Hi there


Hello!
Nice to meet you
Hope your day is going well


How are you feeling today?


yes I am well. Thanks


Test coming up on October 15th
The teacher is rushing us students
Can you help me understand a topic?


Geometry.. let's tame the wild.


do you want to get on the board


Yeah let me show you what they gave us to complete


I know teachers may some times rush to finish the syllabus


ok waiting...:-)


Hope you can see


Yeah
First semester and she's already rushing us ㅠㅠ


can you rotate it 90deg anti clockwise


WHat do you need help with - slope?


https://example.com do you even rotate it?


I'm new to this website


it's Ok. let's start


Thanks


first plot the points.


are you OK with that  Q#5


Point A is x= 0 and y = 6


got it


do you see it on the board


So we start on the y axis?


lets try B to understand


Okay


x = 3 and y = 4


go to 3 on the X- Axis


cool


now C


Help me with that one please!


x= -1 (left of zero) and y = -2 (down below zero)


in RED you see it


Yes I do


now slope (AB) = 4-6/(3-0)


(4-6)/(3-0) = -2/3 | let me know if you understood it


Yes I did


That applies to all sloped


slopes


do you see the formula on the board


No


now


it is derived from pythogras theorm


The m represents the length right?


(that's what our teacher said)


yes measure


Okay


2^2 + -3^2 = 4 + 9 = 13


did that help?


Yeah


nice. you are quick to grasp


apply the same and you are done


let me know when you are done.


solving


Question


Any other help


Where did you get all these numbers from?


which ones?


the coordinates are given


No
You square
Not those

2^2
3^3


oh A(0,6) and B(3,4) |

= sqrt [(6-4) ^2 + (0-3)^2]
= 4 + 9 = sqrt(13)


So that's the side of side A and B?


yes


m(CB) = sqrt(52)


you will find AB = DC and AD = BC


I can wait till you solve it. OK :-)


You're so nice thank you!


there for you to succeed


Can you help me solve the second question
It's a bit more confusing


Then I'll do this one on my own


Is it on the board?


OK will do


Yeah
The one next to the first one


can you plot them for me


Can you zoom in on it if possible????


good?


Yes sir


Can you see???


try new color


good - A


B?


good - B


C and D


cool


Oki?


yes. you done it


use the same formulas


simple?


I have trick for you.


Okay what is it???


if line travels up or right slope is +ve


else negative


Oki thanks


Slope of AB 3/2?


for this one or previous


This one


change in y / change in x


Is it 4/3?


Hold on
Brain isn't working


Help


it's OK.


so 4


do it slowly, take your time, breathe


So my teacher told me a different way


tell me


Let me show you a different way on the board


See how I did thay


Like rise/run


let me see


change in y = 4


sorry A point is wrong


Ahh


Now wonder I was wrong


Yes, teacher is right


so now you see 4/1


change in y/x


How am I to do that?


Ahh wait like 4/1


yes


good catch on pint A


point*


Oki so
Side BC
2/9???


try the change in y/x; you will not be wrong


and note the direction slope is negative


how did you get 2 and 9


Rise/run


Rise from c
Run to B
Our teacher taught us that 🤣


rise is (2-4)


from 2 to 4


so rise is fine


How about the other one???


run is 2 to 10


So you're telling me it's 8?


yes -2/8


or -1/4


rise and run can mess up your +/-


Yea


change in y from B to C = 4-2 = 2


change in x from B to C = 2-10 = -8


Slope of CD 3/5???


y/x = (-2/8)


Okay


bingo


and see it is +ve


so you know you got the sign right


So
DA -1/4?


I have to go now. Hope it helped. You can fav me to do another session.


Yes
Sure


Thank you


D is right


also m AB and m BC is on the board in RED


have fun!


Have a great rest of your day


You too


cheers


good to see you on Ben


You too
Thanks


hello


hello! wanna check my answers for about 30 questions, but let me know how many you can check


30 is too much


yes I know


what is the topic?


lemme upload the first section its odd questions only and you'll see what the topic is


Have you done them?


yea imma put my answers in the chat just lemme know if its write or no


right or wrong*


21.5i, 23. i sqrt10. 25. 12 i sqrt2 , 27. -i 3sqrt2. 29. -13. 31. -2 sqrt 6. 33. sqrt 3


lemme know if ur able to read that its hard to write in chat


those are ok


yay! do u have time to check more? its ok if no!


a few more


ok


but you seem to know how to do them.


yea but they kinda change, you don't have to grade all the oddd ones I'm just gunna give you my answers for the ones I'm not too sure ab


39. -2 , 45. (-1+ i 3 , 51. 1-10i 53. -13 + 4 i sqrt2


Those look correct.


yay!


I think that will do it for me.


ok have a good day!


yout too


i need help with my homework D:


alright! I'm here to help :)


what problems are you working on?


4-6 right now


idk what im doin D:


alright, give me a second to take a look at it!


okay, I see!


okay, so, what is an odd function?


what do you know about them?


that the exponents are odd


yes, that's right!


anything else?


any fun properties they have?


idk anything else thats all my teacher taught me D:


okay, that's fine!


so, odd functions have a really useful property that'll make all of these problems a lot easier


so imagine you have some generic function f(x), right


make an odd function for f of x


any function for an example


f(x)= x^3-9x


amazing


okay, now, given that, what's f(-x)?


the opposite of it?


what do you mean by opposite?


(you're right)


like x^3+9x?


yes


try plugging in -x into x^3


do you get x^3 or -x^3?


yesss, exactly!


okay, so, f(x) = x^3 - 9 and f(-x) = -x^3 + 9


what's true about the relationship of the two?


is there an operation you could use to get from one to the other?


theyre like the conjugate pairs


idk.


no, that's a great thought!


yeah, the - 9 changed to a + 9


but the x^3 switched signs too


all of the parts switched signs, here


which is equivalent to multiplying by...


yessss, exactly!!!


by multiplying f(x) by -1, you get f(-x), right?


so -f(x) = f(-x)


and this holds for all odd functions, you should play around with it later!


oki


does that make sense? it's a pretty tricky concept, I always struggled with it


yea i kinda understand


alright--we can come back to it at any point


just remember for now, -f(x) = f(-x)


okay, so lets say we look at the first relationship, where g(a) = -17


we want to find what a makes this true, right?


uh huh


okay, so, let's apply this relationship


-g(a) = f(-a) for odd functions


so what's -g(a)?


yess, amazing


okay, so lets plug that in to our equation


17 = f(-a)


sorry, g(-a)


can you find a place on the chart where g of something equals 17?


ooh, close!


here, does x = 17 or does g(x) = 17?


g(x)


looking at the chart, g(x) is at the bottom. is the 17 at the bottom there?


yea


for which one?


there you go!


amazing, okay


so if f(-a) = 17, what's -a?


wait how am i supposed to know which is g(-a) and -g(x)


-g(a)*


okay, yeah, sorry!


I think I didn't explain that very clearly


the thing is, they're equal


so either one works


we could do it the other way around


so like if g(a) was 3 for example, than -g(a) which is -3 would equal g(-3)


or other way around, you could plug it into the other side and get the same result


I'm sorry, it's confusing to explain it over messages


its okayy


you can speak if you want 😭


I'm in a library :sobs:


oooo


okay, wait, let's go back to the problems


I think (I hope) it'll make a bit more sense afterwards


so far we've got g(-a) = -g(a), and -g(a) is 17


we know these are equal and there's only one value for a


so g(-a) = 17


and g(12) = 17


as you found out earlier


so, what do you think a might be?


uh


close!!!


yes!!!!!!!


because g(-(-12)) = g(12) = 17


so what would a be?


uh what


you already did it


just confirming lol


YES


amazing job!!


essentially, what you need to do for this is solve the equation -g(x) = g(-x)


it's just like an algebra problem, except that you have to deal with functions so it's a bit trickier


does that sort of make sense?


uh kinda


lets try to solve for b and maybe ill get it lol


yes, let's!


okay, so, do you have any ideas on how we can start with this one?


(it's okay if not too!)


-g(b)=g(-b)?


amazing!!!


is there anything you can fill in there?


ooh, close!


g(b) = 11 for sure, nice find!


so what would -g(b) be?


ohh


perfect!


okay, so now we have -11 = g(-a)


any ideas of where to go from here?


do you see any g(x) that equals -11?


uh -11 would be -4, so opposite it would he 4?


YES!!!


amazing work!!


great job sticking with it, this is tricky


alright, one more to go!


c is a little bit different, but nothing you can't handle


do you want to work on it now?


uhm can i try it on my own and see if i can get it


yes, I'd love that :)


i got 8


amazing! that's what I got too


yay :D


amazing work, this is quite tricky and you handled it so well!


the way my teacher taught it was super weird tooo… ill show u later when we get on the next page 💔💔


and then looking at 5 and 6, you seem to have the right idea


because the property f(-x) = -f(x) means that it point degree symmetry


which basically means that if you rotate one half of it 2 quadrants clockwise, it overlays the top of the other one


which it looks like at least for 5 it definitely does!


i have no idea how to to 6


that's okay!


let's plot points, that's always useful


what's a point on that side of the graph?


*the left


that you already have?


(-1,-2), (-2,-3), (-3,-2), (-4,-1)


yep, those all look great


okay, let's start with the first one


wait i think i did it


ooh, okay!


yessss!!


good job!


ok and then the next page is hell.


I'm so sorry, but I have to go now :(


oh


okayy


Alex thank you


please put in another request, I'm sure someone else is available now!


Hello! I have a pdf full of the equations that I have done in class but did not understand well. The reason why most of them are all answered is because we did them in class together but I still did not understand them. Can you go in order on the pdf and rewrite the equations with different numbers and I will solve on my paper and the whiteboard.


I'm on page 9


Its on the whiteboard as well


Hey Liam! im taking a look now


so you want a question multiplying fractions?


*first


can you see what ive written?


sorry im back


yes


thats not like the equation on the whiteboard


im talking about page 9


oh okay let me come up with something


k


thanks


ok, if this is too hard let me know, but where do you think we would start?


distribute first


yep! you may want to simplify any fractions to make things easier too


so u divide 10 by 3 then multiply by 2?


you would divide 3 by 10, then multiply by 2. really close though!


thats a decimal


thats fine, you dont have to simplify 3/10 any further


so its 0.3?


actually do you mind writing your work on the board for me to see?


sure


that?


almost! so for the 6.6, i know we had 0.3 before it was multiplied by 2. it might help to keep 3/10 as a fraction instead of a decimal


actually lets back up a little, do you know how to simplify 2/10s?


yeah im confused


idk how to solve anything like this bc our equations that our teacher has never equals a decimal


hi


Hello!


My chat was lagging, sorry for the wait.


oh it's fine !


How can I help you today?


Is that all of the questions?


no


but let's start with this question


Alright.


What do you think is the first step of this problem?


