that we're adding up


from uh


0 to 19, right?


So, 02 + 12


+ 22


+ 32 all the way up to


square


So, let's see how that can help us.


Um


are you allowed to just look up that formula or do you have to derive it


Uh, can you rely on another formula that has already been established for


we can look it up


a combination of the squares.


yea


OK, so


there should be an established formula for this one.


We could derive it, but I don't really think we want to get into that. Let me go get my uh


let's see


I can just Google it.


probably


is the best way


Let me go ahead and do that


See if I get a formula


Let's see


Some of the first N squares.


All right, so


we have it


um


I can write, I can write down the formula


Did it


for you on below.


if you already haven't got, oh yeah, I see you think you got it. 19 times 20 times.


39/6. Yup.


So


that looks like a good way to


you had already known that one, Liam. That's great.


just looked it up


Yup


Excellent


Do we have any other problems?


OK


um, we can go a couple of different ways here. We could


factor out a K, but


uh, I, I'm inclined to


try plugging in numbers again.


and seeing what pattern comes out


So why don't we do the same thing we did on the last one.


and


start plugging in and see what we get.


Mhm


right


I don't think you want the cube to, I don't think you want the cube done the last two.


that you put down


So you've got 25 cub, that should just be 2 times 25.


and the one before it should be just 2 times 2.


So let's just


fix that a little bit


You get the, there we go, right there, yeah.


in there. OK, so let's just see what we get for the first couple, see if we get a pattern here.


adding by 5?


So


starts with a negative


starts with a negative number, doesn't it?


yup


Starts with -1


and it goes


to uh 8 minus 4, which would be


Um, I'm thinking that maybe this is not the greatest approach.


Um, maybe we should back off of this and try something a little different.


ok


How about if we um


how about if we factor out the K.


and then


pull, pull that


pull the K out


ooh


that might work


and refactor that into K times 9 minus 2.


Right


So


if we um do that.


I think that's 24, right?


no


Oh sorry


right


That's a 2, right


Um


let me ask you this, Liam


not seeing a pattern


Let me ask you this, um, are you allowed to


to simply look up


KQ, the sum of K cubs and


look that up


yes


ohhh


I think I know what to do


because we may be making it too difficult. So why don't we just do it as the sum of two series instead of trying to do it this way, we're off on the wrong track.


Yeah.


We'll just do the sum of KQ minus the other one, and I, that should be easy.


So, uh


if you want to look up some of Liam or I can do that.


You go over here


Yeah, there's a formula


and square times N + 1/254.


OK


Well, I was thinking just go back to the original without even factoring it out, but you can do it this way.


as well


So we know the first one is 25 times 26/2, right?


Keep going, you're doing great


could you try it the other way


So the 1st 1, 3:25.


I want to see if we get the same answer


25 times 26.


times 51


divided by 6


m 50


Well, unfortunately, when I use the calculator, I did not get that answer, so


we must have some logic fault here.


Let me, let me go back up.


The answer I've got


I'll write it on there for you when I use the calculator to sum it up.


Um


was


let me go calculate it one more time here just to make sure I didn't.


I got this 10


So, let's go back and see if we see any problem and we'll


we did here


KQ minus 2K.


The problem may be that we can't fact we can't sum the series like that.


uh, outwardly


I think that that might be a problem.


Wouldn't it be, wouldn't it be just simpler to look to do it, go back and look at just the original


and take the sum of cubes


yea


just as two series, because I think we're, we're making it hard and we don't need to.


Well


sorry.


Yeah, that's the way to go


Too2 series


Good


OK


So the first one I, I looked it up. Do you already know the first one? I can write it.


for you if you need me to


Mhm.


All right, we must be still not on the right track here.


Um.


yea..


so let me, um


I think there's just a little bit of error in here. Would you wanna let me try it?


sure


Try it, since you've given it a valued effort.


I'm gonna go below and just kind of


start over


see if we can


I got a


take a minute here and get myself together.


So I want to go back to the original


All right. My hand's a little shaky here, but we'll


try it out. So


we're gonna do it as 2 series, some


of K cued


from one


to 25


plus


minus, sorry.


minus


2 times


the sum of K


of K


I'm hoping that's right. Sorry about the sloppiness.


OK, so then


we know that this


could be the first one should be


25 square


we can bring the 2 in front of it


times 26 square


over 4


and then


the next one is 2 times.


times 26/2.


So hopefully


that's a little simpler and maybe it'll work, maybe it won't.


So the twos cancel, right?


So let's see what we get


and clear this out


25 squad


times 26 square.


divided by 4


minus 25 times 26, 25 times 26.


is 5 650.


