation it is the equation written out


ok cool


so what are the two values you are getting?


can u do this with me on the whiteboard


what are the values a, b and c in our equation?


a=0.01x^2 and b= 1.18x c=2


no


thats our equation, do you agree?


so if you were to compare that with ax^2+bx+c=0, what would the values of a.b and c be?


a, b and c


what?


are you following what I am asking?


yes I am following


so whats a b and c in our equation?


those are the coefficients


-6, 11, 3


correct!


so now plug those values in the generic equation I derived to get the two values of t


so u can get ur answer by the graph 2.074 seconds


thats the positive value


whats the negative value


do we have to have the positive and negative


yes


I will explain why


you see the ball could have only been at the ground when it was kicked and when it hit the ground


on the ground*


ball on the ground implies y =0


agree?


when you solve for both values of t, you know at what exact times the ball was on the ground


when you subtract one from the other, you know how long the ball was in the air


so whats the negative value?


I don't know


What's b^2 - 4ac


idk


a=-6, b=11 c=3


yeah


You should be able to solve the (-b - sqrt(b^2-4ac))/2a


Check the equation I derived


You already have (-b + sqrt(b^2-4ac))/2a


Which is 2.074 (you told me the answer)


Now give me (-b - sqrt(b^2-4ac))/2a


how to do that


Do you know how to get the square root of a number on your calculator?


yes


ok what is b-squared - (4 times a times c)


b*b - (4ac)


Give me that first


is that right


That's b^2


Keep going


what do you mean


What's the result of b*b - (4ac)


like that


You 121 - (-72)


Now square root of that


Subtract b from it


No hold on. Its -b- sqrt(b^2-4ac)


No. b=11


So from my equation


Give me sort sqrt one more time


sqrt


So -11-13.89


Now divide this by 2a


is  that right


u there


No


Whats 2a?


2 times a


Whats a


Good. Sk whats 2a


-6x2 = ?


So that's 2a


Yes whats the answer


How can 24/12 be equal to 2?


2 but I did the decimal


-24.89/-12 = 24.89/12 = ?


Do it again


Does that match the positive value of t you gave me?


yes


Perfect. Now let's do the other value.


so for the equation -b/2a


What was sqrt (b^2 -4ac)


-b is -11


You solved the sort above


Sqrt*


I forgot


The other value of t is


(-b + sort (b^2-4ac))/2a


Good. So whats -b + 13.89


can u see the board


No this is simple subtraction


Do it on chat


it on the worksheet that is on the white board


What is -b + 13.89 where b =11 ?


what to plug in for that


Can you please follow my chat and answer my question?


yes


ok can u answer my question


Wrong. Please do it again


Now divide by 2a


Negative or positive?


Ok what are the two values of t we have derived?


so I am confused on the fierst


Let's get the answer first and then I will go over whatever is confusing you


What are the two values of t


-0.24083 and 2.074


so how did we get 2.074


Correct. So the total time that the ball was in the air is 2.074 -(-0.24083)


That's the answer


yeah I forgot how we got 2.074


using that


If you scroll up and read the chat you will find the answer


what is -b


I just need the -b and a


2.074 = (-b-sqrt(b^2-4ac))/2a


that does work


square root 193 is 13.89


-0.24083 = (-b+sqrt(b^2-4ac))/2a


that doesn't work for -b value


That's how you get the two values of t


It will once you figure out what you are plugging in wrong


the bottom u divide by -12


Correct


I don't know -b value


Look at the equation on the problem sheet


yeah a did


So whats b


So whats -b


OK then


0.916 does not get 2.074


You have to practice using a calculator


ok


Sqrt (193) = 13.89


-b = -11


So whats (-11 - 13.89)/2a


can u help with 4. b.


Well did you get this one?


yes


thank u


So whats the final answer?


For 1c?


No it is not


seconds


and -0.24083 seconds


It is 2


how is it two


It is 2.074 - (-.0.24083)


What does that come out to be?


So approximately 2.32 seconds


yeah


That's the answer


so got this can we move on to question 4.b


Can you post it on the whiteboard again?


My whiteboard is wiped clean


hello


how are you


I’m good how about you?


good thank you for asking


ok give me one moment please


If it’s okay could you check my answer?


Of course!


yeah sure


OK, so we can see the, uh, now is 6 less than


4C + 10


and uh less 14.


So first of all, we minus 6


no minus 10, both sides, right?


So we get


so now you can see we get 4C in the middle.


So


um get the single C, we can divide 4, so it's -1


1. So that's the answer.


Make sense


Ohhh okay yes!


any other question?


How would I graph this?


So it's -1 less than C, so we cannot get negative 1, right? So for -1, we get


So, yeah, and for one is greater than C. So we cannot get one year. So it's, it's, yeah.


that line


Ohh alright thank you!


No problem. Have a good day


I need help on proofs


Alright, lets see


ok


ok, I got it


so I understand the reasons part, I just don't understand how to get the statements written out in the correct order.


I just dont understand how this site of your work


wdym?


do you know how to solve it?


no, that's why I need help


lets try opening up the angles


say, the angle <DHF is the sum of each smaller angles?


so <DHF=m<1+m<2?


exactly


and if you do the same for the other angle


and <EHG=m<2+m<3?


yeap


oh, then


can you finish it?


then we remove the <2 from both sides


yes, thank you


you are welcome


anything else you might need help with?


no, thank you


ok, take care


bye


Hello, Oakville


afternoon


Do I have to put the values in a decimal, or in another format/


what oes the red text say


(unmatched paren), syntax incomplete, (unmatched parens), syntax incomplete


this is tricky, your answers are right...

maybe write n*pi/2 (where n is an odd integer). try it


Okay, I will try it out


I mean, your answers are right, I don't know how else to write it


Like this?


What does that say?


n pi over 2


Oh, I see


It says syntax incomplete


oh


specify tant n is an odd integer


Yeah


No worries, thank you for the help though!


Have a good rest of your day and week!


hi


hi!


I don't understand this question


okay sure, happy to help


do you know how to solve this question?


i could definetely try :)


so do you know which angles they are talking about?


when they say ADB and CDB?


I think


Yeah, I think


so, do you know anything about the sum of those angles?


something about 180


I forget


yes!


the sum of angles ADB and CDB is always 180


why?


because the straight line which the points A, D, and C lie on always has an angle 180 degrees


ohh


whats up with point b then


in this case, point B doesn't really play any role in the problem


okay


So, to solve the problem, you would find 2 angle measures that sum 180 degrees


any two numbers that add up 180 degrees?


but, you do have to be careful because if you notice, angle ADB is larger than angle CDB


so angle ADB does have to be larger in measure


so any two numbers but adb has to be a larger number?


yes


but they have to add up 180 degrees


so an example would be 150 and 30, or  160 and 20


ohh okay


yeah that makes sense


happy to help!