Yes, that's correct


Are you familiar with PEMDAS?


yes


Since we have 0, we can erase that onw


Not quite right


9 - (-1) si the same as 9 + 1


if we have two - signs they become +


Yes, you are right. Great job!


wait isn't it -2?


Can you show me how you got that?


I am sorry, 8 is correct


I forgot that it was supposed to be 9 - -(-1) so that would give us 8.


I am currently working on page 7 #31


Yes sure! Just give me a few mins


Would you like me to start with the one you are currently working on?


Also I want to just let you know from the beginning that I only have time till 1:30


Ok, I want to start on page 7 #31


alright perfect!


you can write the equation on the board


Yes sorry for the delay I think my computer is having some connections issues


Its ok, maybe try and refresh


that usually works


So sorry my page keeps going in and out I am going to end the chat and try to find my router. I really apologize for the confusion


Hi Hi Ben!!


Hey! How's it going?


Pretty good, you?


I'm doing well!


That’s good!


What can I help you with today?


Okay so im working on a homework assignment rn, and i was wondering if you could help me through it


Sure!


How would i go about solving this?


So you would take (2x+23)+(9x-5) and make it equal to 95 then solve for x


Then once you find x you will plug it into 2x+23 to get ABD


Ohhh okay


Ben


Of course!


Is there anything else I can help you with?


Nope!


Ok! goodbye!


Hi, how can I help you?


hi


I need help on number 29


Alright


I'll write the steps on the whiteboard


ok


So let's factor out the numerators and denominators


So we know that x^2 is just x times x


Do you know how to factor out expressions?


yeah


not when the leading term is 1


Okay, i'll show you a step by step on how to factor


So when it starts with 1, we know that inside the parenthesis will have one in both because 1 times 1 is 1


the probelm is i only know how do when x is first term not second


Use this formula a^2-b^2=(a-b)(a+b)


So for 1-x^2, it would be (1-x)(1+x)


oh  i like x as first


Ok you can write that as (-x+1)(x+1)


Do you know how to factor this next one: 1 + x^2


well what i did for first term is i did'


which is same as -x^2+1


I see. When it says factor, we want to get rid of any powers on the x as much as we can


yeah but cany we do -(x^2-1)


x^2 can be simplified more which is why we use the method of two separate parenthesis


and then do -(x+1)(x-1)


ye


Yes, you would get the same result. You can do this method!


ok


So now what about 1+x^2? Can you factor this out?


i mean no


You can't factor this expression, it's already in it's simplest form


So we'll keep this as is


yep


So let's move onto the next fraction


Let's factor x^3 + x


So we have a cubed root which is also x^2 times x


yeah


So lets make a parenthesis, and we lets take an x out


x(x^2+1) is the simplest form for this expression.


Now we have the denominator x^3-x


Let's use the same process


Instead of a positive 1, we use a negative 1 because we have a negative x


Now, let's set everything up again


But before we write down this last denominator, we can see that this can be split up more


We can further factor x^2-1 into x-1 times x+1


ok


so we cancel now?


Yes!


What can we cancel out first?


the x


Yes! Great job


Let's combine this all into one fraction


So we have 1-x in the numerator which can be rewritten as -(x-1)


Let's rewrite again


yeah


x+1 is the same as 1+x


And x^2+1 is the same as 1+x^2


yes


So we have duplicates of x-1, x+1, and x^2+1. Lets cancel out these terms


All we are left is with is a - which can be rewritten as -1


So -1 is our final answer!


what about domaims


domains


Domains in general ?


no for this problem


we need to find domain


Let's use the denominators for both fractions


ok


So the denominator for fraction 1 is 1+x^2


Since x^2 is greater than or equal to 0, 1+x^2 is greater than 0


Now for fraction 2, the denominator is x^3-x. We need to check to see if this expression is zero or not


yep


So we set this expression equal to zero


So when we solve for 0, we get x=1, x=-1, and x=0


Therefore, the domain is {-1,0,1}


why cant we sex x^2+1=0


We don't set x^2+1 to zero because it has no real solution


how come?


Because when you do set this equal to zero you get x^2=-1


The square of any real number is always positive but -1 is negative


what if when we multipled we got x^2=1


Multiplied when?


what if isntead of x^2+1


we had x^2-1=0


But that isn't the denominator in the first fraction of this problem


what if it was


x^2+1=0 has no real solutions because x^2+1 is always greater than zero


what  if x^2-1


does it have a solution


x^2 is greater than or equal to zero, therefore 1+x^2 is greater than zero


It has no restrictions


yeah


so whats domain


of x^2-1=0


The domain of x^2-1=0 is all real numbers


Equations don't have a domain


im saying if in denominatoe


denominator


We don't look at individual equations and find the domains of them


Rather, we tried to find any restrictions for both equations and create a domain from that.


yes what if x^2-1=0 so know in future


how to solve


I'm confused on what your asking. Are you asking to solve for its solutions?


i wanna know if was our domain]


what domain would be


The domain is -1,0,1


no '


Okay, let me rephrase. When you have a fraction, look for where the denominator equals zero


cause x^2-1=0


The domain of x^2-1=0 is all real numbers. All polynomials (like x^2) can be defined on a number line, therefore making it all real numbers


you cant do all real numbers


I'm confused what do you mean you can't do all real numbers?


Step 1: Set denominator equal to zero and solve:
𝑥
2
−
1
=
0
x
2
−1=0
𝑥
2
=
1
x
2
=1
𝑥
=
±
1
x=±1
Step 2: Exclude these from the domain.
Domain:

All real numbers except
𝑥
=
1
x=1 and
𝑥
=
−
1
x=−1.'


1 and -1 are just solutions, they aren't excluded from the domain


they are the restrictions


fpor x


for


So restrictions occur when you have denominators or square roots of negative numbers


x^2 is a polynomial, and they work everywhere on a real line.


im saying if a denomnator


if x^2+1=-0


in a random denom


There is no negative zero


yes ik


You don't set it equal to zero


yes you do


to find domain


Yes, you're right! Sorry, I'm getting confused here. But there are no real solutions


Because you can't have x^2=-1


Therefore the domain is still all real numbers


what about x^2=1


can you have that?


That would be when you have x^2-1=0 and you solve for zero


You get x=1 and x=-1 therefore domain is all real numbers except -1 and 1


ok


and you can have x^2-1=0 for this problem if we swicthed up the sign from + to -


so then that would be domain for our problem if we had a diff sign


Yes but it would be a different problem at that point. Different problems give us different domains.


You can't switch signs in problems otherwise it will complicate future steps.


yes but if we had 1-x^2 instead of 1+x^2


that would be the domain


for this problem


if we subituted


Sure


ok so im correct if we sub that would be domain


for this equatiojn


Yes, if you change the denominator you get a different result for domain


The combinations are limitless


just wanna make sure '


for rational equations


you can solve x^2-1=0


in denom


cause last time i think i said wanst solvable


/no domain


Yes you can


ok


Is that all, or do you have any other questions?


thats all


I'll end the session here. Have a nice day!


Hello!


Hello :)


I am working on radicals


oh good


I've kind of got the gist but I have questions on certain parts


l start on the board


i dont quite understand what problem you are stying to solve, is it square root of 39?


yes


from here I need to simplify but I don't know how to with out a calculator, we cant use them.


so, i dont think you are doing this right


you are separating the 36 and the 3


and trying to say that the squareroot of 36 is 6 and so the squareroot of 39 is 6 plus 3/12?


Yes but I have to simplify it


the 3/12


that is just 1/4


which is .25


ok so your trying to estimate what it is without a calc


but how do I find that out


Yes


ans you get 6 + .25


so you get 6.25 as the answer


wonderful work


Thanks, could we do another?


realquick


9 + (4/18) = 9.22


the real root is 2.1957 so very good aproximate


, sorry but I have to go, im sure there is another tutor waiting to help you!


sorry, BYE!


Okay, thank you for your time


Hello!


How are you?


Good.


Can you check my probelms


as we work onthem.


Sure!


Please post them.


Find the derivative of f) = x \sin(x)
h(x)=x2sin(x)


i can work on it


sec


How's it going?


h′(x)=2xsin(x)+x2cos(x)h'(x) = 2x\sin(x) + x^2\cos(x)
h′(x)=2xsin(x)+x2cos(x)


Does that make sense?


Yes. Thank you!!!


Hello


Can you help me with Factoring completely- algebra 1


Hi!


Of course!


Thanks :)


I'll give you an example problem to go by.. can you also do a visual representation.?


sure!


on the board?


I see the image


Thanks


So our job is to factor


yes sir/maam


Sir 😊


This is a bit of a tough problem, but we can do it!


okay...


like factoring completely


yep


I have an idea


okay....


Can you hear me, by the way? Can we use audio?


i can't hear you..


hit the mute button


i can  hear you now... :)


by the chat in the blue


Great


OK, so what I'm noticing about this problem is that we can, the idea I have is we can divide it into two


So I'm going to use my pencil, we can kind of separate this part.


and this part


And the reason why I'm doing that is because I see we have like a 5 and a 10, which are, you know, similar, and then a 4 and an 8, which are also similar. So let's see if that um if that helps us solve the problem.


Do you wanna try factoring each of these separately and see if that helps us with the solution.


yeah...


Great. So I'll let you do that whiteboard


So just for clarity, I think you're trying to um


re-multipply, but you're trying to factor, so I'll help create like kind of the bare bones. One second.


okay.. by the way, can I take notes?


Of course, you can take notes, yeah. Like write down anything you want.


Thanks!


Basically, like, you know


try to put these into two different categories like this one will go here.


this one will go here


if that makes sense


OK


OK, so


yeah, I think, I think we're, we're a bit off here. One second. So we're not trying to multiply. We're trying to trying to factor.


okay..


So they take away the arrows for one second.


Um


so let's just deal with the first part. Let's actually ignore kind of the second part. Don't let me create a little division here.


Our blue, we'll have our blue line.


Can you erase it so i can see everythingclearly


It'll be our dividing line for now. Actually I'll even make it simpler. I'll just take out this.


part altogether


So, yeah, I can erase everything.


thanks!


So basically, if you're just going to factor this part in green, how would you, how would you factor it?


What would you take out


Then you can write it on the whiteboard


You would take out the 3 and 3, basically the exponents


you would subtract them


Yeah, so, so you can, you can write in the uh the factoring.


in this part right here


OK, yeah, so


Y squares or not, it's not um


yeah, cause the common thing here


yeah you subtract it...


is that I, if I may, I think we're still a bit confused on like factoring versus multiplying. By the way, I've really nice handwriting. Um


Thanks!


but so basically, if you see in the or the uh in the


um green, like this, the underlying green parts 5 and 10.


Well, 5 times 1 equals 5, and then 5 times 2 equals 10. For a common thing will be 5, not 15.


okay


And then also, we have Y, which is common to both.


And so if we take out, I'll just do this, this part here, maybe you can try the second one.