And if I


625 minus


we get the right answer.


So, I think we just make it too complicated, making it too hard.


wait up


so what happened here


Where's that, Liam


Um, well


I'm allowed to take


I'm allowed to factor to pull the two out, right?


why?


Um, well, if we were to write each of the terms two ways, we could probably prove it. Um,


so if I


um


we could try to prove that. I think it's correct.


Let's see


So I could write the series both ways and see if they're the same.


Let me try that


2 times the sum of K is the same thing as sum of 2K


Well.


Oh I see


Are you gonna, you want me to work on that or are you gonna do that like down below. Make sure that they're the same thing.


They should be


since it doesn't contain k


then it's alright


OK, yeah


to move it


I see


Anyhow, uh, we made it too complicated. We should have stuck with the simple approach.


let me write it down


Sure.


so k and k^3 formulas are similar


Um, yeah, they are


except that k isn't being squared


sort of similar, right


And it's dividing by 2, not 4, but it's similar.


one last one?


OK, let's think about this before we run off too quick.


Hmm


We could just write out the first few terms just to see if it helps.


But


OK, that's


what now?


one gives us 3.


2 gives us


3 gives this.


lines


and 4 gives us


Let me just take a minute and look at this and see if anything


we


or


re it


or 16.


OK


something like this


OK, let me, um


let me put


I wanna pick a number


a, a fairly big number and I wanna put it in the original series


Yeah, like 20


Let me, let's pick that and put it in the original, in the calculator and see what we get to for the, the correct answer. So let me take a minute and do that.


Oh man


All right, very interesting.


Um


um, I think I did it wrong, sorry. Let me try it again.


Got to fix that


so..


So I'm getting a decimal


value of like 8.79 when we picked 20.


So I'm gonna


I'm gonna write down


well, I've got the answer written down. It's about 8.79.


for 20


So


if we plug in 20 into your formula, if we get something


similar


So you have got it down to 1/2 plus N.


yes


or 1 + 2 over N, so 1.


plus


So that doesn't come out to be the same thing. That comes out to one


Let me make sure I'm doing everything correctly.


So all we're doing


oh, I think I see what I did wrong. Hold on.


Sorry.


I messed up


Oh, let me fix what I did.


All right


I think I did it correct;y


Your answer is right


It is 11, when we try 20, it's 11 10s and you got 11 10s, so your answer is right.


ok


thanks example.comLiam


Thank you. Way to hang in there.


bye


Bye-bye.


hi


Hello


nice to meet you


Hope You're having a great day


you too :-)


so I have this test on friday


and we're learning about this 30-60-90 triangles


and this 45-45-90 triangles


I have a page to solve


okay


could you help please?


sure


I tried solving parts of it


do you see it?


I see it


I don't even know how to do any of these tbh


hang on, need charger


take your time


well first i'm gonna say: x not n


That is x......


It's because I write cursive


and when I write fast


It tends to look like an N


sorry for the confusion


ha! you should fix that


you will confuse your teacher too


okay ma'am


I just did


are you there?


I am


#1 looks just right


for 2a


what if we call hypotenuse length "h" ?


what is leg length?


um..


11.31 something????


what is leg length "in terms of h"?


what do you mean?


you're using 16?


yeah


why?


our teacher said that if we cant explain it, use an example


okay


but you can make a rule for *any*  h


like you did for any x in 31


sorry


https://example.com be fair..


I am so confused, I don't know what to do


in #1, you said that hypotenuse is equal to leg times sqrt(2)


yes?


yea


so if you go in the other direction, you *divide* hyp by sqrt(2) to get back to leg length


you have a second step in 2a that is unnecessary


what other direction?


in 1a you went from leg to hyp


2a is from hyp to leg


I don't get it


1a is asking us to solve them


2a is asking us to explain


its just that


I don't know how exactly to explain


let's drop back a step


the hypotenuse is the long side, right?


yes


so 1a shows that to find the length of the hypotenuse given the length of a leg (x), you multiply x by sqrt(2)


okay


that is going to be the answer to 2b


if you are given the length of a leg...


you know a leg length, how do you calculate hyp?


for 45-45-90


add the 45 and 45


or 45 times 2


those are angle measures


...oh my bad


you square the leg lengths?


that little pic is the rules for 45-45-90 side lengths


it is true for EVERY 45-45-90 triangle


okay...


if you know the length of a leg (the two legs are the same length because isosceles, I.e., base angles are equal), you can find the length of the hypotenuse


by multiplying leg length times sqrt(2)


your problem one uses x; the illustration uses a


you told me that before


I'm asking 2 a


you asked me about "the other direction"


yeah because you mentioned it


2b and 1a are "find hyp given leg length"


okay


2a Is "find leg length given hypotenuse"


"the other direction"


ahhhhh


I got you!


so you need the inverse operation


your first step on 2a is exactly right


but you don't need another step!


so how do I word it


you see green?