:) thanks for ur time


no problemo!


have a great day!


Hello, how are you?


hi


I am well.  thank you for asking.


how can I help?


Can you see this?


oh the starting


can we start here


where?


so I have to right


constant function


linear


like the parent functions


should i do


f(x)


or y


it's the same right?


f(x) is probably preferred.


yes


So is this right?


wait how do u find the leading coefficient


for C


nice


i was wondering if i was doing it wrong


but nah


no


you got this


Oh also I'm just reviewing for my quiz


I'm ngl I haven't been listening to my teacher at all


kk


so im just going thru my notes


so there's def a lot i dont know


but the beginning i do


as the value of x gets smaller, the value of y increases.


all good


but odd degree and positive leading coefficient


mhm


sorry, you are correct


isn't it downward?


ye


yes


I was tricked by the first term.


great work


wait


no work here


y


did i do it wrong?


sorry


wait a minute


to find the x intercept


you set y = 0


0 = x + 5


x = -5


0 = x + 2


x = -2


0 = x - 1


the y intercept is incorrect.


x = 1


x intercept is correct.


for y intercept u set x = 0


y = (5)(2^2)(-1)


yes


wait


when it has a multiplicity of 2


that means that it turns right


let's mark the zeros.


you did.


good


where is the y intercept?


looks kinda wonky


would i Algebra 201 on quiz for doing somethin like dat


yeah


sure


dam


this graph looks beteer


compared to desmos at least


smooth it out


like a U or upside down U.


getting smoother.   good job


thx


x to the fourth makes a W.


cursive W


huh?


its wrong?


no


it's good.


I'm saying x to the fourth power makes a W.


right?


um


i mean it looks like a W


kinda right?


yes


wait can u look it up on demos


it looks a lil different


I got the same thing.


all good


Now you try


what does that even mean


what was i doing before?


that means it is the student's turn to work on the questions.


lol


these are a little tricky.


term at the end


huh


wait sorry i was looking at something else


no answerrr


iss dat hright?


wait


6 or -6


0 = -(x+6)


0 = -x-6


x = -6


is that how u do it?


yes


don't put the -1 with the x + 6


qdym


distrupte right?


keep the x + 6 separate from the outside negative one.


distribute


no to distribute


so how is it done


ot msynr


maybe we do distribute....


well i got it right somehow


so


the negative one has to go with one of the terms.


but -1(x+6) = 0


then -x -6 = 0.


then x = -6.


well either way


that's the same as Ms. Davis


kinda weird right?


yes


indeed


new sectionn


is this all right?


do you need help with Example 2?


sorry i was looking at something


can I make a suggestion?


is that wrong?


just a different way


wats the difference


not my bes


best


Michael i gotta take a math break


you are doing super work.


nothing to stop you from making 100!


lol i didnt get one wrong


but for my notes


i only did pages 0-12


and there's 35....


but ima take a lil nap


I apolgoize.


and do more


i need to go to bed.


please sign on again.


Brooklyn


thank you for helping!


great work!


you're welcome.


yeah i actually didnt do bad


i knew most of it


not at all!


i was on a streak


bye


have a good night


Hello!


Hi!


Are you able to look over my answers?


Yeah of course


lets see


I think it is correct


both of them are


Okay, thank you.


no problem


do you have any other questions


Not yet, that was it for now.


okay then


Bye!


Can you turn your microphone on please


Marcus


what for


It's easier for me


To just listen to what your saying


mm okay well if you have a question then am fine with explaining with my mic


Okay well what is 34x+78=3090


Hi.


Hi


wait but its technically the same thing lol


its just typing out what i say


Yes but I like being able to hear someone because I don't really look at the chat


well thats fine then. do you really need help with that question tho


Yes


Mm, OK, so.


for this question, you have to


we are finding eggs, so we have to um


send the 78 to the other side.


And then divide you by 34.


OK, wait, let me phrase this with that. So you have to


subtract 78 from both sides, and then divide both sides by 30 folding pink eggs.


lol


i hope you got that tho


That's funny it thought you said eggs and yes I understand that now


lol ok


at least you get it


mhmm thats how you do it


would that be all


I have one more question


okayy


What is 79x+45=300


OK, so I think you'll be able to attempt this question because of


um


it's basically the same thing.


as the first one. So, yeah.


Is this right?


yup


Thank you so much for helping me with those questions I really appreciate your help and time have a great rest of your day


okay byee. welcome btw


Hi David, what seems to be the problem?


I am struggling to solve this problem on the white board. it is polynomial equation


sorry if I'm reading this wrong, does that say 1.3x^3?


No, that is a #1, not a point, sorry for the confusion


ahh I see


Alright, so how have you been trying to solve this so far?


Well I'm struggling trying to decide which method of factoring to use


i see, well do you know how to solve a quadratic equation?


A ns M method?


and*


Thats one way you could solve this equation


But wouldn't you use GCF first?


If your teacher wants you to do it that way we can do that


But theres easier ways to factor this


not exactly


I want the easier way


Alright


so if we were able to turn this trinomial into a quadratic, that would make it much easier right?


yes


Then we could just use the quadratic equation


so AC method?


so how could we take out one of the x factors?


I don't know


Well, we could factor our x from all of the terms here


We could take out a x^2 or just an x.


just an x, since we cant take out x^2 from 48x


ok


we coudl also technically take out 3x, since all terms are divisible by 3x


which would be what?


great!


48x/3x is 16, by the way


also, make sure to keep the negative signs


i was doing 24/3


which is 8


sorry about that, might have been confusing


is that right?


Almost, the negative sign was on the 8x term, not the 16


Great!


this is perfect


now what?


now we know one of the solutions is 0


so we need to now factor the inside quadratic


so how would you factor x^2 -8x + 16?


A and M


so what would it factor to?


is that correct?


Almost


This multiplies to x^2 - 16


try switching the positive to negative


there we go, now this multiplies to the correct quadratic


now what would be the full factored form?


great!


thats the answer


ok


does it make a little more sense now?


yes


sounds good, any other questions?


no


nice, have a good day!


you too!


hello


so what is your idea? How would you solve that?


i dont know how can u solve it


please


what is the goal of that problem?


we want to write something like:


the a, b, c, d and e are the coffeccients


how did I know that th4 is the higest power in that equation?