If we take out 5 Y squared. 0 yeah, by the way it's 5 squared, not not not to the 5th.


so you would subtract the 10-5 and add the exponents?


5 ways squared


and what we have left, we're gonna have Y


plus


And now we can, the multiple we multiply on as kind of our, our checking step and factoring so we can we can multiply when we check. So if we put this into that


and then this into that


5 voice square times Y is 5 y cubed. We have that here.


Then 5Y2 times 2


is 10 Westcard. We have that here.


So that's how we know we factored correctly.


Does that make sense


Yes sir


Awesome


Now we're gonna try that with our second part of the equations. We've done the first part.


Now we're gonna try our 4Y minus 8.


So I'll make the parentheses and you can give it a try. Oops, a different color.


So take this part in pink and yeah you have to factor it into these two.


And we're trying to pull out the common terms.


From this 41 and then 8, what do they have in common? So again, I see, I see you've written 32


um, but we're not, we're not multiplying here


That's not the first step. Their the multiplying is the checking step, but here we're trying to like almost like divide if that makes sense.


oh yeah, my bad...


okay


No problem


Yup, good first step


Uh yeah, so 2 Y times 4.


Um, I'm kind of confused because like when you multiply, um,


2 times, I think 4.


I kind of get confused with that.


cause I do


multiplication instead of division, and fact isn't factoring like division, right? Correct?


I just rejoined. Can you hear me


Yeah, I can hear you. I can hear you.


OK, awesome. Um


yeah, I could, I can hear you too as well. Um


so the, the two I did a really good job there.


Um, that's our common term. We need in this next portion right here, which underline in green.


we need two terms


We need something uh


this green part, we need something plus something.


because we have two terms here in the 4 Y minus 8, so we need something plus something or something minus something here if you want to give that a try to see what our team's terms were. It's going to re parallel what we just did with the 5 like squared on the other side. We're going to do the same process here. We took out the common


current


Um, so, for this, basically, would you like multiply 10y times 4y?


So we're gonna come back to that 10Y part later. Um, we're focusing on the pink part now and we'll bring it all together in, in a minute.


OK, cause I thought you multiplied, cross-m multiplied 5Y and uh 4Y and then you cross multiply 10 Y to 2 to 8, um.


So yeah, um, so, I, yeah, so I I


OK


I would, well, this is a factoring problem, so I would try to not think about multiplying. That that comes in the later steps in the checking steps. Like I, I would almost think about dividing, like factoring is, is you're trying to divide out the common terms, um, it's multiplying isn't really the step. It's kind of like reverse multiplying.


Um


so I'm not sure where you got the cross multiplying cro cross thing, but I wouldn't recommend that


Yes, sir.


when you're starting to solve the problem because I think that's that's confusing us a little bit. Um, yeah, so basically, so in this green underlined portion here.


So basically we're trying to do something plus or minus something.


Mhm


So we have our two terms in pink, 4 Y and and and minus 8


and we divided out, um, actually, so yeah, this is a mistake. So this is why I shouldn't be here. Um, so it just, it's just two cause two, actually, it's more than 2, so what, what number is common to both both 4 and 82 is certainly, but even more 4 times, we can actually do 4, only we put 4 in there.


because we want an even bigger number. We want to factor out as much as possible.


So


Um, so a common denominator between like a common factor between 10 and 4, or?


we, we're in the pink right now, so don't worry about the green one and I'm sorry, I'm sorry.


Yeah


Oh, a common denominator between 4 and 8 is the highest one is 4, basically. Yeah.


Correct. So that's where we're gonna, that's where we're gonna put our parentheses right here, the 4.


That's 4. And so now what, now we're gonna do basically something plus or minus something.


blank, plus, blank


plus or minus blank


Um,


Um, so what, 4 times uh equals 4 y, and then 4 times N equals -8.


That's what we have to try to fill in.


4 times, wait, so you would do 4 times, uh, what again?


Basically 4 times is what equals 4Y.


04 times.


It's, it's actually very simple. You don't overcomplicate it. 4 times what equals 4 y.


4 times he equals 14 times 1 equals 4Y.


So when we need to have a y in there.


We're 44 times 4 times Y equalsy.


and then


Yeah, Y, I'm sorry, I heard 1, yeah, it's 4 times Y. So 4 times y, yep, the second one.


Yeah


and then 44 times 4 equals 8, no, 4 times 2 equals 8. So, like, yeah.


So we have our, our plus or minus 2, so we, we need to have a negative 8 essentially -8. So which one are we going to use?


um minus because it's negative.


Thank you


OK.


Bye.


so not plus, we're gonna take out our plus. So now we, now we have it. OK, now we have kind of the bare bones. So


we have 4 times whitecos minus 2 equals 4 Y minus 8, that that goes in together. So now we have our 22 separate parts of our problem, the green and the pink.


OK


And so you've taken out the biggest term. Um,


and, uh, this is kind of a hard problem to start with. It's kind of a more algebra 201, but we're going to do our best. So


I'll say


OK, one thing I kinda confused you on, which I do apologize for is that we're gonna, it actually will be a plus too for different reasons. Um, it's because this is a


Because, was it, is it because like they cancel out basically cause + like like if for instance, if you did -6 times too, wouldn't like that be negative, like 12.


um, I'm not sure the cyst comes from, um, but where you got the 6 from, but basically what what I


Like, no, it's that's just an end, like that's just an example.


Oh, gotcha. Um, I'm having a hard time visualizing, but um it's possible that could work. But anyway, anyways, what, what I kind of misled you on is that when I put the parentheses around the 4 Y minus 6 up here at the top. Um, by the way, can you see my cursor or no?


Uh, no.


Probably not, OK. Maybe I can ask you to add that in.


Anyways, um, so when we, when we put a parenthesis around this, we have to add in basically + 8.


Yes, sir


You have to do plus right here because -4Y and then minus + equals negative. That's a complicated thing, but that's, that's, that's kind of a detail, but it's not the most important part to. It's not the principle we're working with. Anyways, now, now we have, we've factored this appropriately now. We haven't like finished our factoring job though. Do you, so we have our, let me do underlining green.


We have a green park, we have our pink part. Do you see, do you notice any common term we're going to actually try to factor a second time. Do you see any comment in this?


Yeah, exact.


Um, I see like the common terms between why like the green part, like Y + 2 and 5 + 2 under the pink part. I, I think that's because they both like have um the Y


coefficient. Is that cofi coefficient or?


Yeah


Um, yeah, student, yes, it's kind of hard to kind of like, yeah, a factor I would say is probably the best term. Yeah, great job. So we're gonna actually have to fax this again. Um


um, so


we're going to do


I think if I, if I show it first, it'll kind of make sense.


Mhm


Um, cause yeah, I would, I would definitely recommend doing more of these problems. Um.


great


I have a lot of more of these problems. Um, I was planning on doing this because like I have a test coming up. So I really need, yeah.


For sure, yeah, we're here to help you with the test. OK. So


Yes sir


this is pretty much the final answer and I'm, I'm sorry to give you the final answer kind of without working through it, but I think it's important um for this problem to kind of visualize. um, but you see Y + 2, we had that in common, um, and both of them, and then we did, um, we're going to use a different cone blue.


We have, we, we took out basically the 5 minus 4.


And that was our thing here.


Um, so that was, that basically this whole thing, this, this is our final answer.


for how we our original thing.


OK, so,


But it's basically it's a, it's a two step, it's a two-step process. You have to do the, you have to isolate


What was that


No problem.


first step to get the second step. You have to, cause what I'm confused on right now is how you got, cause I'm very slow visual learner, and so whenever I'm learning stuff, yeah, but this makes sense, this makes sense. It's just that like


so that's the final answer. 5Y it's the second minus 4


Y + 2 is that no.


Yeah, exactly. So, but it's a two-step process. You can't, you don't want to get this intuitively. So if you look back at our original problem.


I'm gonna clean it up a little bit for us.


OK


Um


some pink as well.


Um, it feels like an original problem


Mhm


We have the 5 Y cubed plus 10 Y squared minus 4Y + 8. we, we took that, we divided it into a green part and then a pink part. Um,


So, basically, you, for this, you would like divide. So if you would like factor out, so basically you pick out the stuff and divide it.


or then


OK.


yeah, facts and, yeah, I like the term use factor out. Um


so we, so when I, when, when I looked at this problem first, what I noticed uh let me let me see if I can copy and paste it.


Oh yeah, great. I'm gonna, I'm, I hope we can still see you at the top. Um


so if you look at our, our bland statement at the top.


which I'm circling in black.


One second


Mhm.


which is now blue, unfortunately.


Um, the like the the basic black um thing I circled, that was the original thing we started with, and I looked at this and say, man, man, how can we factor this?


They looked at 5 and 10, and then I was like, oh wow, 5 and 10, they look, they sound pretty similar. I can factor out to 5. And I was like, oh, why why squared and y cubed.


Yeah, wait, wait, wait. So you can, OK, I get it. I get it now. I get it now. OK, so for 5, basically 5 words to 2, this would basically be multiplied.


the 3rd, 3, I'm sorry, my bad, go ahead.


by this, and then this would basically be multiplied.


So we multiplied by this, and then it'll be multiplied by that too.


OK, OK, I get it now.


Yeah.


So


Yeah, yeah, so it's kind of like it's reverse multiplying. You're trying, you're you're unmultiplying it essentially. Uh, you know, you could think of it like dividing and factoring, um, cause I know, you know,


the way you know


Yeah, I get it now. OK.


Yeah, yeah, I'm glad, I'm so glad. Yes, it's, it's, it's a hard, this is a hard problem because it's like a, it's like a double.


this, this is a hard problem to start with because it's like you're, you're double factoring.


Yeah, cause it's, yeah, it's something else. Thank you so much.


Um, my pleasure, yeah.


Makes sense. It makes sense.


Mhm


Yes sir


Yeah, so just whenever you're looking at, at big problems like this, you see, boom in this, in this first part with a circle in black, I was like wow, I see a lot of, I see 4 terms in a row, how am I gonna deal with this? Just so you can look for common terms. You know, I see a 5, I see a 5, I see a 10, I see, you know, those go together. I see a 4 and 8 does go together, um, and they can kind of work from there. And just, you know, the, the, the, the, the multiplying part. I saw you drew some like, you know, some half circles there. So yeah, just always do that at the end cause you want to make sure your work checks out.


Yeah, it's, yeah, just


Yeah. OK, thank you so much. Oh my gosh, I think I'm gonna pass my test. Thank you so much.


yeah, I'm so happy, happy to do so. And let me know if you need, uh, I actually do have to go soon, but I hope I, I, I hope this helped and I hope you'd, I would just recommend to do a few more of these.


No pressure


Yeah, thank you so much. Thank you so much.


Have a great afternoon.


Likewise, and you can always feel free to uh uh uh um like rank me or like, you know, get feedback afterwards, there's the feedback after the forma after the session ends.