So I could write "to find the length of a leg given the length of the hypotenuse..Divide X by Sqrt of 2"?


I think for clarity i'd say ... Divide the length of the hypotenuse by ...


but yes that's the process


starting with h


and for 2b, swap "length of leg" and "length of hypotenuse", and say multiply instead of divide


am I making sense?


Yes


the relative lengths shown in my snip are always the same


I have the backside of this page if you have time?


sure


isn't this board fun? :-


:-D


yeah :)


LOL the fingertip


Don't ask,


let me look at your work a sec


you do what you must...


its windy and my parents wont let me lock it so I had to hold it up


so...


the pic looks wrong


long side of the 30-60-90 should be 35?


The teacher gave us the triangles


I drew a draft of it


I'll show you what my friend did


35 makes more sense with the scale of the pic


dunno, she gave us that


do you see what I'm talking about tho?


You're talking about the 3x side right?


The hypotenuse


why do you think it should be 35??????????


see pink circles


problem says that cable at 60 degrees connects at 35 feet on the tower


Cable 1


I guess she drew that for us because there was that error?


so she's going with pic, not description


that's okay


so if that height is 12 (long leg of 30-60-90), what is the length of Cable 1 (hyp)?


ummmmm


.....I don't know


we have an "other direction" issue again :-)


to get from the short leg to the long leg, you multiply by sqrt(3)


we need to find the short leg given the long leg


and then the hyp


12 = x * sqrt(3)


what's x?


am I supposed to say the value?


yes


.......um


so you square 3? to cancel out the square root symbol?


is it something along those lines?


no


or am I way off?


what do you do to 12 to find x?


divide by Sqrt of 3?


perfect


you can actually just use 12/sqrt(3)


unless your teacher says otherwise


and you can put it in a calculator


do we multiply both of them by the Sqrt of 3 again


oh no


12/sqrt(3) is actually the "bridge span"


then what is the value of the hypotenuse?


see the pic?


I do


looks like you should leave the radical?


we usually do that


oh I see what you mean about the multiplying


no radical in denom


do that thing you were talking about


then write what you get on the board


erm...


12 Sqrt3/ 3?


yes and then you can simplify!


4 sqrt(3)


perfect


that is bridge span from tower to Cable 1


pink on pic


what is Cable 1 length?


(this is the easy step)


https://anothersite.net do I do that?


omg i'm scared


don't be scared


look at the little pic for 30-60-90


hypotenuse is twice as long as short leg


short leg is 4 sqrt(3)


oh I was typing that :(


oki


now wgat


what*****


how long is Cable 1?


8 sqrt(3)


okay just checking


that's perfect


the hard part of these things is when you have to divide to get from one length to another


get familiar with the little pics for 45-45-90 and 30-60-90


and how side lengths relate


........................I wish the sq roots never existed


LOL sorry about that


let's look at that other triangle


the 45-45-90


do we divide them?


you have your triangle labeled right


so bridge span to Cable 2 is ?


perfect


and the cable length is ?


...............24 sqrt2?


yup


that one was easier :-)


yea


other problems?


nope!


thank you so much for your help


You were fun!


you're welcome!


oh i'm glad


have a beautiful day!!


remember your pics!


you too


yup! thank you


bye for now


Mia


Hi!


Hi Jamie! What do you need help with?


I want to learn how to solve equations with two variables


Alright! Could you give me an example?


want an example


ok


Yes please!


Okay! The first thing we can do is to solve for one variable in terms of another variable. Do you know how that works?


yes I know one method would you want me to show you it first and then show me another method?


I can try! There's really only one method I could think of for solving this beyond graphing though


Can you show me the best method


I would do it algebraically. Like I said, solving for one variable in terms of another, and then plugging it back into the original problem. I can do it out if you'd like a demonstration


i know that way


is there any other way


Well, another way you could do it is pretending that a and b are the same as x and y. That way, you can solve for a and b independently as if you were solving for the x and y intercepts of a line in standard form


So, instead of 41 = 2a + 3b, you can do 41 = 2x + 3y. Then you can solve for the x and y intercepts (which I'm assuming you've learned before this? If not I can explain it)


Does that make sense?