I tihnk you are away. Some tips how to solve this:
- a will be 1 (note the red arrow on the board)
- finding b, c, d and e by hand will be hard, so we can use a trick
- can you think about a polynomial which has roots -2, -1, 3 and 4?
- can you think about a polynomial which has -2 as a root? what about a polynomial having -1 as a root etc?
- if f is a polynomial having -2 as a root and g is polynomial having -1 as a root, what can you say about the polynomial f*g?


Hi Marcus


Hello


If this is your first session, welcome to Brilliant Minds! How may I help you?


I was hoping I could receive some help in completing a homework assignment.


OK. I see problem (5) on the board.


Is that the problem you wanted to work on?


That’s the first one.


Should I send the rest right now?


No. Just keep problem 5 for now.


What limit did you find for problem 5 ?


I was having trouble completing the problem.


OK. First off, if you plugged in x=-2 into the expression, you'd be dividing by zero, correct?


Yes


So the limit could be +∞ or -∞.


Did you learn about "limit from the left" and "limit from the right" ?


I learned about it but I’m confused on when I should use the rule?


I'll explain. We'll start with "limit from the left".


Let's look at the value of the expression for a value of x that is just a little to the left of -2. Can you try x = -2.001 ?


I got 0.001


Can you try again? I'll write on the board, below your uploaded page.


Don't forget the negative sign in the denominator.


0.999/(-0.001) = ?


Did you find the value?


Good. -999 is correct.


So the answer is negative infinity?


Yes. The limit "from the left" is -∞. Now we look at the limit from the right.


Do you see the graph I uploaded?


As we move toward x=-2 from the left, we follow the purple arrow.


As you can see, to the left of x=-2, the function goes to -∞.


Can I do this without a graphing calculator? We aren’t allowed to use them for these problems.


Yes. We're also doing it without a graphing calculator. I'm just showing you the graph so you know what the function is doing.


Now try a value just a little to the right of -2. Can you try x = -1.999 ?


Okay.


Yes. And 1.001/0.001 = 1001, correct?


Yes.


So this tells us that the limit from the right is +∞.


And because the limit from the left (-999) is different from the limit from the right (1001), we say the limit "does not exist" (DNE).


Because -∞ is different from +∞, the limit DNE.


That makes a lot of sense, thank you!


You're welcome.


Can you help me with more problems?


Yes. We can do a couple more if you like.


I see problems 8, 11 and 14.


Can we do those?


Sure. What's your guess for problem 8?


infinity?


Yes. +∞ or -∞ ?


Correct. For this problem, we're only interested in the limit "from the left". So the limit is +∞.


What would you guess for problem 11?


For the limits approaching infinity I’m not sure what rule to use?


The function is a fraction, with a polynomial on top (numerator) and another polynomial at the bottom (denominator).


Can you tell what is the "order" of the polynomial in the numerator (top) ?


Smaller to larger powers?


Look for the highest power of "x".


Correct. And what's the order of the polynomial in the denominator (bottom)?


The same, with the highest power of 20


That's right. Here's the method we'll use.


When x goes to infinity (x→∞), we can ignore the lower powers, as I'll show on the board. Focus only on the higher powers.


After removing the lower powers, can you simplify the fraction?


The x^20 on top and the x^20 at the bottom would cancel out, correct?


Ohhh. Yes i forgot.


So -2


Yes. That's the limit.


Okay


For problem 14, because x goes to infinity (x→∞), we use the same method. Ignore the lower powers on top and at the bottom.


Would the answer be 1?


Not quite. Can you find the "order" of the polynomials on top and at the bottom?


On the top it’s just x^7 and on the bottom it’s x^5 - 9


Yes. There's only one term on top. But at the bottom, we can ignore the -9.


Can you simplify the fraction?


Yes. You're dividing two powers of x So you subtract the exponents, correct?


Yes


So x^2


Right. Now can you find the limit as x → ∞ ?


Is it x^2?


Yes, but we want the limit. As "x" goes to +∞, x² also goes to +∞, right?


For example if x = 1000, then x^2 = 1,000,000.


I’m confused


The limit is simply ∞. I can explain further if you like.


Yes please


Do you see the graph of y = x^2 I drew?


As x→∞, we move toward the right along the x-axis.


Now follow the black curve for y = x².  As x→∞, y→∞ following the purple arrow, correct?


Correct


In other words, the graph continues to infinity as we move toward the right. So the limit of x^2 is simply ∞.


Okay. Thank you


You're welcome. That completes the solution, and it's all the time I have. Any quick question before I go?


Does it work the same when the limit is approaching - infinity


Sorry when x is


Yes. I'll show you on the graph.


As you move toward the left (x→-∞), x² goes to +∞ because a square is always a positive number. So the limit of x^2 as x→-∞ is again +∞.


Okay that’s makes sense.


that*


We can end the session. Feel free to make more requests on TutorConnect as needed, and other coaches can help you. Have a good evening.


Thank you, you too.


Hi Alex, how are you?


hi! I'm good, how are you?


I am doing well. How may I help you?


I was wondering if you could help me with a math problem? my last tutor recommended I get help from someone else bc its kind of hard


I would be happy to help.


I will take a look at the question you posted.


I think I got it. Just double checking something.


ok


Ok. Are you familiar with how to find the inverse of a function?


yes


Can you write the inverse of y = mx + b.


The equation you have is not entirely correct. For the inverse, you want to solve for x in terms of y.


Let me know if anything is unclear.


so then what's the inverse


I'll walk you through it. We want to solve for x in y = mx + b, so let's start by putting the b term on the other side of the equation. What would we need to do to accomplish this?


subtract b


That's correct. Let's subtract b from both sides of the equation.


do I do it in the old problem


Yes.


It should be y-b = mx + b -b


That's correct. Now how would we remove the m from the right side of the equation?


divide


That's correct.


You now have the inverse. Nice work.


x = (y-b)/m is the inverse of y = mx +b.


is that all?


Now we need to find conditions on m and b so that the function and its inverse are equal.


ok


The fact x is written in terms of y for the inverse may lead to confusion. We can write the inverse as y = (x-b)/m. It means the same thing. Let me know if this is unclear.


makes sense


Ok. So we want to choose m and b so that y = x/m - b/m and y = mx + b match. Let's start with m. Can you think of a value of m that can match things up?


m = 1 is a good choice. Let's substitute that into both equations and see what we get.


We should get y = x - b for the first equation and y = x + b for the second equation.