Thank you.


My pleasure. Have a great day. Bye-bye


hi


Hi Alex


I need help with a homework assignment


please put it up


Im supposed to find the perimeter of quadrilateral ABCD


ok


so would I find the perimeter of what I traced on the board?


Yes


let's do that


do you want to give a try to find the length of AB first?


sure


10 units


good


so you don't really need help


I will solve the problem and then at the end can you check if I am correct?


If I get my answer as a long decimal I should round it to the thousandth place right?


that would be fine. not sure about the question's requirement


so 27.484 units?


let's say


let's see


yes!


you got it


any other problem?


can you stay on the line in case I have any more questions while I am working through this assignment?


sure.


I have to go do something. Can you stay on the line and I will come back when I am done?


yes


I will work on another screen


ok. I will let you know once I am back


sure


I'm back


you here?


I'm going to go now. Stay on the line and I will let you know once I am back


back now


sorry I have to drop now


bye


I am back


Please let me know when you are back


Hello!


How can I help you?


I'm working on an assignment that has domain and range


Okay. That is great!


I'm not understanding it and I honestly really couldn't tell you how to find either domain or range via function


Okay. Do you want help defining what is domain and range or applying it to a specific function?


Or both?


My assignment is asking for specifying the domain and range depending on the function given


Okay. What type of function?


Radical, linear, cubic, etc


Radical, I'm pretty sure


M=3√n and n≥0, that's one of the functions


Well, the function already gives you the domain.


Do you see it?


No


Okay. I can help with that.


I will draw a quick graph.


This is called a radical function.


It is any function with a root 2.


Does that look familiar at all?


Nope


Its okay. We can work towards it.


What do you know about domain?


I know that it means x, that it's between the highest and the lowest point on a graph


Yes. It consists of all the possible x-values of a function. I will draw that on the graph. Remember x=input.


The domain is all the possible x-values for a function.


n is your input.


However, there are two ways you can think about the domain. 1). look at the graph (you can search radical graph in the future): you can see where the function is over the x-axis 2). look at the question: this question already specifies what n includes--n is greater than or equal to 0


Is that starting to make sense?


A little bit


Where is it unclear?


I'm not sure how to piece what I see together


M=output (mostly called y), n=input (mostly called x)


Okay. I got it!


I set up the equation as M=3√n≥0


But I'm not sure what I did, what to do with it, or what it means


Oh. n is greater than or equal to 0 is NOT a part of your function.


That is a separate entity I believe


So you don't plug in the variables


the function is only M=nroot3


The domain is n is greater than or equal to 0


There should be a comma between them on your question. You don't plug in the variables. You only use it as what n can be.


So everything on the x axis is greater than 0


For this function, yes.


Let me write out the question


All included variables are greater than or equal to 0.


on the x-axis


Yes, so what would the range be


Well, the lowest x- value you can plug in is 0. Right?


Yes, because it's anything greater than or equal to it


Yes. Great work1


And there is no way to make 3 root n negative. Right?


No, because roots can't be negative


Yes. Great.


0 times 3 is 0, so M can be equal to 0. But it is never negative.


And if you look on the graph, the y axis goes up forever.


So the range should be M is greater than or equal to 0.


Does that seem correct?


Why wouldn't the range be all real numbers


Because it cant't be negative.


Can you make n root 3 (which is equal to M) negative?


sorry 3 root n


Oohh, so the range in the function is defined by the domain, if n can't be negative and has to be greater than or equal to 0, m has to be the same, right?


Well, that changes on the function. The domain is not always equal to the range. Imagine a vertical shift up 1 for this same function. The domain would be the same but the range would be [1, infinite)


So it depends on the starting point basically, so if it was n≥4, it would start at four and be [4,∞)


That is 4 the domain. The range would still be [0, infinite). What I am talking about with a vertical shift is a +1. See graph :)


You are right about that being the domain. The range is altered by a different value though.


Your problem does not have a vertical shift. So don't worry too much about it for this particular question.


So it would shift up depending on the y function, so if it m=3√n+4 it would still start at 4


The range would start at 4, yes.


The domain is still [0, infite)


So the range for this function would be m≥0 because it starts at 0 and continues that or [0,∞)


Yes. That is right!


Do you understand it well enough?


Im getting there, if I were to see it on a test I would freeze


Yes. You can always just use the graph. There are only a few you will  ever see in Algebra 2. You have to use the original function and apply the transformation sto get the domain and range.


This is radical. I will put a few on the bottom of the current graph.


Have you seen these?


I think I have but I can't be too sure


Okay. It is the start of the school year, so you will.


Just remember that this question already gave you the input (n, often seen as x)


I'm in Algebra 2 algebra, so we kind of go through topics very fast, it doesn't help that I missed this topic in algebra 1


You already had the domain/


Okay. I also skipped Algebra 1. Khan Academy. It truly explains everything very well. Algebra 2 does become much easirer with a lot of Algebra 1 practice.


That's what I've heard, I'll make sure to stay on top of that!


Yes. It is great. Remmember to keep inputs and outputs straight and to always look for what the problem already gives you.


x and y are not the only possible function variables.


Question, if f(x)=x⁴ and domain is xeR, all real numbers would the range be all real numbers to?


For this question, I believe so.


The root is even so all numbers will be positive. The lowest (x=0) will be negative.


Great job!


sorry x=0 will be 0


NOT negative


And for this question I'm going to write it out


You can write it out if that helps you. :)


Okay. This is absolute value.


The range is [0, infinite) and the domain is all real numbers (here, the horizontal shift does not matter)


How did you get that


Do you see the graph?


Yes


What are all the possible x-vales?


values


Over what portion of the x-axis will it cover?


Anything between -10 and 10


Why do you think that?


Wait, anything less than or equal to -10 and 10 because of the symbol


No. It is all real numbers because it stretches infintely on the x-axis in both directions.


How?


The graph is a V and its sides are contining forever (per the nature of the graph). The arrows represent infinite.


But wouldn't it be negative


all real numbers includes possible negative values


So what does the domain indicate


the x-values that can be inputed


the range is separate on the y-axis


Liam, I am so sorry but I must leave the session. You have been great. Contact support or requesting another session to continue your learning.


Thank you again for all your help


Your welcome!


hello


hiii


ow r uu


good


how can i help you today


I need help preparing for a unit exam


did you want me to walk you through solving this problem?


yes that would be great


alright sounds good


so do you know what complementary means


yes but I forgot


alright so complementary angles are angles whos sums add up to 90 degrees


ok thats what I thought


so we know that these two angles that we have to solve for add up to 90


ok


so then it says one angle is 3 degrees less than 2 times the other angle


which i wrote as x=2y-3


so now that we have that we can plug 2y-3 in for x


ok that makes sense


so when i plug that in i get 31 =y


or 31 degrees for angle 2


however the question is asking for both angles


so we can plug in the value we got for y


to find x


and we get x=59


any questions


nope


alright sounds good


anything else you need help on today


no thank u so much that helped a lot


k


well good luck on your exam


and have a great rest of your day


u too


Hello I need help with solving this I honestly don't understand it since this has no numbers


ok


basically it just wants you to get b on one side of the equal sign by itself


yeah ik but like how


so


if we want to isolate b


what should we remove first from the left side


b?


We want to remove all other terms from the left side so that we can solve for b(isolate b)


what should we remove first?


i dont see anything u drew i see black on the side but i can't see what it says my screen is small


that was an accident


a


well we should start with "m" because it is the only number outside of the parenthesis


o


you should always try to deal with the numbers outside the parenthesis before the ones inside.


does that make sense?


mhm


great


so what is our first step then


-m?


oh multiply


close..


distributive


well we want to remove m from the left side so we wouldn't want to distribute it right?


oh


divide?


Since m is multiplying by the parenthesis and we want to remove it from the left side, what should we do


yes!


so we should divide both sides by m


which isolates b some more


so m/r?


divide by sides BY m.


divide both sides BY m


so were dividing (b-a)m by m


and r by m


can you write it out on the board/


i submitted it i got it right


ok so basically


that's great!


im done with the homework but i mainly got it don with help but i really don't understand it


so is it fin if i rewrite out the equations


and try to actually understand it


like u help me?


of course!


go ahead


Thank you there's 9 problems btw


ok


here's the first one


wait


i'm gonna take a picture of my paper and then can u write all of the equations and then ill put my paper away? bc i don't want to see te answers


i wanna try and actually solve and understand it


okay!


ok give me one second


I'm glad you want to learn the content so that you don't fall behind!


yep!


here it is you can ss it or write each one on your paper


ok thank you


yw


lmk when youre done


alright


ok first one


so were solving for h


can you put it on the whiteboard


so when it says solving for a letter that means it wants it on the outside as h= or a= or whatever it is


yes


it doesn't matter which side its on, as long as its isolated(by itself)


ok


since there are no parenthesis or exponents or anything then we can start with either the l or w


i dont see it


what's your first step?


on the whiteboard btw


now i do


what are we solving for


h


so we start with l?


by  subtracting?


so basically if its multiplying you divide and if its add u do subtraction ?


yup!


just do the opposite


but wait


how are l,w, and h related


theyre all together?


are they being added, subtracted, multiplied, or divided together


subtracted?


since there are no negatives


when there is no sign between them and they are just next to each other, they are being multiplied.


ooo omggg


yeah haha


yeah u right


wait so


if it was N=wha it would be multiplied


if there's nothing there like completely nothing like no add multiplication


u multiply?


if N was alone on one side?


if something is alone it is not doing anything


No


wait I'm confused


what are you asking


like ifts N=ecf (im putting random letters)


we would multiply automaticalyl since theres nothing


like no addition, subtraction sign


or division


yes, that means that e, c, and f are all being multiplied together


kk gotcha


same with parenthesis, m(c+b) is m times (c+b)


ok so like this


yep


so thats the answer?


no, that's still the original question


we still haven't done anything to isolate h!


ohh right we solving for h


but we multiplied the h as well?


and not the v


see this is where i gt confused at


we want to isolate h,  so we need to move everything else (l and w) to the other side


since l, w, and h are all multiplied


we can move one of them to the other side by...---


dividing?


yes


ok can u give me a problem just like this


but with diff letters


and i solve on my own


do you understand how to do it?


how did you arrive at that answer


we solve for h so by diving it brings the V


and we put the V on top since we dividing so it doesnt go on bottom


ok, do you understand?


i will see if i do with a new problem just like this


ill do it on my own


no i man


like


nvm that is just like it


like this?


yup!


great job!!