Hey Jamie, I don't mind if you're working out my explanation, but could you let me know if you're still here?


Hey Jamie, I need to leave now. Good luck on Algebra 1!


okay


Hi


how can I help you today?


I need help with what's on the board


sure


you have any idea on it?


kinda of


ok


what do you have in mind?


can you tell me? and we can start from there?


first we should do 2 1/3-1 3/4


why -?


because when you look at a problem and you see left you should automatically think subtract


OH


yes, but what is the problem asking for left?


the sugar


yes


so what should we subtract


5 1/2  and the 1 3/4


not quite


what is 1 3/4？


the sugar per batch


OHHH


think, if we want to find how much sugar is left, what should we do?


so we should do 5 1/2 -2 1/3


let's first tell the process in words


what's left = ____-_____?


can u tell me what you mean by that?


what's left = total sugar originally - total sugar used


make sense?


so to find the total sugar we have to Multply?


you sure?


Mia originally have ....?


5 1/2


look in the question


yes!!!!!!!


now we know how much she originally have


then let's find the total sugar used


so how much sugar did we totally used?


uh


can I do the math?


sure


2 3/12 is the total?


you sure you did the calculation right?


these are mixed number


let me re check again


not plain fraction


you found the problem?


no


am confuse what you mean by that?


the equation is right, just the calculation


so for mixed munber you can't just multiply each part


oh you want me to find a common whole?


you have to convert them to plain fractions, then multiply the numbers


OK


but i still got 2 3/12


you sure that's how you get the common fraction?


oh so that what you meant by that


oh


I mean for 2 1/3


you can't just leave the 2 out


same for 1 3/4


you have to convert 2 1/3 to ___/__


i am still confused


for example


OHHH


you have to do that first


then you can multiply


then turn it back?


because 2 1/3 is a mixed number


turn it back after you do the *


now you do it for the other one


yes


now let's do the *


correct


now is back to original - used


the number we just got is used


but I thought that was the total


and original is in the question


the total used


then we just have to -


what do we get?


correct！！！！！！


congrats!!!


you got it!!!!!!!!!


YAYyy


any other question?


but I have a question


the question  we dis is multiple choice and it does not say the answer 1?


let me check


ok


my bad


didn't find that


oh


the denominator...


its 1 4/12


you sure


I mean 1 5/12


correct!!!!!!!!!!!


Yayy


this time should be right


congrats!!!!!


any other questions?


Yes


sure


It also does not say that..


heres the answers that it says


ok that's weird


yea


I really don't find a problem


yea I think they put the wrong answers


Maybe you want to ask your teacher, it might be a typo


well, other than this question


do you have any other?


that you need help with


can you help me with another one?


okay thank you!!!


Well, this question is exactly the same as the previous one


yea let me put a another one


I meant the solving prosses is the same, but with different number


Can you help me with PedMas i think thats how u spell it


wha do you mean by PedMas?


Parentheses I think it was division multiplication addition and subtraction


oh


ok


sure


what problem do you have on it?


I cant find so can u just give me a random problem


how's that


Good


you want to try solving it, and I  can point out your problem?


okay


you do * and / brfore + and -


what you mean by that???


you can't add 3+8 frist


you have to do 27/3 first


cause / is higher level than +


oh kk


so that means we have to do9+8??


yes


I got 17!


correct!!!!!!!


congrats!!


yayy


thank youu


you're welcome


any other question?


no that's all


ok


bye


have a great day!


you to


Hi Leo, I'm Maya - what are you working on today?


Hi I would like some review on the different inequality signs


these: < > ?


yes and the greater and less than or equal to signs as well


Ok :)


> is greater than


The larger area of the sign matches the larger number


< less than - works the same way, the larger area of the sign matches the larger number


Okay


This one is: x is less than OR equal to 5


So it can be 5, 4.999, 4.998, etc


this one is x is less than 5, so it can be 4.99999 but not 5


Right


have you used absolute value with inequality signs?


I think so but could you remind me what that is again?


This one is x is greater than or equal to 5, so 5, 5.00001 etc


sure


bad example, hold on :)


no worries


In this one, the absolute value of x is greater than 3 so x can be greater than three, also the negatives of these numbers work - I'll show you on a number line


okay


All of these numbers higher than three fit in the equation, they are all higher than 3


but also the numbers less than negative three, because when you take their absolute values, the number left is higher than 3


So negative 4, take absolute value = 4, and that number works in the equation


So inequalities with absolute values will often have answers that look like this - 2 sides of the number line


And the other tricky thing about inequality signs is - they flip when you divide or multiply both sides by a negative number


So if you are trying to solve this problem, you would divide both sides by negative 3 - I'll show you


So, you do everything as you would normally, but since you are dividing both sides by negative 3, you flip the inequality sign - tricky!!


yeah for sure


Do you think you can also help me solve a system of equations with the substitution method?