Does this make sense so far?


yes


Ok. Now for y = x-b and y = x + b to match, what should we choose for b?


Yes, that's correct. If we pick any other number, the sign won't match. 0 is the only choice.


So m = 1 and b = 0 is one set of choices. We are however not completely done.


What other value of m will make the slopes match between y = x/m - b/m and y = mx +b?


Im not sure


m = -1 will also work. Any other number but 1 and - 1 will lead to the slopes being different from each other. Let me know if this is unclear.


Ok. What would we get for the two equations if we substitute m = -1?


-x+b for both


That's correct. So which values of b would work for the equations to match?


isnt it still 0


Zero is one such value. Any value will work since we have the same intercept for both equations.


The equations will match no matter what we put for b.


so then what do I put If anything works


For this part you can just say m = -1 and any value for b.


ok


So the final answer would be m = 1, b = 0 and m = -1 and any value for b. There are two sets of solutions.


that's hard


It's definitely a more difficult problem.


thank you


You are most welcome. Is there anything else I can help you with?


yes pls


Sure.


I took a look. So the way to interpret g(x) is if you substitute an x-coordinate into g, g(x) gives you the y coordinate. So part (a) is asking, what is the y-coordinate if you substitue the x-coordinate of -1?


That's correct.


Part (b) is asking, which x-coordinate, if I substitute into g, will give me the y coordinate of -3?


I don't know :(


No problem. When you asked to solve a function for a value, you can see where the function intersects the y-value and then draw a vertical line up to the x-axis.


The x-value gives you the solution.


Yes. So the trick is to find where the graph intersects -3 and then find the x-value corresponding to the point of intersection.


so its g(-1)?


g(-1) = -3. If you substitute x = -1 you get y = -3 in the graph. The way to write the solution for (b) is x = -1.


ok


For part (c), it is asking which value of x gives me a y-value of -3 in the graph. That's how you interepret the inverse function of -3.


isn't it -1 then


Yes exactly. (b) and (c) are asking the same question but using different notations.


For part (d), it is asking which value of y in the graph corresponds to an x-value of -1?


so do I put -3 or do I substitute for x and write the equation


When you are asked to solve equations, you just put x = the solution as the answer.


For part (d) you can write x = -3.


thank you so much for helping me today


You are welcome. Have a good evening.


you too\


Hello


Hey how are you


I am fine how are you?


im good thanks


could you check a couple of questions for me


Okay


those look correct


those look good


ok


all set?


for what


you said you had a couple of questions, so I thought you were done


oh no I've got 9 more


9 is not a couple, actually


I could get someone else to help me if you like


we can go on but I am just saying that a couple does not mean 20


I don't understand how that affects my work


the bottom one is not corrext


I am just saying that if you have have a lot questions to check, you should let the tutor know that you have a lot of questions to check.  Don't say "a couple". Make sense?


Hello, are you still there?


yeah I am


the explanation is very long


is it right


thats one way to do it


alright then I should be good


thanks for the help


you are welcome e


Graph the inequality x≥−4.


hello sure I can help with that


I've already got that far


first draw the xy axis


Bro. I already did that \left(-4,\ 0\right)


Its going to land at (-4,0)


yes wait


then the area above is shaded in


because y must be equal to or greater than -4


for this case


does that make sense?


sure


it is very similar to graphing y= -4 just you need to color the area above that line


any questions?


no


okay hope this helps! good bye


Hi Jamie


I got -2 can you check my answer?


I got 9


can you show me how you did it?


evaluate 9-(3x-6)-y?


yes


with x =2 and y =-2


can you tell me if I'm just right or wrong ?


I see


you are wrong


oh so it's ten!


good job


any other question?


hi Sarah


Sarah


How are you doing?


Mr. Jensen?


good


and you?


i'm fine thanks for asking


how can i help you today?


Math :)


sure.


gimme a min


Couple mins


please type or add the question on the board


to get the question


sorry if im taking long my computers lagging


it's fine.


done


ok


do you want the answer of 5 a, b, c?


yeah i guess


where are the ques?


idk i think u prob cleared the board


want me to put it up again?


is it? sorry i didn't notice


yup , please


kk gimme a sec


can u give me a sec i gotta grab my notebook :)


so basically i have wrote the formula for rate of change


ya sure


kk im back


the triangle symbol refers to change


please note the following formula


it would be simple to solve your problem


would you try by yourself once?


i dont know how to do this :(


ok i'll do one for you


so let's see ques 5a


so to find rate of change from 2 to 4


subtract 11 to 3 and 4 to 2 and divide both of them


did you got it?


so 11- 3?


ya


and 4-2?


so 4


is the answer


good


try the next one by yourself now


from 4 to 6 find the change


is it 4 again?


ya!!


you got it


ok pretty easy


yup it is!


would you like the try b?


didnt we jus do b


oh sorry! i thought we were doing a


actually the answers are same


never mind!


so we move in to c


lets do c


ya


ok


what the change from 3 to 7?


is the answer -0.5?


no!


oh oki


how would we solve it?


just a min


kk


is it 2?


no


it is 1/2


how?


gtg


i guess you divided input by output


so add all of input together


then add all of output together??


and then divide?


it would the change of output divided by change in input


did you got it?


not really sorry


it is just like you did b


so for 3 to 7


so 3-7?


subtract the output 2 to 0 and input 3 to 7


or 7-3


that would be - 0.5


cause we are finding the change


it can't be negative


its 0.5


7-3 is 4


yes and 0 - 2 is -2


-2 / 4 is -0.5


no it should be final - initial


so 2-0


oh ok


can you  now find 7 to 11?


yeah i think


ok , so try it.


would it be 0.5?


ya!!


good


thx


welcome


see u later?


ya sure.


bye


have a nice day ahead.


bye.


you too


Hello Maria! What Can I help you with today?


my math homework my sub is not good


she said was ugly


she said I was ugly


I feel hurt


Oh I'm not sure that's appropriate behavior for a substitute. Maybe you should try to report that to a principal


Lets move onto the homework assignment, shall we?


I guess so


but it really hurt my feelings


but can u help with work


She don't call me baby boo.


Hi, Liam. How are you doing? :)


hii, I'm good :]


Welcome to Tutor Provider :)


How can I assist you today?


thank you


I need help studying for a test tomorrow


but im just practicing the platform today


Okay, could you share me the materials with me regarding the text?


Oh, feel free to use the whiteboard!


okay well, thank you for your time I am going to get off because today I was just gonna try it out.