Ok next onee!


wait let me write this


on paper


redo it


done next


okk this is diff


add h?


we want to remove the other things like y and w


we don't want to move the thing we are solving for


ok so add w?


or we work left to right so y?


it doesn't matter what order you pick since there are no parenthesis or exponents here


either works


kk


like this?


if you subtract y from y-w-h, what happens to the y


(y-w-h) minus y


in y-w-h, y is positive but now you are subtracting a y from it.


so... what will you get on the right side after you subtract y?


y is gone?


oh its positive


yes, its basically like y-y


you are subtracting the y away, making h more isolated!


wait so subtract again?


oh nvm i see


wait so its yw-h?


bc the w becomes positive too


no, y was there, and now you subracted y from it so now its gone.


that's it, nothing else happens.


wait what


can u write that out


i need to like visually see


the number of Y's is positive one. there is a single y.


right?


now if you are going to subtract a y from that side, you are SUBTRACTING or REMOVING a y from that side. Thus, the y on this side will be gone.


ok


ok i see holdon


Emily rewrite this out


can u like write it with the pin thing on hre


like subtracting the y


ok, I have to go for a few minutes but I'll try to come back soon


when will u be back?


lmk when your back i will go brb as well please dont end the session


back


I am sorry about that, I left my home and I didn't have network connection for a while to reconnect to the chat.


Hi again


Hi sorry I had to leave


I did respond to you, but I don't think you saw it.


Oh I’m sorry


Idk my phone is messing up


You can upload the image again.


Do you understand what mean is?


Is it were you add all the # and then devide


Divide


Yes, similar to average.


Ohhhh


Ok


For a, it asks for the fastest typical race time, this would be focusing on the average.


I’m also taking notes so take me a while


Okay, take your time.


Ok I’m. Ready


You can read above on my comments for a.


Would it be 3.99


Second


That isn't the fastest mean race time.


That’s the fastest time right


B has 3.96


Do you meant by "second" as in driver b?


Hello


Yes, I'm here.


Do you meant by driver B when you refer to "second?"


Oh wait driver c


Sorry yeah b


Yes, because the number of seconds is lowest, which means fastest.


Do you understand?


Yes I do


Moving on to b, this focuses on standard deviation. Do you understand why?


Why?


Because standard deviation is seconds away from the mean. With more variables, it asks for which one has more variables differing from the mean calculated.


Do you understand what I mean?


Why


Sorry


Yeah I understand


But can you explain like a example


There are different types of standard deviation: low and high.


Ohhh


Let’s say you have the following test scores:

80, 82, 81, 79, 83

The mean (average) is:
(80+82+81+79+83)/5=81

Each score is close to 81, so the standard deviation will be low.

Now compare that to this set:

60, 90, 75, 100, 35

The mean is:
(60+90+75+100+35)/5=72

These scores are all over the place, so the standard deviation will be high.


Do you understand what may be the answer for b?


I want to say C


But I’m not sure


That is correct. To rephrase b, the question is asking for the highest standard deviation.


This would mean the number of seconds.


Am I right?


Yes


We can move on to C if you are ready.


Hello


Okay. For C, we can predict the one with the fastest race time and the least variability.


Ok um is the deviation the lowest


I'm not quite sure what you're referring to. For question C, they are asking you to use mean and standard deviation.


This means that the fastest race time and the least variability could be your prediction for the next race.


Do you understand what might be the answer?


C has the fastest race but the deviation is 0.19 seconds


No, look more carefully on the fastest race time


B


Has the fastest


Sorry I keep messing up


Yes, and the standard deviation is also quite low.


From the information provided, what do you predict?


Be has the fastest race time and a deviation of 0.12


Yes, that is correct


Ok:)


Moving on to question 2, it states that the average fabric is 23 mm long with variability of 0.6mm


How would we find the mean


They say the mean in the title.


Oh, I realized it asked to interpret it in the context.


I just did that. Sorry.


Do you understand what the meaning is to put it in context?


It gives you the measurements. Mean is 23 mm; standard deviation is 0.6. Put that in the context of the fabric.


It's open response.


Oh ok I was gonna say that but wasn’t sure if I had to dived or sm


Okay. Would 3 be the last question?


Yes


Okay, let's move on to 3 whenever you're ready.


I’m ready


It asks for all statement that is true, which means more than one answer can be circled here.


What do you know already that you can circle as true?


B and d


Yes, do you think there is any other answers or is that all?


Just b and d


Yes, that is correct!


Great job


Yes thank you so much:)


Sorry for all the trouble


You're welcome!


You don't need to apologize.


It was a pleasure tutoring you. Have a good day!


You to bye:)


Hi Emily, I'm David, how can I help?


Hello. Can you help me solve polynomials? Dividing and Simplifying


Sounds good!


Do you have some problems to go over or should I find them


I also need to take notes on thiss


alright


You can find them- I don't want to go in the Quiz and grab questions as that violates the Code of conduct.


Yeah that makes sense


Could you write one example question though so I know the difficulty we're looking for


like come up with one


Uhmm Simplifying.... like bx^1/ b^3 or something along the lines of that...


Simplifying.. idk how to come up with one of those


so just bx


Yea.... i guess..


Idk


alright, i'll try to find some let me know if they're what you had in mind


Okay. Thx you


this type of problem?


which one- the 1st one or the 2nd one?


Either


the 3rd one is simplifying


or dividing- so thats good


this type?


Yes.


The second one is subtracting, so that's a no- I already learned how to do that


How would you solve that one so you can walk me through it and give me thesteps on how to accomplish that


sure, we can start with this one


Yes those and the one you pointed at are kind of similar to the ones on the test.


Okay thank you.


do you know how to do fraction multiplication?


No... not sure what that is...


Just like


1/2 x 3/8


oh yes.


you multiply the bottom numbers and top numbers


You find the commonf denomiantor first


common*


well for multiplication you don't have to


you can actually just multiply the two bottom numbers


so 16


and top numbers


oh okay


so 3/16 is 1/2 x 3/8


okay


anyways that's how I like to think about these


So let's start by identifying like terms


oka.


which ones might simplify each other


*okay*


5 and 1


maybe underline the ones that can simplify each other in the same color


3 and 7


meant to be a 2 lol


oh okay, :)


so we can actually


separate them


do you see why we can do that?


yes


actually no...


can you explain...


for sure!


fraction multiplication you multiply the bottom numbers and top numbers


so all the bottom numbers times each other is?


3 x 7 = 21, correct?


and 5 x 2 = 10, correct?


yeah


so x^21 and y^10


but why are you multiplying the exponents


it's division


oh...


oh wait sorry im being confusing


okay


i meant in fraction multiplication


oh


it's all the bottom numbers multiplied by each other


so 45 times x^7 times y^2


which is the same as this


i'm not so sure


Am i making no sense


alright forget the fraction stuff


no your making sense, I just don't get it...


Is there another method to solve this? One that would be easier?


yeah for sure


let's do it another way


okay :)


so let's go back to here


we identified like terms


okay..


what about 15 and 45


how might those two simplify


well imagine you just had 15/45 as a fraction


would that be its simplest form


okay...


no.. you could still divide ot


it*


Perfect!


what would you divide out


15 and 45 have a common factor of 5


thats the GCF


close


they have one slightly larger


oh.. uhm... 15?


Yep!


Exactly!


oh. okay.


so what would you do with that


how would you use that to simplify 15/45


you would divide 15/ 15 and 45/15


that would give you...


so we can cancel the 15 and 45


and make them 1 and 3


okay so you would subtract the exponents?


so it would be 3-7, corrct?


perfect!


and then that would be the exponent of x would be -5 and the exponent of y would be positive 3


check your math on the -5


oh...


3-7 isn't -5


oh -4


I'msorry.


Good catch!


I'm sorry*


No problem!


Alright, sorry I confused you at first


want to try another?


No.. You didn't, I just didn't get it... I'm getting it now, thanks.


Yes! That would be wonderful


You can clear the board


Then it would be easier to write...


okay.


This one is trickier


is that a c?


is which


the one by 7 with the exponent of 4


meant to be y


oh.


thanks. :)


ofc


okay


so how would you start


7/56 = 8


i mean 1/8


Perfect!


Not quite


oh...


because just plain w


isn't w^0


it's actually w^1


56 has a w^2


yeah


but the top one one is w^1


so 1-2


does that make sense?


Yes


nice


okay... is it right?


it's close


oh... okay.


but I made this one extra hard


and my handwriting on the board isn't great


so let's work through this one together


you got 1/8 right


It;s all right, Mines sucks too... :)


then x^6 over x^3


x^3 you got


ok this one


over w^2


what should the subtraction be


-w


-w?


there we go


good catch


okay..


then y


y^4 over y^2


you got that right


but then


I threw in an extra sneaky x


x^4 on the bottom


David i see it


so we take our x^3


over x^4


and our x^3 turns into?


not quite


remember the subtraction


which is 3.4


not division


Yep!


oh yeah... I forgot about that.. My bad..


all good!


and then we have z


okay..


which is z^1


Oh yeah,.. I forgot about z


and there's no z on the bottom


so 1-0


and we end up with this


how'd you get that?


4 stays by itself since it is not divided by anything.


That's how i got it.


z doesn't have a 4


that's y


Oh...right... Good catch,,


alright, i'll let you do this one on your own


okay.


correct?


close


9x is right


but z with nothing next to it


Yep!


and C^0


plain c would be c^1


and 2-2 isn't 1


and what is C^0 the same as?


imagine you divide a number by itself


nothing...


OH YEAh.... i forgot... It Cancels out


oh... 1


and 1 times a number is?


the #


so we can just get rid of it


okay.  I get it now... can you help me with simplifying


yep!


like the photo i posted


like this?


no...


actually.. idk


I'm not sure..


Maybe


can you give me an example?


maybe a homework you did?


like; "what is the simplified product/ or is this simplified; bx^1/ 56


simplified product


sounds like multiplying


is that what you mean


no... not multiplying... simplifying


I'm kind of confused


could you write it on the board


uh... give me a minute i'm goign to look in my HW..


alright


Like this: The length of a rectangle is represented by the function L(x) = 2x. The width of that same rectangle is represented by the function W(x) = 8x2 − 4x + 1. Which of the following shows the area of the rectangle in terms of x?


And this: Choose the correct simplification of the expression 8 times b all over a to the power of negative 5.


so which one do you want to start with


1st one....


If possible.


Yeah


so how do you calculate the area of a rectangle


l x w x h


l * w * H


that would be in 3d


oh 2x x 8x^2


2x x -4x


yep!


and 2xx 1


and you get?


i mean 16x^2


one more x


oh yeah


that would be 2 times 16x^2


oh... 16x^4


no sorry


you got it with the 16x^3


oh.


and then it wou,d be + 2x


good catch


Okay.. is that correct?


Yep!


then the second one


okay..


not quite


okay...


so on top


we could add 8b x 1


right?


yes


because 8b x 1 = 8b


and a^0


and then 0-(-5)


huh?


Wait... I'm c0onfused...


Confused(


all good


so we have a^-5 on the bottom


Mhm...


and a^0 on bottom


top


not bottom sorry


it's allright.


and to simplify we subtract the bottom from the top


oh.


so is would be


so 0 - (-5)


double negative though


yeah exactly


:D


okay.. I get it


Yay!