I can try


thank you


can we try this equation


y


y=2x+1 x+y=7


Ok, in the top equation, the y is already isolated, so that's good


I'll substitute it in for the y in the second equation


Does that make sense?


yeah


Great!


What would you do first here?


combine the like terms


How about here?


then I would subtract 1 from both sides


Perfect


then divide by 3 on both sides


is that how I would solve it?!


Yes, perfect!


Once you have x, you can put it back into either equation to get y


Okay


Thank you for everything, it really helped


Great! do you have any other questions?


do you think you could quiz me a bit on algebra in general? If its not too much to ask.


sure, how about a slightly harder substitution problem?


yas thank you


how about this one


y=3/2x-4 2x-3y=1


Is the one on the left correct? no parentheses?


no parentheses


Ok, we can substitute y into the second equation


The first thing I would do is multiply the 3 across the parentheses


When I do that, I change it to a plus (negative 3) and multiply the negative three across the parentheses so I don't lose my negative sign


Does that make sense?


yes


Then do we add the like terms?


you can divide by negative 1 and cancel negatives


multiply both sides by 2


Then divide both by 5


then we can plug 22/5 into the x variable to get y right?


yes :)


So 3/2 times 22/5 then subtract 4


The decimals make it a little easier to go back and check the last equation


2x-3y = 1


right


2(4.4) - 3(2.6) = 1


I understand it now thank you


That was a crazy one - I hope that helped!!


yes it did thank you so much!


You're welcome :)


Have a good day!


You too!


Hello


hello!!


what would you like help with? :3c


As of right now I would like help with angles


Interior angles, exterior


oki do you have a practice problem we can work on? :3c


yeah, The measures of the angles of a triangle are shown in the figure below. Solve for x.


the measures are  34, x, 49


oki do you have an image of the triangle?


yeah i just dont know how to send it


next to the shapes on the left


you can upload images


hi Jamie


Hello!


let's get started


do you have a math problem for us to work on together?


Ok so i have a quiz on, solving a quadratic (factoring and roots), writting equations of parabolas, operations with complex numbers, solving quadratics and completing the squares, and using the discriminant, and finally solving using the quadratic formula, so i kinda need a review on all of them since most we did before break, and ive been having a hard time getting an A in math, i usually get Bs or Cs


do you have specific math problems that I can help you with?


and I'll explain as we go


ok so for example, 8x squared - 55x = 7, i need to solve by factoring but im kinda lost


I put it on the board


did you learn that factoring means finding 2 numbers that multiply to the last number and add to the coefficient of the x term in the middle?


yea but like we also learned the other ways like putting a space in the place of C, and we had to pick the easiest, we also learned -bsquare root b - 4ac, but the factoring method you mentioned always trips me up im a bit confused on it


well, the factoring method I mentioned only works exactly that way when the quadratic starts with x squared. When it starts with 8x^2, you multiply 8 times the -7 at the end to get -56.


then find 2 numbers that multiply to -56 and add up to -55


oh i see


what we need to do first is find those 2 numbers, a and b


ok


55 and 1?


close


56 and 1


closer


one has a - sign


56 and -1


try one more time. has to add to -55


-56 and 1


yes


ohhh ok


see how that works?


the next part is kind of cool


break up -55x into -56x+x (or you can do x-56x, either way works)


you with me?


group the 1st 2 together, the 2nd 2 together


why did we add the extra x


what can you factor out of the 1st 2?


we wrote -55x as -56x+x, using the -56 and 1 that we found before


wait maybe im thinking of a different emthod but dont you eventuall get it to (x-56) and (x+1) = 0


no


oh ok


again, that would work if the quadratic started with x^2


ohhhh ok


and if we found 56 and -1 as the numbers


it's a little harder when quadratic doesn't start with x^2


what number and what power of x can we factor out of 8x^2-56x ?


right


magic just happened!


why is there a 1 and not just +(x-7)


we'll need it for the next step. I can multiply anything times 1 without changing its value, can't I?


yes


do you see something that we can factor out of the last line on the board?


yeah


we successfully factored!


now find the 2 roots


would one be 7?