Okayy, byee :)


Liam


hi I need help on homework assighment


Hi Amelia! How may I help you


Oh okay, can you show me the question?


question 17


Ok, give me a few seconds


What do you think is the first step?


I mean 18


sorry


Oh its alright


Do you know what an average is?


yes add


and divide


then divide


Wow smart!


So what numbers should you add first?


42 57 62


Ok, are you allowed to use a calculator?


no


I know how to tho


Do you want to show me how you add them on the whiteboard?


that


Wait did you draw on it?


For some reason it won’t let me see lol


Oh i just saw it


il just write


Sorry, what was the sum you got?


Now what number do you divide it by?


Oh wait, you may need to check your work


I just wrote on the whiteboard.


Can you add them again?


there


7 + 3 + 2 is equal to?


Good job! You may want to check your work for the ones place again


Do you see an error?


3 divide 162


Nice! And you said to divide it by 3, right


Yes! Can you write that?


Do you know how to divide that?


that


Is that a 24?


Close! But let me show you


3 goes into 1 how many times?


So we move to the next place


3 cannot go into 1, so we move to the next place


ok


Now, 3 goes into 16 how many times?


times


3 x 6 is what number?


I understand


Nice! So we multiply 5 and 3


it goes 5 times


And we subtract that from the 16


And we bring the 2 down


Good!!


What do you think is the never step?


Next*


uh


hhhh


move


lol, now we see how many times 3 goes into 12


this is called long division


3 x 12 ix 12


Great job! Can you show me how to do that?


that??????????????????


Liam


Yes, subtract it


uhhhh


You’re doing good, dont worry lol


And we write the 4 there


Now, what is the average?


Good job! Do you understand the question a little bit more?


ya


number 20


Alright, just to tell you, we have ten minutes left.


Let me see


ok


Do you know what a multiple is?


or 32


I mean 2


How about this, what is the definition of a multiple?


Yes, so basically it is skip counting.


Wait sorry, im ooking at the question


Okay


Can you list the multiples of 6?


Or you can write it on the whiteboard


Almost! You can start from 6 and keep adding by 6


For example,


Do you see what im writing?


ya


Do you notice a pattern?


yes


Great! Can you try to list the multiples of 9?


3 1 9


Almost!


First, we start from 0.


Each time, we add by 9


For example


What do you think is after 0 if we add by 9?


0 + 9 =


Hey Amelia, just to let you know our 30 minutes has ended. I hope I brought some knowledge and helped you with some parts of your homework. I can tutor you another time, but I have to go now.


Good job! Keep adding by 9 and you should see a pattern


Hi Sophia


hello can you help me look over a calc test I failed?


OK.


usually I can share my screen with the doc, but the button disapeared so it may take me awhile to write it on the whiteboard


OK. I understand.


Done


I see it.


in my orginial answer I put that it doesn't guarantee a value of c which is 2.


He said that was wrong and said that it does and f(x) is continuous everywhere except at x=-2 and -2,3 are not in (0,3


I was confused.


Give me a minute to see why your answer was wrong.


First, if you plug in x=0, what do you get for f(x)) = ?


And if you plug in x=3, at the other end of the interval, f(3) = ?


Perfect. And because 0<1<6/5, the theorem guarantees that "c" exists such that f(c)=1.


oh, I guess I got confused because 2 didnt exist


That's the first step. Give me a minute.


Next, we need to solve 2x/(x+2) = 1. You already did that and found x=2, which is correct.


so would the full answer be The IVT theorem, guarantees a value of c in the interval. C=2


Correct.


can we do another one?


Sure.


done


Let's start with 1(a). Would you know what formula to use to find the AROC ?


It should be f(b)-f(a) on top.


Or in this case, g(b)-g(a).


Yes. 4/18, or 2/9 if you simplify.


is that it?


That's it for 1(a).


if forgot lb


I'm not sure what you wrote where I circled.


the formula


The question is not very clear, but the IROC at x=7 is (g(9)-g(5))/(9-5).


I will rewrite it


better?


Yes. x is between x=5 and x=9. So the formula I wrote above will answer question 1(b).


"3" is correct.


Could we do another?


OK. One last problem.


I forgot what/ how to do this


To begin, what do you get if you plug in x=2 into the expression?


Not exactly. The numerator is x^2+4 = 2^2+4 = ?


Right. Because the denominator goes to zero, the limit will be either +∞ or -∞, correct?


how do i choose which one?


do I do positive because they are both even?


Because we're looking for the limit "from the right" (x→2+), try to plug in x=2.01 and see if you get a positive or negative number.


is that right


Yes. The limit is +∞. But some teachers would say that the limit does not exist (DNE).


okay it was a mutlliple choice and infinity was one of the answers so I will go with that


thank you so much!


You're welcome. Have a good evening.


you to


hi Leo


Hi


Welcome to Tutor Provider!


Thank you


Are you AI?


not at all. I'm quite human.


Alright


do you have a Geometry problem for us to work on?


No


I'm preparing for the SAT


OK


I'll be leaving now, I have a class to attend to


so we're done?


Yes


what was the purpose of this session?


just to find out if coaches were AI?


Kind of


OK, well now you know


You seem AI


really?


I must be really good AI to pass the Turing Test


I mean, it's so random.


I used to be a software developer, doing AI research


Cool? Anyways peace out


yeah, you too


hi!


hi Sarah


could you help me study for my algebra test?


yes I do


do you have handout or note that we can work on?


yes, i do


may you please upload them onto the board?


how can i upload a pdf?


you can
sharefile.comare screen (only share pdf window) 2. using snipping tool (on laptop) or screen shot (phone) and download the picture and upload that picture onto the board


what device are you using?


laptop


I see it now


so i got 1-9 down


i want to see #10


can you scroll the pdf file down a little bit


thanks


so he told us that there are certain problems he wants us to focus on bc they would help us the most on the test


uh huh


what are they


the ones he told us to focus on were 9,10, 17, 18,21,24,25


let's work on #110


he said 26-29 would count as a bonus


okay


what is your solution?


we can start with your idea


so a says if the lines are parallel


yeah


so we would have to get the first equation in y=mx+b


correcttt


good jobbb


whay would you do with the k?


or why are there so many variables?


this is quite complicated


I will explain why they have so many variables later


let's work on k


think about this: you want to eleminate k on the left side to make slope-intercept form


what calculation you can do (of course, on both sides is required) to eliminate k


divide


correctttt


divide by what?


absolutely


uh oh


that looks weird to me


you forgot the parenthesis


oh yea, sorry, i just put it like that instead of writing the k underneath the -3x and the 7


yeah


but yea, i understand what you mean


please simplify


would i just distribute the k, so it would  be -3xk+7k?