Do you have another problem like this?


I can write one


okay.


okay


yep!


nice!


correct?


close


oh


6 - ( -2)


Oh my bad


all good


Thank you so much!


wait sorry


it's not -4


6 - (- 2)


Wait... was is positive 4


nope


oh...


the double negatives cancel


to make positive 2


oh... oh yeah...


My bad...


so what would it become


Okay.. Thank you.


i meant the double negative of the 2


6 - (-2)


so 6 + 2


oh


does that make sense?


Yes it does! Thank you!


Great!


Thank you so much today...


ofc!


I'm going to take my quiz... I feel pretty confident now, David.


Sorry i confused you at first


Sounds good!


Good luck!


Nope... It's okay.. It was bad on my part...


Thank you, have a wonderful Sunday!


Hello!


hey!


What questions do you have?


Anything about Radical Equations


Do you have a specific example you'd like to go over?


Cool! Do you have any ideas how to get started, or are you stuck?


I am stuck


So step 1 is usually ISOLATE THE RADICAL


basically get it alone on one side of the equation'


But that's already done!


Step 2 is to get rid of the radical!


What operation undoes a square root?


square


Right!


Let's square both sides so there's no more radical


Does that make sense?


yes


Cool! How would you solve this quadratic equation?


make it equal zero


this is where I get stuck


Watch out with that +12 first!


Are you adding or subtracting 12 from both sides of the equation?


subtracting


So you end up with +12 or -12 on the left side at the end?


minus 12


Ok!


Now you're stuck here?


Do you remember factoring?


Can you factor the LHS (left hand side)?


Nice work! And checking is super important in general, but especially for radicals. It's easy to end up taking the root of a negative number if you don't check your solutions!


Perfect!


Any questions about the steps to solve that one?


I think I understand it now


Thank you


No worries!


Hello


Hi How can I help you?


I need help finding the x intercept of a certain equation


Of course! Do you want to share the question to put it up on the whiteboard?


Ok


Great! Do you have an idea on how to go about this?


Yes, change to point slope form


On paper I got y=x+7


So, that's really close but it's not exactly right. We know that point slope form is y=mx + b. So we have to isolate the y by subtracting the 2xs from both sides.


What does that give us?


I'm going to put the steps on the whiteboard as well so you can visualize it.


Exactly! Do you know what to do next?


divide ll by 7


you got it!


so what does y equal to?


perfect! So now you have it in point slope form. Do you remember what exactly the x-intercept means?


where the "first" point meets the x axis


Yup! The x-intercept is where the line crosses the x-axis. At that point, y = 0. So, if we know that, do you have an idea on how to solve for the x-intercept?


I guess insert zero into the equation?


yup! What would you substitute 0 for?


y


do you want to solve it or do you want to solve it together>


I'll solve


Great!


correct?


You're super close but I think something went wrong. Let's go over it.


Do you see what I'm writing on the whiteboard?


yes]


Ho'd you get that?


How'd you get that?


Which part?


That whole chunk


Ok, so you divided -2/7 by both sides. Right?


And when you divide a fraction you multiply it's recipricol which you also did.


which in this case is -7/2.


oh i thought we kept the sign, ok


I meant omitted the sign


So, then you do -2 times -7/2. You multiply the numerators (-2 x-7) which gives us a positive number since we're multiplying two negatives (14) and then we do the denominators. A whole number has a denominator of one (-2/1) so it would be  1x2 which is still 2. So, then you get 14/2 which simplifies to 7.


That's alright! You keep the signs in this case.


Does that make sense or would you like me to explain it a bit more?


Oh I have to go now, sorry


That's alright! I hoped this helped! Have a nice day.


Hello!


hello


Can I get some help with subtracting polynomials


it would be a good idea to write it as a subtraction, using parentheses for each expression


ok


do you know what I mean?


I understand like (-4x^2+7x-8)-(10x^2+3x+9)


Be careful. that is not what they are saying


Oh ok, then Im not so sure


I did already make an attempt


what is being subtracted from what?


is (10x^2+3x+9) being subtracted by (-4x^2+7x-8)


I am not quite sure what you are saying. can you write the subtraction on the board.


or in the text, if you can't write on  the board


Its ok whiteboard is fine, can you read my writing


Yes, but you changed some of the signs


Hey I'm sorry I have to go but I'll ask my teacher about it


hi


can you help me with a problem please


Of course, can you show or explain it to me?


lemme try to screenshot it


No problem, take your time.


there.


Ok, thank you. Let's start by thinking of the steps to solve this.


In a situation like this, the first step is to make them like numbers. Can you do that for me?


oh like numbers?


I don't know how to do that


No you are correct


oh


Sorry, that was bad wording on my part


Hi Alex!


Hello!


What would you like help with?


I was wondering if you could make sure i'm doing this right so far


Sure!


Looks good so far! Keep going


Mr. David!


can you check my answers


Yes


Looks good! However, the frequencies are a bit off


o


how


The 70.5-75.5 should be 11, while the one after it should be 4


This is because of the boundaries, so one of the numbers doesn't belong


Can u fix the colors then please


icounted 12


ty


There you go!


That makes it 11 and 4, there were just 2 numbers misplaced


i dont see a change


oh u recircled


i mean like can u fix the numbers too in color


so i wont et confusd


Ok!


Is it more clear now?


yes


Are there any other questions you need help with?


Let me paste the screenshot and lmk if this is right


here


Yes! Sorry, I think my drawing wasn't clear, the first 4 on the frequency should be 11!


o


thats the only thing that needed to be changed?


Yes, everything else is good!


I have another one to do


Ok so with this one don't I add 1.5+13.5 then divide by 6


Yes!


kk


Oh, sorry, you subtract not add


so its 1.5+2?


and 6 columns?


Yes!]


can u check


Frequencies look good


am i doing midpoint right


Yes


can u check my calculations


Could you recheck the midpoint for 7.5-9.5?


Correct!


Everything looks good now


next one!


ok!


no keep it


im gonna screenshot this to save


oh ok!


Can you make the box rq just to save some time


with the columns


sure


9 columns  i believe?


yes


Do you want to finish it from there?


no i thought


ther needs to be like 9 sectinos


oh sorry. There are 5 columns (classes) here because you start at the initial class boundary 0.5. you keep adding the class width = 9 until you reach the maximum data value


oh ok


so 0.5+9


Yes!


are these correct


ok can u check my frequency


Yes, it looks good!


then subtract 0.5-9.5/2


recheck midpoints


i got 4.5 for a lot of them


oh sorry, you should be adding


so .5+9.5/2


o


can u chec my answers


can you redo the last one?


done


Yes! looks good


let me save this


Sure!


i need help with this


ok


So first lets take x as the original value of the house when it was purchased


The house increased in value by 15%, so its current value 100% +15% = 155% of its original vlaue


can you put this on the whiteboard please


sure!


brb


Let me know when you're back


back


so istarted it for you, can you try to make an equation based off of the information?


we divide


x?


can you make it an equation using x?


ye we dont know the value when it was purchased and brb again sorry


no problem!


Tell me when your back! I'll have to go after this problem.


so you know x is the orignal value, so make an equation using all the info


would it be 1.15 times 368,000?


not exactly, the 1.15 is a percentage that represents the current value


try figuring out the relationship withx


no we divide


and make an equation


yes


so it woule be 1.15x=368000


oh


mhm


and that equals 320,000


ok, thats all the time I have right now. Your doing good!


Bye!


ty


hi


what do you want to work on?


my homework


okay


let's get started


pk


ok


my question says what perimater  of the square is shown


let me draw it


so the question basically asked calculate the perimeter right?


ya


okay so since you know in a square that all four sides are 9


then what do you think it means for the calculation of the perimeter? (I know what it is)


Not quite perimeter means you have to add up all the sides


so it's 9+9+9+9


back yet?


hello


hi


I'm back uh connection error


OH so back to work


so the perimeter you have to add up all the sides


which is 9+9+9+9


so what do you get?


it's 36


show me your process


I need help solving this, but as of now I will be right back for a few mins!


i'm back


i need help with c


ok


this is just asking what the change in the y is for moving over one space on the x axis


you can simply count it on the graph


not quite


Uhh idk then


how do you find that like can you use he pencil to draw where u look at


it is actaully best to use the formula since they gave it to you


yeah i looked at years which is the x axis


and went to one year on it


is it 10 dollars?


per hour?


find y for a year and then find y for the following year and find the difference


ohhhh


nvm i see what u did


its 0.92


yes exactly


let me screenshot this to save


let me finish writing it


so you have the full process


are my answers correct so far


a is correct


c is correct


what about B?


yes that is correct


Mark


can you check my answers


nvm ik that its right but I do need help with this, this is new to me as well but its kinda like the same concept with the graph


Hi Alice


can you help me


I'm reading...


Can you give me 4 minutes to solve, and then I'll explain?


Alice


Did you learn what "cot" represents?


sin/cos


That would be "tan". "Cot" is cos/sin.


I'll write that on the board.


ohhh


ok


This is not an indeterminate form (0/0). So the solution is not difficult. What is cos(π) = ?


Are you sure? Can you check with your calculator? Make sure to set your calculator mode to "radians".


im not sure


If you don't have a calculator with you, you can use this online calculator: www.mathcalculator.com


Type cos(pi) and click on the "RAD" button.


Awesome. That's correct.


What about sin(π) = ?


Right. So we can simplify the limit a bit.


(x - π)) → 0 as x → π.


The denominator goes to zero, so the limit is -∞.


I don't know if your software will let you enter -∞. Some teacher would write this as DNE. It depends on your teacher.


OKKK


will you help me with this one


OK. The first step is to factor the numerator. It's a difference of two squares, like a^2 - b^2. Can you factor x^2 - 9 ?


Correct.


Now let's look at the denominator. For what value of x is x+3 = 0 ?


um


Yes. If x = -3, then the denominator is zero. But because we're not allowed to divide by zero, f(x) is undefined, and "discontinuous" at x= -3.


That's why you see the open (white) circle at x = -3 on the graph.


This is called a "hole" or "removable discontinuity".


yes


That's all the time I have. Any quick question before I go?


Looks like you're away. I'll end the session to help others. You can always make another request.


Hello Marcus, How are you doing today?


hi i'm doing good


do you know about domains in algebra?


Yes


ok :>


do you know how to do these kind of problems??


How can I help?


Yes, I can help you understand the problem


ok so I dont rlly understand how domains work at all


this is my first time learning about them


OK


Identify the value of x,y in the graph


are you a teacher or a student?


and i dont reall know how to do that...


for example when x is -4 and 4 then y = 0


so the value of x -s beyond choice A


choice A says that in the graph x is within -3 and 3 but that is not true it goes beyond that in the equation


does that make sense


hi


Hi how are you doing today?


good


ok i need some help on this geometry problem it shouldnt take very long


okay


Ok so i had to screen share, but i need help on question 12


this is simple


please let me know if you can see the screen


for me ill walk you through it im going to write on paper


then screenshot and share it


ok sounds good


the question is gone


I don't see it


back?


leaving in 5 minutes if your aren't there


okay your not there so bye


hey Taylor


Hello!