-1/8 would be the other?


done


yay


did that make sense?


factor when you can. when you can't, use quadratic formula


ok for the next one the question is to compute the discriminant, and then determine the number and type of solution for the given equation; 4x squared = -5x - 3


ok to clear the board?


you write this time


move everything to the left side of =


do you know the formula for discriminant?


isnt it -b square root b squared -4ac


simpler than that


discriminant is just the part inside the radical: b^2-4ac


ohhh ok


find the discriminant here


in the full quadratic formula, we would need to take the sqrt of -23


real number?


its imaginary right


yeah


and, full formula has a +- sign, right?


it does?


rightt it does


I'll call the discriminant D and write some facts for you on the board


ok


when D = 0, the + and the - give you the same thing, right?


yes


so instead of 2 answers, you only get 1


ohhh


what about rational and irrational


discriminant tells you all sorts of useful things


2 complex roots


in our example, yes


yay


when would it be 2 irrational tho


D>0, but D not a perfect square


then you'd have something like sqrt 2, which is not rational


ohh ok


ok heres a tough one i dont understand


The formula N = 2x squared + 4x+1 represents the number of households N, in a certain city that have computers x years after 1990. According to the formula, in what year were there 49 thousand housholds with computers in this city?


just replace N wit 49000, solve for x


*N with


need everything on one side as a quadratic that = 0


subtract 49000 from both sides


k


I'm gonna guess that we can't factor that


yea thats where i was stuck


quadratic formula


starts with -b


not -


- times - is plus


right


so adding to 16 instead of subtracting from it


k lemme calculate that


yeah


2 solutions, one neg, one positive. do we need both of them here?


yes


x is years AFTER 1990


can x be negative?


no


so, only need the positive answer when you write the next line


so is that the answer?


need to evaluate that with calculator


ok


the way the problem is phrased, I think they want you to use a number of years that is an integer


after 155 years, it's still a little under 49000


need to add years to get over 49000


and they ask for the year, so calculate


we'll both be dead by then


ha yea


and then we won't have to do algebra anymore


yes my dream


I'm still doing it, and I don't want to tell you how many years it's been for me!!!!


i cant even imagine, well thank you for the explanation!


yw


Hi there! How can I help you today?


hi im working on writing a linear equation on a graph


i have ixl idk if you know what that is but i just have to answer questions


and idk what to do


I do know what IXL is, thanks for asking. Would you like to take a picture of the question and post it here so that we can work on them together?


yes


im doing y=mx


I see


Do we know what slope is?


yeah


rise/run


So, this is pretty easy in my opinion.


You just have to find the slope and put the y intercept right next to it.


oh


Can you tell me what the slope is?


Close, are you sure it's 6?


oh 1/5


Correct!


Now, where does the line cross the y axis?


That's all you had to do!


oh ok


We just had to enter our values from the graph, into our formula.


Would you like to do some more questions with me, so that I'm still here to help you if needed?


i'll upload the pic


Alright, this time I'll let you do it and I'll just tell you if you are correct or wrong and if you are wrong I'll tell you.


ok


The reason is that, I want you to be able to solve this even without me.


You'll do great, though!


y = MX+b you've got this!


is it y=2/3x+1


Close, which way is the graph going?


down


so -2/3?


That would be correct!!!


Because, the graph is going into the negative territory, which shows that it's headed into the negatives.


ohh ok


y= -2/3 +1 is correct


i have another


Sure, bring it on!


im not sure about this one bc of where it starts


Tip: If you don't know where it starts, then try starting from the y-intercept.


What is the y-intercept?


That would be correct!


so is it


Now, start counting from -5


Close again


Which way is the graph headed?


oh


down


so -1/2


Correct!


Don't forget about when the slope can be negative! :)


oh ok


well thats all


thank you!


No problem!


I hope I helped you learn a new skill today!


Also, if you need help again, or feel confused/stuck on something, then please do make a new help ticket and we would be happy to help you! :)


ok


It was a true honor teaching you today, and I hope you have a great rest of your day!


hi


hi i was wondering if you could help me with my geometry question


can you see my screen?


yes


it asks for a reflection over the given line.


Oh no


hello?


its this question


So you know


Oh


Hello.


Can you hear me


I have worked with reflections over the x axis and y axis.


could you show the example for the question?


I can hear you now. I'm sorry.


Um, can you hear me now?


Yes, I can


Oh, OK, that's good. Um, I was wondering if you could help me with my geometry homework.


OK. Um, I need to see the example. I've worked with reflection over the X-axis or the y axis or of a vertical line.


You.


but if you could click on


Yeah


uh where it says in the top right, show example. I wanna see how they plot that.


It just shows that, and at the bottom it says lo dotted lines. It just says negative.