it is division, not multiplication. But your point is correct


so what would it be?


ohhhh


yeah, you get so closee, good job


now, what do we do on step 2?


for b?


no, for a


we haven't found the value of k


would you subtitute smth? Like bring in the other equation?


that way we will find the intercept, right?


yes


but the question asks for parallel lines which have no interception


but we still need the slope


hint: relationship between slope of 2 parallel lines


its the same


perpendicular would be the opposite reciprocal


yeah


so you know the relation ship


yes, but what does the other one have to do with this? because that slope would be 4


correctttt


so what -3/k should be equal to?


ohh to the -4x?


yah


could you just put y=-4x+7/k?


no


because slopes of parallel lines are equal


-3/k = -4


as we can see, the relationship help us narrow down to 1 variable


and we can solve for k


it is righttt


well done


so for part a, in Boston


so perpendicular? Would i just use the 3/4, but since its the negative reciprocal it would be -4/3


that negative reciprocal is casted on the slopes of 2 perpendicular lines, not on k (random variable)


okay


you can put slope (1) equal to negative reciprocal of slope (2)
or slope (2) equal to negative reciprocal of slope (1)


would the k be negative?


yes


no mistake


good job


let's work on 17


oh okay, im sorry, but i have to go, thank you so much for your patience with walking me through this problem


alright


you work well


bye


hope you have a good rest of your night!


you too


hi


GA Liam


how may I help u?


here I need to simplify this problem


do u mind typing example.com is easier to read...


well there are a lot of exponents and IDK how to write them in a computer


pastebin.comn u copy and paste it?


the question is from paper


Proceedceed....


so...


no is k


done


sweet..good handwriting


So how do u think we should start?


by the parentheses


correct


which one u want to start with?


just circle the one you want to start with


like the x by 2


x squared??


yep


So do u simplify how do u treat the exponents?


only use the exponents 2 and 3


ok..but what do u do with those numbers?


llke the answer is 8


how did u get 8?


oh like 2 squared by 3?


do u agree with that statement?


no


no?


by multiplying 2 times 2 times 2


when u multiply letters with same bases add the exponents together


so your answer would be....


ohhh


correct


lol


so is x by the power of 6


k


make sense?


yes


ok..let's work on the other parentheses


so it will be 5x+15x ?


let's add everything in that parentheses first...


what would u get?


no..what is x+3x?


did u write the problem correctly?


yup


ok


what is x+3x?


mmm


now if u multiply by 5..what do u get?


correct


so please re-write the problem again so far with the latest simplification


is that the re-write?


what do u mean by re-write


the problem I just rewrote-write it so far...


yes then it is


then it is what?


where is the 4?


the 4 was multiplied by 5


ok..I didn't ask you to multiply anything...I asked for a simplification inside the parentheses. Pleaseease follow my directions...otherwise you may not get the right answer


okay


please fill in the information where I put the 4


k


now simplify the 5(4x)and continue to write it in the parenthesis


awesome...


now you have simplified everything in the parenthesis...


how do u simplify further?


yes? like the 20 times 4 ?


correct


please simplify


but also could it be 4 times x ?


hi ?


hello


Hi!, How are you? :)


Hello. I'm good. How are you? Then you touch on that actually. I mean you can't they don't respond that fast. The ****. Oh, it's, it's it's like saying what I'm saying the type.


oh.


God


Oh dude, why you


My apologies.


That's ok, I understand


I need help.


Do you want me to tell you the question?


Are you able to hear my microphone?


No, I cannot.


Alright that ok, Tell me your situation.


OK, so I'm doing the graph function. It says the entire graph of the function H is shown in the figure below.


Could you paste in a screenshot of your equation/graph?


Yes, I have, I got you.


Can you see the screenshot?


Yes, Thank you, Lets get started. :)


What exactly are you confused with?


I don't understand how to do this at all.


Ok, FIrst i will ask this, What is range and domain?


I am confused about how the way my teacher explains it, and it is confusing.


Um, ain't is in range.


Oh, ain't the main like the middle number.


Ok, so range is basically up and down coordinates, domain is left and right coordinates


OK, thanks for letting me know.


So, to help solve your problem you need to first find your minimum value corrdinates, Do you think you can do that?


My minimum value coordinates you said?


yes


Hint: the vertex is always the min or maximum value


Essentially the vertex of a graph is where the point of the parabola starts.


is the vertex 4 and 0.


You are very close, Not quite, Check again.


4 and -1.


Yessir, Good job now using those coordinates, we need the domain and range, I will help you figure this out


OK


So, Domain as you understand is how far up and down the coordinates go on the graph, Specificially the parabola


So is the domain 0 and 10?


If both side of the parabola face both directions on the x-coordinate plane, Does it go forever?


Yes


So what would that mean the answer would be?, Look at the options you have, as the domain goes forever both sides, Which is most logically correct?


Wouldn't the answer be 0 and 10.


But if it goes forever, Don't you have to include all real numbers? You got this!


I'm not understanding.


If the graph extends both sides of the x-plane forever, that means it includes all real numbers such as or -1.-2.-3. So the domain would not be only numbers but what phrase?


Imagine this, You walk on one side of the road forever while your friends walks on the opposite side of you, He represents postive number and you negitive. If you both had a domain or how far you walked it would be all numbers


I'm not understanding I was, I'm.


Yeah but like, oh, so it would be all real numbers.


YES!, you got it!


OK, I understand it now.


Now, Lets move onto the range


Range as you understand is up and down coordinates


Yes, I understand.


They are asking where does the range start and go on forever upwards or downwards. Down the grapj face up or down?


The range starts at -1 and ends at 10.


To find where the range starts, Can you tell me the y-coordinate of the vertex (4,-1) is?  (X,y)


When you explain a graph it is not limited to the graph, It may seem 10 is the maximum number but it goes on forever upwards


I don't know, I'm confused.


Can you click on the listen button at the top right corner


I don't see the listen button.


Ok, ! minute, I will figure this out


ok


I seems my microphone system is bugged out, I will try to elaborate better by chat


Whats is the y vlaue of (4,-1) or the vertex


My bad, I tried to erase the thi so I get.


-1 is the y-value as it is formatted (x,y) correct?


Are you asking me is why less than a ready to -1.


Not exactly, Its Why is the a range all y-values greater than or equal to -1


*Why the range is


It's like you're comparing just you talking to us. I'm not talking. I mean, do you know what's, what do you know what's range? Range is interval, like interval between two numbers, right? And everything, it's not be greater than certain numbers. Like you're comparing chair and


GPA.