I hope you want leave the session like the last person did I don't know why they left they just left didn't say why or nothing which I though was really rude but I'm not tripping fr


ok sure, it may have been a conection issue, but i wont leave you


ok so I want to go over 5


because I'm not sure did I get it right


and we cant go on to 7,8,9,10,11,12,


can


ok cool


so it looks like the question asks for (2n+2)(6n-1) is that right


it +1


(2n+2)(6n+1) thanks


imma show what all I did


great!


can you read this


yes, you have good handwriting by the way,


and this looks wonderful and the math is done correctly


one final step is to. combine like terms at the end


so the 2n and the 12n combine to make 14n


but with that change it looks great!


thank you


and your 6 looks correct too except for not combining like terms as a last step!


wym 6


talk about 2 times 6?


on the paper


the next problem


i read it earlier


so I didn't combine like terms on number 6


yeah


the two middle terms


that both have an "n" or whatever the variable was


so it would be 24 and 2 ?


right


yeah, it makes 26


ok so next ones


is imma write it down


ok cool!


see it


ok done


soo x we dont know right?


usually we put 1?


that correcty


ok so


the hidden "1" is before the x


we use the foil


yep


so f for first


o for outer


I for inner


l is for last?


correct


ok so I when it comes to this part I be getting confused


is this right?


yes


x times 6x


so 6x^2


ok I'm not sure what's o


that's 12


Jordan


I'm confused so I is x and 2?


no 12


I ment o


okk


is 6 x squared


so 6x and 2?


no


the oter


the o is going to be the outer


so the x and the 2


which makes 2x


like this?


yes


ok and for I is inner


so 3 and 6?


-3 and 6x


to be more precise


and dor last


is -3 and 2?


-3 and -2


which makes positive 6


ok


soooo it will be I'm finna write it down


ok good!


i like the color organization


thank you I do that so I don't get confused


wait ionk


where to start


x and 6x


to make 6x squared


I'm not sure how to write that


so that 6xsquared - 2x - 18x +6


hello!


Idk how to solve this


So what is a good measure of central tendency?


uhh idk lol


Mean, median, mode?


For this data, how long would you expect a normal call to take?


ok so the outliners are 12 and 99


Yes.  For sure. You got it.


is that all im finding? basicaly the outside numbers


You can do the math, but you have the intuition and that’s more important.


Its numbers way outside the other ones.


So thats all it means?


Yep


kk


You got it!


give me 1 sec


gonna paste another problem


Ok


would the outliners be 9 and 10??


What do you think?  They are much closer.


uhh idk i used my intuition last time lol


Like if I give you a set of numbers 1, 9, 10, 11, 200 there is definitely an outlier.


1 is an outlier


Yeah, maybe 1 isn’t even an outlier. 200 definitely is.


actually ima work on this tmrw im gonna gts


It’s not just the lowest and highest number, it’s how far away they are from the rest of the set.


Hello! How are you?


Good I’m helping my daughter with her homework we think the answer is thousandths


For which question?


8 and 9


And hundreds for 10


For 8 the number is three thousand, two hundred and fourteen point five hundred eighty seven, with the number on the 4. For 8, that would be the ones place, because the number is 3,214. The 4 there would be the ones digit.


Oh


I guess I’m confused


Ok and 9?


Thousandths


So when it's saying what's the value of this number, the easiest way to look at it is to take the number out of the context of the problem. So for 9, which 260,623. If you remove all of the other numbers and replace them with zeros, you're left 200,000. This means that the 2 is the hundred thousands place


Mark, can you hear me?


Um, so I'm explaining it to her to replace them with zeros.


So what he's saying, Sarah,


sorry, I'm explaining this to her


See, he's saying on this one


In 8, its 3,214. If you replace everything else in the number with zeros, you're left with 0,004.587. In 4.587, 4 is the ones digit, the 5 is the tenths, 8 is the hundredths etc


on 200,000, right? If you replace all these with zeros, like, right, that would put the two in 200,000s because it's 200,000s.


and 8


if you replace


So on number 10, if you do the zeros, it would be


because


I cant see number 10


Ok hold on let me


6 underlined


the 6 is highlighted right? yeah 6 is hundreds place


OK, can you re-explain number 8 again.


Another easy way is to say the number out verbally like "one thousand, six hundred", there you're saying its place. Another way to explain number 8 is that 4 is the first number to the left of the decimal, which means that it is in the ones place.


Does she know what it means to be in the ones place versus the hundredths, thousandths etc?


The easiest way to remember it is to read the number out "three thousand, two hundred and fourteen". This is 3,000+200+10+4. 4 is in the ones place because its greater than 1 and less than 9.


hello


hi


where are we starting?


do you have a problem that you are working on?


not really i'd like to get prep forsat


idk where to start the prep


oh, you picked algebra 1


oh mb


sorry have a great day!


you too


Hello!


How are you?


Good.


How can I help?


Yeah


so


can we do some practice


like stats practice


Ofcourse!


I will put in chat


nd my work on board


Sounds good!


In a right-skewed distribution, which relationship is typically true?
A. Mean < Median < Mode
B. Mode < Median < Mean
C. Mean = Median = Mode
D. Median < Mode < Mean


sorry ignore this one


e actually done thuis one


In a two-tailed test with α = 0.05, what is the critical z-value?
A) ±1.64
B) ±1.96
C) ±2.33
D) ±2.58


Okay.


For a two-tailed test at α = 0.05, we split the alpha level (0.025 in each tail)


Does that make sense?


Ok ok!!


If the correlation coefficient r = -0.85, this indicates:
A) Strong positive correlation
B) Weak negative correlation
C) Strong negative correlation
D) No correlation


|r| = 0.85 > 0.7 indicates strong correlation. The negative sign indicates negative correlation.


Any questions?


I got C


Correct!!!


thxx


Hello


hi! I was wondering if you could help me with my Lincoln High algebra assignment?


what is Lincoln High?


Lincoln High


ok.


should I paste my question on the board?


sure


I'm just supposed to state whether its a function or not and why


what do you think about it?


I don't know


a function means that for each x there is one and only one value of y


so, do you think that for each moment in time, there would be one value for the mass?  Could there be two different values for the mass at the same moment in time?


there's only one?


I would think so.


ok thank you


you are welcome


bye!


is that it?


Have a good weekend.


you too!


hello


hi!


how can I help yo utoday?


i need help with finding the rules of these tables


ok!


let me take a look


so lets start with table 1


do you see a pattern in the x column?


it goes up by two


exactly


and then when you look at the y column compared to the x column do you see a pattern


it is multiplyed by 4


so thats your answer


can yuou turn that knowledge into an equation for table 1


x


kind of


that was a good guess


so we know that y needs to equal 1 for this equation


so can you think of how we would do that?


like for example if we have the x value you know to multiply by 4 to get the y value


its ok let me explain it in a differt way


basically using the equation you need to be able to find y right? so here you have y=..... so if we plug something in it would be y=__x


so if you have 8=__ * 2 you know what that blank value shold be


exactly!


perfect


so thats your answer for number 1


does that make sense?


yes


what about 2 though?


ok so when we look at two this one is a ltitle trickier


but its kind of just trial and error


for example, what if you tried adding or subtracting one before you look for a pattern


so we're looking more for the pattern between the input and output


so when i say add or subtract one it's more of pointing to the y column


so if you either added one to every number on the y column or subtracted on from every number on the y column could you find a pattern


not quite


but good guess


ill show you what i mean on the board


do you see how im subtracting one from the numbers in the y column


can you do that for the other numbers in table 2


do you have what number each fruit is already


no


ohhh i see


well you know watermelon now right


because you can guess watermelon based on table 1


is pineapple 7?


lets see


in table 1


you count up by 2 every time you move down the x column ri


yes


so 2+2 = 4


so how would you find watermelon


add 2 to 4


exactly


so whats watermelon?


perfect!


so now if we look at table 2


we have two complete rows


and after subtracting 1 from each number, do you see a pattern between them?


whats the pattern?


it is add 7 minus 1


it is for the row with 6 and 12 but not for the one with 9 and 19


bevause 9+7-1 = 15


not 18


think about multiplication


multiply .....................


yeah


lets do this one together


so when i look at this


what is 6x2?


and 9x2?


yep!


exactly!


do those numbers look familiar


multiply 2,add 1


good job!


can you put that in an equation


so 2x+1?


perfect


and then can you find pineapple, lemon, and pear now?


yes


yay and then can you write it on the whiteboard


or you can just tell me here


great job!


ok lets move on to table 3


so first step to looking at any of these problems is to look fro the complete rows


so which two rows are complete?


the one with watermelon and other fruit


close


do you see a number on both sides of watermelon


if a row is complete then it needs to have a number for x and a number for y


i think it is two complete rows


yes but which rows are Ava


ill give you one


the first row is complete because theres an x and y value


x is 5 and y is 25


now you try


7 and 49


exactly


so with 5 and 25


an 7 and 49


do you see a pattern


multiply by itselfs


yes


do you know how to write that?


no


so if a number is multiplied by itself, that means it's squared right?


so when you write that you do a superscript 2


did you see how i wrote it


that means any x number you have, you will multiply by itself


so it is x squared


when you type it it should be x^2


but yeah


it's "x squared"


so can you find the other fruits now?


in the y column


64 and 81


yeah!


and there's another one beside 6


perfect


ok Liam i only have 10 minutes left so we can start table 4 but im not sure we'll be able to finish it


but first things first we're gonna plug in the numbers for the fruits


oki


i only need to find the banana number


yes


so for this one can you see a direct pattern between the x value and y value?


it's ok if you can't


does that work for 8 and 36 though?


no


exactly, so for this one you actually can


can't find a direct pattern between the x and y values


so that means we need to look at the differences betwee the x values and the differences between teh y values seperately


so looking at the x column, what does each number go up by?


exactly


y goes up by 5


perfect!


so that means each time the x value goes up, y goes up by 5


exactly!


banana is 51


well for here we would need to find what y equals when x equals 1 first


it would be 5, though, won't it?


lets see


when x = 6, y= 26


when x = 5 y=21


when x=4 y = 16


when x=3 y=9


when x=2 y=4


when x=1 y=-1


so when x=1, y=-1


so that's what we're going to start with


y=-1 + ___x


if we plug in any number


so lets do 7=-1+___31


what do we get


this one's kinda hard


oh wait no


what?


sorry this should be the slope formula


have you leanred the slope formula?


yes


can you plug this into the slope formula?