Ah, the slope is gonna be perpendicular. If our slope is 1/3, we would use a slope of 3 and


use one, take each vertices and plot


the new slope


uh, so.


If you want, there's more examples we can see, like this one, it's 1/3 and then how do you take any?


the slope is gonna be 3, so they go up 3 and over 1, OK?


OK


So are we gonna do the 1/3 x minus 3 or that first one you showed me.


Um, this one.


OK, so we need to know, OK, 1/3


um.


I


Yes, OK. So the slope is 3.


It's


So


you know


take that point, go up 3.


like


go over, yeah, and then go to the left.


one


So I thought, I plotted there, right?


Yes, yes


Well.


I do the, do I do the same one for this one?


same thing, go up 3.


over 1, plot


not connect, yeah, you connect and yeah. The first


It connects by itself.


yes, and then go to the 3rd 1, go up 3.


go to the left, one.


So it really didn't reflect over or we maybe go up 3 again.


Um, you wanna.


or go, or go back to the original.


Yeah, um,


but that didn't show a true reflect.


wouldn't we, wouldn't we go down 3?


No, no, go all the way up 6.


and go over to


Right here?


did you go over 2?


Oh, what do you mean over to like?


Yeah, go, OK, go up 6.


Now go to the left


2 units


plot


same thing on the other one.


Mhm.


OK. I'm not, somehow I'm not, I'm, I'm doing a slide. I'm not doing a


they do a flip, didn't they?


Yeah


I mean, I don't know cause it shows it like that, so it's like.


Ah


but that's almost parallel to the green line.


yeah


wait, I'll see


you know


That is weird. OK, do the line, that one they're using that one.


Weird


They're using the slope


and then they slide it and


flip it


slide it and flipping.


Let us try again.


I take


Please.


OK. Let's go back to ours.


Um, do I unplum?


Yeah, take that away


Yeah.


OK


Take, take the point closest.


and do the slope of 3.


Uh


So, up 3 or 1?


oh no, no, no, the one


farthest to the right.


the left, fartherest to the right.


This one?


Yes, go up 3


over 1.


Now, how do we do the dotted line thing. Hmm.


That looks good


Uh, which point do we want to try now? Try the lower point.


Wait, which one?


Yeah, the, the one near the -9.


Uh this one.


No, no, no, go low, there we are.


Oh, this one


OK, go up 3.


Go up 3 more maybe. Yeah.


Go over to


No, that's not working.


on.


OK. Take the last point away.


Yeah


The last point, um, the one we just did.


OK. Use the point mute -7.


Yeah.


You go up 3


I


over


No, no, no, no


Ah, this is good.


I don't know how to get it to flip.


It's OK.


That is weird


Uh, no, this is really hard for me to like,


Are all of yours that type of question or some gonna be different?


Um, I already did every like everything else here. I just need that one, and that's uh to complete the assignment.


Let me check on my, let me look up


like


hair.


what I can find here.


I.


Oh, poor baby


Yeah.


Yes.


Mm


important thing.


They're not.


seas


including when times so.


I forget the sales poina consider devio.


This is I only come up and I think because I mean yeah I'm no I I might be.


I know.


internet.


It says find the perpendicular distance.


What.


from each vertex. So that, they're not showing that mathematical computation.


Yes


My mom miss that too but hello?


I'm sorry, what, what did you say? My parents were talking.


It says find the perpendicular distance from each vertex to the line.


Yeah.


You actually have to do some uh computation there.


So


OK.


if I'm at the -7.


like


I'm going up 3/1 so I'm making the right triangle, in other words.


No.


um


I was trying to see what their math was.


continue.


I'll see there's a lot.


and move the same distance.


see


quite


Mhm


me.


OK. Uh label the three corners.


I want that on high.


OK, we've got the three corners.


Count


OK


I can see.


the diagonal count the squares diagonally until you hit the line. So


if, if I'm here at -7 and I go 1


Well


It's like 2.15.


It's


That's weird. And then I'm gonna go


one


that's not bad. It's.


2, 2.5.


I know it's sign up on it.


Yeah, that's what's going on.


OK, so erase.


Then you want to look here.


Um, I raised a point.


Yeah, yeah


Both of them?


Yeah


So


I'm trying to count


this is


from corner to corner.


OK.


I'm going 12,


2.15 gets me to the blue line.


OK, is it?


OK


So then I want to go 2.5 units again, 1.5, 15.


What was


the


So go to -7-2.


Go to -7, 2, yes.


Maybe some kind of too.


Now


go to


I don't know, can you see my little hand?


Um, let me see.


It's around this


No, no, no, uh,


OK. You're at, your other vertices is at -7, 7, correct?