Not quite, Range is the y-values. In basic terms the up and down coordinates and in this case since the vertex is 4,-1 that means it starts at -1 y-value and goes up forever including -1


It goes down forever or up forever based the where the graph faces up or down


So the answer is why is greater than or equal to -1.


YES!, You got it, Do you fully understand now?


a little


Ok so, If you start and -1 depth on a submarine, And you can go up forever that means including the current depth and forever above is represented by y greaterthan or equal to -1


Does that clear it up a bit?


yes thanks


Awesome!, Anything else I can help with?


no


Alright :), Have a great rest of your day!


hi


hi! how can I help you today?


ok, so let's work on graphing these one by one


so for the equation x-3=y, what would we do


we would probably start by graphing the equation. since the condition is x<=-2, then we would graph the equation y=x-3 until we hit the -2 on the x axis


I drew a red line at x=-2, do you think you can graph x-3=y?


does this all make sense?


yes


we would do the same thing for the other equation as well


hi Jamie, I actually have to leave now, if you need anymore help, you can request for another tutor and they'll be able to help!


hey how are you


hi how can i help


could you check my answers for me


ok


can you tell me how you came up with the answer you selected?


you inverse each point


correct


so answer is correct


can you tell me the inverse function of y = x +2


correct so do all the value pairs satisfy the inverse equation on the selected option?


for example is -3 = -1 + 2? and so on?


sorry I meant is -3 =-1 -2?


and so on for the selected option?


I'm confused isn't it C


it is. what I am trying to get at is "do all the value pairs in the selected option satisfy the inverse function in your opinion?"


the answer is yes but I want you to be confident in deriving the answer


oh okay


ok whats the next one


answer is correct


okay thanks for all the help


Hi Ben!


Hi Emily


I'm stuck on this a past coach was making it a bit confusing


I was wondeing if you could help me with the formula like do the first and then I'll do b and C


I just don't know what youre supposed to solve first since the formula can be interpreted in many ways of what to start off with first


I'm reading...


For (a), we calculate the compound interest after one year. The deposit is made at the end of the year. So the value is simply $1200.


X times 1 i know that part


I'm looking at the formula on your page...


For (b), you use the formula with t=2.


ok


can you do it just step by step


like what u solve first then second using "Aa" and ill understand it easily that way


OK.


Does it help?


not really


i mean like step by step


Let's look at the formula and apply it to part (a). The payment is PMT = $1200. OK so far?


The interest rate is r = 0.09


yeah I just need to know what to add what


and subtract what by what


i know all that toher stuff bc i have it written out aleady


Let's do 1+r.


OK so far?


We need to calculate what's inside the brackets [ ] first.


ok so u do 1+0.09 now what's the next step?


Then you raise 1.09 to the power of t=1. So 1.09^1 = 1.09


then subtract?


Yes. Then subtract - 1.


now what


1.09 - 1 = 0.09


mhm


then what


Then we divide 0.09 on top by 0.09 at the bottom: 0.09/0.09 = 1


Finally, 1200*1 = $1200


thats it?


That's the answer for (a).


kk now b


Yes. (b) is like (a), but t = 2. So you'll have 1.09^2 instead of 1.09^1


k


0.1881 divided by 0.1881?


r = 0.09. So you'll have 0.1881/0.09


ok


(b) $2508.00 is correct.


(c) is correct.


Ill past the next problem in a second, going to use the bathroom keep this stuff on the David here still tho


OK


bck


I'm still here. We can do one more problem.


(a) is correct, although you may want to include the cents: $850.00


Yes. $1734.00 for (b).


Yup.


Well done.


That completes the solution, and I'm out of time. Any quick question before I go?


Nope, thanks!


You're welcome. Have a good evening.


Hi Liam! How are you today?


its posted


Ok, lets start with number 1: They are asking for h(8). The function h(x) is 2^x. What do you think we need to do?


im not surew


is 256


Yes! You got it!


i dont understand how to do it


Lets go to nine now! They are asking for g(-8), so we have to plug in -8 into the g function.


Ok. Let's go through it together.


Since they are asking for h(8) we need to plug the number into the h function.


okk


Lets try nine, they are asking for g(-8), so we have to plug in -8 to the g function.


What is the g function?


g(x)=x squared -1


Correct, so if you plug in -8 into every x you see, what do you get?


soo 8x8


Yes so 64-1 which is 63.


Let's go to 8, they are asking for f(6), which is?


What would f(6) be?


6x3 squared


Not quite, if you plug in 6 into x it would be 3(6) + 1


soo 3x6


Plus 1.


What would that be?


Yep!


How about you try 1-5 on your own. If you need any help just lmk!


is number 3 five


Not quite, so if you plug 0 into the h function what do you get?


4 is 5


Can you show your steps to come up with the answer.


i actually need help


Alright sure! No worries, lets go to 2.


2 down is 8.34


Just plug in 3.67 to the f function.


3(3.67) is?


i got 11.01


so 12.01


6 is 15


Yep you got it!


Let's try question seven.


What is 3^2 - 1


7 is 8


Yep! You got this!


Let's do 3!


is 3 two


Not quite 2^0 = 1. Then you plug 1 into the f function.


Thus 3(1) + 1


Yep!


Lets do 4. What is four?


is 5


Not quite 3(2) + 1


Last one! What is 2^9)?


Aka 2^9


do you see the new one


Yes. These are all examples though.


OK


So the function for 1. Would you like to give it a try first?


can you help me with the page I just added?


Yes I can. It is really similar to the first page with examples. Would you like to try yourself first or would you like to go over them together.


im not sure


Alright no worries.


Let's start with this.


What is the constant in question 1.


What cost doesn't change.


maybe 25


Yep and what changes?


the 10


Yep! So we need to multiply the 10 by an x.


Then add the 25 as it is a one time fee.


So what would the function be?


is it 85


I will help you with the first one.


So it would be f(x) = 25 + 10x


So if you plug in 6 for x what would it be?


Yep you got it!


soo what is the choice


I wrote it down. Let's go to two. Based on what we discussesd, what is the function?


okk


yess


So basically, if the price changes, you need to tack on an x.


soo 12x8


The function would be f(x) = 12x, yes.


Then for B, you plug in 8 into f(x)


Yep!


Lets go to 3.


It already has 40 and it is getting added 5 per minute.


So which number would have the x.


Wait, can you sign it on the whiteboard please


Almost, it would be 40 + 5x.