you can choose any two rows


Liam i need to go now but ill show you what i mean


so basically, we have x, 8 and 7, y=36 right


so plugging it in the slope formula we have (36-31)/(8-7) so we get 5/1 = 5


so now we know the slope is 5


so we know that y=5x + ____


and so you can choose any point to plug in


in order to fill in the blank


so we could choose 9 and 41 for example


so it would be 41 = 5(9) + ____


which would be 41 = 45 + ___


so can you guess what the blank would be?


if you subtract 45 from both sides you would get the answer for the blank


so then we know the equation is y=5x-4


anyways I have to go now, but if this is still confusing feel free to ask for another tutor!


oki


You made a lot of prorgress though today Liam so good job and good luck!


hey


what do u need help with


Hi can we do some basic math so I know how to navigate the world


Really simple


yea sure


any topic in particular


Anything to do with money or calculating days


Word problems


ok


and what grade level r u


im gonna write a problem on the board and you can tell me if its too simple or too challenging


I wrote it down


Uhhh so doubling would mean his money would be 6


Alex


so for example after one month he would have 6


Because one month has 4 weeks right


yea


And a week is like 7 days right


but u don't need to use that for this problem


So umm


How do i figure this out


ok so im assuming u don't know how to right equations yet right


write


Yeah


ok so basically we just need to multiply four times then


so basically


u start at three


uhh no


do u know what a exponent is


do you know how to apply it


Um like ¾


3²


do you know what for example 2^3 is


that's two to the third


do u know what is equals


uhh not quite that's two multiplied by 3


so 2^3 is 2 multiplied by itself 3 times


so written out its 2x2x2


yea


so basically another example is 4^3


that would be 4x4x4


or 5^4


Hm


Thank makes sense


so basically in this problem


the equation would be 3 x 2^4


Three times two to the power of four


so every month


the original three is doubled


but since its not adding every time its multiplying


you have to multiple the original 3 by the amount it increases or decreases by to the power of the amount of time that passes


Mmm


So four months


We would times the double number (2) by four


No, how do I word this, we would make the 2 get to the power of four because thats the months and the two represents the doubling


yup


does that kinda make sense


2⁴ iss


So now it is 3x16


3×16 equals48


so basically u can also think about it this way


its also 3x2x2x2x2


and each 2 represents a month


so when you multiple the 3 by each 2 it counts as each month passing


and that's why there's 4


That makes way more sense


After 4 months he has 48 dollars


nice job


do u want to do another problem by urself related to this


Yeah! This will have to ve the last one since I have to go to sleep soon


Its 12am where I am


oh yea


ill type the problem out here because its probably faster


bob has five cookies. every day, the amount of cookies he has triples. after five days, how many cookies does bob have


5 cookies times 3⁵


yup


The three represents the days passing. So it's 5x3x3x3x3x3


What's 18x3?


its 54


in the future though if u have access to one it's probably easier to use a calculator


the numbers can get pretty high in these types of equations


Hmm


Noted


So after a week he has cookies?


wait wait wait


hold up


I think u might've done a step incorrectly


3x3 isn't equal to 6x3


its 9 not 18


I meant 3x3 is equal to 6. Then I did 6x3


Ohhh


here I can write it out for u


1. 3x3=9


2. 9x3=27


3. 27x3=81


4. 81x3=243


and then u multiply 243 by 5


and u will get


Ohhhhh


Sam must have alot of cookies


1215 cookies at the end of the week


yea he probably does


hell probably also have diabetes soon


LOLLL


Sam should go on a diet


I think its a bit late for that


Well thank you so much for this lesson haha, I think I'll go now since its really late where im at


yea good night


Sam I'll be at his funeral since he probably had a heart attack from diabetes


yup


bye


Hi.  How are you?


Hi, I'm doing great


I need some help with questions on the board. There's quite a lot of them


Ok.  Which one is first?


question 79


Ok.  Let me read it.


Oh I think I know how to do the first one


The answer is B right?


Yes.


The derivative is negative, turns to 0, then goes positive.


Although I see that on the first graph as well.


Why isn't f the correct answer though?


Oh ok


Here right?


I am sorry.  Let me relook.  I thought I was looking at the function, not the derivative.


Oh Ok


So.  What we should look for with a maximum is a derivative that is increasing, then hits 0, than decreases.


Yes


So.  f fits the bill


Ok, so the final answer will be D right?


I'm still looking at g.


g(x) is increasing, hits 0, but never comes down.


h(x) never stops growing.


oh I was looking at the minimum


Ok


Can we move on?


f increases, stops increasing, then starts to decrease.  So a max.


yep


So, I believe a is the answer.


Hopefully!


Ok!


Do you have the answers?


No..


Let's look at the next one.


So.  What do you think on the next one?


A?


Right.  But are you only to pick one answer on these?


I believe so


Well A is clearly incorrect.


Can x=a be the relative maximum?


Let me come back to that in a minute.


C is correct because the function is defined at all points.


Yes


D is correct because the limits from the left and right are where the hole is shown.


And E is correct because that limit exists.


Yep so they have a general limit


I'm not sure about choice B


So.  I believe B is correct because it follows what we were saying before.


Ok


Hold that thought.


I must admit that B is 100 percent clear to be a max to me.  The function increases, stops increasing for an instant at the discontinuity, then continues to increase.  I believe A is the answer but not so confident about B.


It's quite confusing but ok


Sorry to add to that confusion.


It's fine! I'll make sure to ask my school teacher.


Good


Can we move on?


Give me a minute to take a quick break


I am back


I'm looking at the next one


I'm not sure about this one. I only know that x=0 is definitely not differentiable.


Ok.  The function is not differentiable x = 0 and x =2.


The reason for x = 2 is that the tangent line at that point is undefined.  ]


The derivative at that point is undefined.


So I believe B is the answer.


why is the tangent line at x=2 undefined?


If you were to draw the tangent to the curve at x = 2, it would be a vertical line with a slope that would be undefined (infinite).


Oh ok


Let me look at the next one.


B and C definitely have derivatives at x = 0


That leaves A, D and E.


A, D and E all seem to have a zero derivative at x = 2


The second derivative part is confusing to me. How do we know that from these graphs?


The graph of a function with a second derivative greater than 0 is concave up.


The graph of a function with a second derivative less that 0 is concave down.


Oh right, I remember that


Let me take a minute to look at the possibilities


D seems to be the answer to me


What do you think about E?


D is not continuous, right?


Yeah


So.  I'm thinking E is the right choice.


It seems to meet all conditions.


Sarah the derivative of "not continuous" parts do not exist?


Shouldn't the derivative of not continuous parts not exist as well? *


Well, both D and E do not have a derivative at x = 0, but E is continuous.  The problem states that the function is continuous over the interval.


How about A then?


Good point. Let me look at that again.


The second derivative is not less than zero for the first part of the graph.


That was a requirement of the problem.


Oh!


So, on A, the first part of the graph has a second derivative that is positive.


This question is very tricky 😅


yep, it's concave up


I have to tell you that I don't care for these type of questions.  They are very tricky and sometimes difficult to analyze in your head!


I like E on this one.


Ok


Let me study this one.


So.  C and D are out because the derivative is negative on their graphs.


Yes


I think it should be B


I like B also.  Good job!


Let me move on.


do graphs like this considered as discontinuous at 0?


No.  That is not discontinuous.


Let's start eliminating.


It is continuous but not differentiable right?


Correct.


E is true, right?


Yea


D is problematic.


The derivative of x^3 is 3x^2 which is 0 at 0.


However the derivative of x is 1


Do need to consider both sides when they say "x≤0"


Let me verify with you that they are expecting only one answer on these problems, right?


I think so


I'll ask my teacher about this question as well


I actually do have a few more questions on this topic. Do you mind helping me with them as well?


So.  I think the derivative is positive for all x not equal to zero.  This is demonstrable by taking the derivative which is 3x^2 for x < 0 and 1 for x > 0.  Both are positive.


I have to finish by noon because of another session scheduled.  Happy to help until then.


Ok


I'm picking E on this one.


Make sense?


Mike


Yep*


What's next?


I just uploaded on top


Thanks.  Let me look.


Clearly, f(x)) is > 0


Clearly f(1) = 0


Oh I think the answer is D


and f"(1) = -


Right.


f"(1)<0 *


D looks right to me


Let me look at the next one.


B is good.


Good.


D looks good


Ok


That's all for now! Thank you so much for helping me today


I really appreciate it


You are very welcome.  As I mentioned, I find these problems to be challenging and like to use the process of elimination.  You are really great!


Thanks, have a good day


Bye


helloooo


how you doing


hello


good hbu?


im good as well


whenever ur ready you can just pop a question on the board


can you help me with this


yea sure


you basically need to make a function with the criteria right


yes


can yo uhel pme


let's start with the basics first


we have 2 points we need to account for


so first just mark where those would be


wait quick question before we continue


can we draw whatever we want


or do we need to write an actually equation for this


actual*


drwa whatever


ok cool


so we can start by plotting those two points


can you put them down?


ok'


are you writing down on paper or on the whiteboard btw


whiteboard


got that


ok sweet


btw im gonna move the left one bc i think it's on (-2, 0)


ok


so for the next one


it's saying as x is approaching infinity, f(x) approaches -1


which kind of asymptote is this referencing?


im not sure


ok so with a horizontal asymptote


it kinda looks smth like this


where f(x) is starting to get closer and closer to a y-value


with a vertical asymptote


f(x) goes to -∞ or ∞


so if lim x->  f(x) is -1


then f(x) is going to -1


which asymptote is that?


vettical


vertical


it would be horizontal


ohhh


yea imagine if this was -1


if you look at a point on the graph to the right


it's very close to -1


i see


nice


so for now


i'll put an asymptote line thing


forgot what it's called


at -1


so we know now that as x moves to the right the graph should go close to that blue line


try this green one now


what kind of asymptote is that and where would it occur?


like that?


yea that's an example of a graph with a horizontal asymptote at -1 but only at -∞


plus we still have the rest of the criteria to evaluate but yea spot on


the asymptote would have to be on the right side because this one will only have f(x) go to -1 if x is -∞


ohh okay


what do i do


is that drawn correctly


if you were following the first three pieces of criteria now


now*


no*


oh i need help


notice how here if you go to the left of the graph f(x) goes to -1?


yup


left is -∞


which way is ∞?


right


yep!


so it kinda needs to be flipped


but make sure you account for the two points


oh


ok


idk how


here's one example


so i just added the green line so that we can reach the other point


but yea that black line is a good horizontal asymptote


what is the green


i just added onto the function you drew


because then you couldn't reach the (-3, 0)


you still there?


Hey Leo!


What do you need help with?


Its a geometry homework assignment that has to do with compasses


Okay, I understand


For the first one, you need to bisect the angle, right?


Do you know what does bisecting an angle mean?


sorry thats the wrong question give me a second


OKay


There's the right question now


You have a problem because it says that the perpendicular has to go thru a certain point, yes?


yeah


So, if you can figure out the right A and B to start with, it is just easy