It is starting with 40 and that does not change.


But the amount being added changes per minute.


That is why you need an x.


Not quite, what is 5(10) + 40


Do you want to try 4 and 5 by yourself?


 for 4 9x7
 for 5 12x3


You got 4 but not 5.


I need help writing the functions and questions for these problems


5 is like 3.


What did we do for 3?


12 is the constant.


Do it does not have an x.


And you add 3x to that.


soo 3x10


Not quite, it would be 3x + 12.


Then you plug in 8 into x.


Yep! I got to go now but just remember what we have been doing! It's the same steps, just different numbers!


Hi Marcus, how can I help you today?


Sure, let's break this down so we can understand it


well let me right it another way


write*


cool, that's a great start! Do you need some help to start, or did you want me to check your work? either is perfectly ok


i need help starting it


ok, sounds good. So for me, big numbers can often be intimidating at first, so I try to break the big number down by seeing how 6 can fit into it. For example, how many 6's can fit into 29, without going over?


in other words, what's the closest number we can multiply 6 by to get to 29


perfect!


so what's 24 divided by 6


Hi Marcus, I see there hasn’t been a reply, so I’m going to close the chat now. I hope you found your answer, but if you need help, feel free to come back and ask for help!


hi


Hey, I'm Sarah! I'll be helping you with your math today.


hello I'm David


can u screenshare by chancd


Hey David? What do you need help with?


I want help with algebra and geometry


Okay, perfect! Do you have any questions you want to go over today?


no


I see. Do you have any specific topic that you want to go over?


preferably like shapes that inside of other shapes and finding out x


Oh, I see.


Do you have any class notes you can insert?


Like those types of questions, or something different?


yea


I see. Can you solve this for me, please?


like the area of it?


if it the area the answer 45


Yup!


Are your questions usually harder or easier?


I can ask ai to generate some questions if u want


Sure, go ahead!


and yeah my questions are usually way harder


ok I posted oen


Okay, let's see.


Is this easy or hard for you?


well visualizing it is pretty hard


I see.


but once I can it would be kinda easy


This is the general shape of the figure.


oh ok


Can you walk me through how you get the answer to this problem?


ok


so


Sarah this question confusing


Would you like to walk through it together?


ye


So, how do you get the circumference of a circle?


dxpi


or 2rxpi


So what would it be for the semi-circle?


Yup!


Now, let's express the perimeter in terms of the square side.


The total perimeter is the sum or 3 sides AND the semicircle's arc. Can you make an equation for that please, letting the square side be s?


Tell me if you get confused.


I'm thinkin


Okay, tell me when you've got it!


I give up


can we skip to a different question


Sure!


uhm so sorry


I gtg


I have to eat dinner so sorry


That's fine!


Bye!


thank u


Hello!


hi


can u help me with this equation


Graph a line with a slope of

\[-\dfrac{3}2\] that contains the point
\[(4,-3)\].


thanks for posting! that makes more sense!


your line has a positive slopen you fix it?


your welcome


can u explain more


nevermind


I understand what your saying


yes I can


you can fix on the white board


no


because its a picture


and not apart of the white board


you can use the drawing tool


I'm confued


the green point was correct


from the green point you want to go down 3 then right 2 to make the next dot (or up 3, left 2)


okay


yes, so (2,0) is a correct point on your line


now just connect the 2 points


ok


Is this delta math?


Westwood High


oh. well, that new graph you put up is correct


see how negative slope makes the line go "down hill" as you read from left to right?


that's good to remember


there's a new one on the board


ok, so first mark the point (3,0)


then use the slope to get to the next point (this time the slope is positive so the line will go "up hill"


is your line going up?


yes


read it from left to right


I wrote it


yes, I think you got the idea


I just got it right in Bright Minds Academy


thanks that's all I needed


hello


Hi


how are you?


I'm fine how are you?


I'm alright, I just needed help fully understanding the properties of polynomials and multiplicity of zeros and graphing functions


i can show you my notes i just need help understanding them more


ok


oh one second i need to make it a jpg


yeah take your time


these are my notes given by my teacher but I do not fully understand them


I also have a homework sheet that I can use as practice


Alright let's go through these first, then we can look at some examples, are there any specific parts of the notes  that you do not understand?


Its more of the second part than the first but i do need a little bit more help understanding end behaviors


alright so end behaviour is nothing but what the polynomial's graph does as x approaches a very large or very small value (infinity or -infinity)


are you confused by what lim means?


no I was confused about the unit things


like if the highest degree polynomial is positive or negative it would affect the end behavior


my teacher taught us that but I didn't fully understand what he meant


ok so i'll explain the cases once, also note, the degree of a polynomial is always positive, you mean the leading coefficient


yes


so do you know what the leading coefficient is? Just the coefficient of the term with the highest degree


yes i understand that part


ok so now there are 2 things that determine the end behaviour:-
1. Degree of polynomial
2. Sign of leading coefficient


the combination of these 2 give us 4 possible cases of the end behaviour of a polynomial


do you follow?


yes i follow


I will, from now on, denote leading coefficent by 'a' and degree by 'd', just for simplicity


ok


case 1: a-positive, d-even
the polynomial will approach from a very large value and exit to a very large value (infinity)


it might look something like this


case 2: a-negative, d-even
the polynomial will approach from a very small value and exit to a very small value (negative infinity)


something like this


ok so positive and even goes to positive infinity and negative and even just does the opposite going to negative infinity?


now if the degree d-odd, then the function will approach from one side but leave from the other


so positive but odd makes it go positive to negative infinity?


something like this, and the leading coefficient decides how this would look


it could be postive to negative infinity or the opposite


negative to positive infinity


for a>0, it would be positive to negative and for a<0, negative to positive


Ok


im sorry


i meant opposite of that


i'll re write


a>0: negative to positive
a<0: positive to negative


sorry for that, now can you tell me what would be the sign of a in the graph i have drawn?


yup


and if i draw this?


perfect, so a great way to remember this is that for even powers, the polynomial exits and enters from the same side and for odd degree (powers) polynomial enters and exits from opp sides


any questions in end behaviour now?


No, I think I understand


alright now the second part right? You mean the graphs


yes


I understand the x intercepts but I don't understand the mult. cross/touch, or the y intercept part


ok let's go through that then first


and I now understand end behaviors


so y-intercept is nothing but the value of the polynomial when x=0


ok


or the point where the function intersects the y-axis(which is logical, because the coordinate of that point would look something like (0,y) which indicates x coordinate is 0)


any doubts here?