Uh, yeah.


OK. I'm gonna go 1


I'm gonna go corner to corner.


Wait,


are you doing it like on the whiteboard?


Yes. Well, no, I'm actually


on your screen, which isn't working. OK, you're at -7, 7. I want you to go


up


diagonal, go, go diagonal, go across.


Oh


to the opposite corner near the line. No, come back.


then


like that


Yes, yes. Now, wait a minute.


Go.


You don't have to work on it.


go a little more


OK.


You're not gonna be an exactly a spot, but that's gonna be close where you are.


I'm


I'm.


OK, now we've got the other point. We're gonna go.


I not it or do I just leave it there?


you leave that one


This is gonna be closed. 1234.


No.


Mm.


123. It goes off the line.


I


That isn't fair


Yeah


Yeah, like I don't even know how to do this. It's pretty good.


Yeah, if I tried to take the other point, it's going


like -11 something.


Mhm.


Um, do you wanna watch the video instead? I have the video, but like they're not exactly the same.


OK


because that's watching it, but like


I didn't understand it.


Just um, just I'm myself, but just let me know if you hear it.


Um, can you hear it


I don't hear it


You don't hear it


Um, do you hear it? The video? No.


OK, let's do, go, go, OK.


I'm trying to figure out how you get that point.


Is that the video


Yeah, that's the video.


Do it, they don't have closed caption on it, do they?


Um, you


Oh wait, you couldn't hear it?


Ah, so start over, start over. Yeah. No, I couldn't hear it, but if it's got closed caption, I could read that.


All right, I'm gonna meet myself and just let me know if you can see the video, OK?


OK


reflect a figure over line level 3.


I'm going to reflect the figure


Y equals 3 x minus 2


we have to click 3 times, 123.


Why, why?


So they are using the slope


equal distance.


How do you know the distance?


Perpendicular


create a right angle.


Um.


13, got that.


It goes up


1 and over 3. I got that, right?


Increments, OK. Got it.


That looks equal, OK. So they're continuing to use the slope, the perpendicular slope.


And I see that.


The hardest one is the one that's farther, OK.


But you still keep going up 3/1, up 3/1.


Mm


OK


So it sounds like just keep using the slope. Just keep using the slope till that point, which is farther away, has to be farther, farther, farther away.


He's trying to check the


distance


Again, slope, slope, slope. OK, let's try.


Um, hello, can you hear me?


Yes. OK. I, he's continuing to use the slope, continuing to use the slope. So let's start over.


OK, go up 3.


But at this point?


Yeah, yeah


It is it.


Go up 3 again.


you say you said.


All right


and over 1


Now see how that looks. If you were to dri


that


that is in a good place. That is a good place. Now go to the -7, 7.


Yeah.


Wait, 7.


Go up 3/1.


That's good


Yes


Now, the farther one down there, go up 3/1.


When you


There


That, that looks good.


Yay


Yeah, it looks good.


We just keep using the slope.


Oh my God, yeah.


the perpendicular slope.


Wait, so we go up 3.


over 1, up 3/1.


Oh yeah. I understand that now, yeah.


See? And you just have the last one is so far away and it's gonna flip over, so it's farther, farther, farther.


see


Oh my God, I understand that now, yeah.


We did, we did the first one too we did it up twice. We did the one that's closest, only one, and then we did the other one. I don't know it 3 times, 4 times. Let's do another one.


Uh, go submit it.


Yeah


Yeah.


I completed it now.


y


Thank you.


And I learned something.


Do you have another one


Yeah. Thank you.


Uh, no, I'm already done with everything.


I only had one. The hardest one, right?


You're quite welcome and again, I learned something.


Yeah. Thank you so much.


You're welcome. Good night.


Goodnight


Howdy !


hi


So this is your first time using Alice?


yes it is


Cool beans and welcome !


People normally post (or write) problems on the whiteboard and we work thru them.


oh i see


Most people use the "upload" button and grab a jpg from their phone or whatever.


I have little cheat sheets that I sometimes post too - like this:


Ready to try a sample problem?


Hello?


Looks like you’ve stepped away so I’m going to log out and help other students who are waiting.  Please log back in later if you still need help.


hello i have a final next week on Tuesday, but i dont have a whole lot of time to study  and i neet to understand how to solve for this


Hi Alex! How are you?


im great how abouut you


I'm great, thanks for asking! Just a heads up, the whiteboard is currently down, so we have to communicate and show work through typing.


oh really like if i write you wouldnt be able to see it


Yep. Hopefully it gets fixed soon but its been this way for a while


How can I help you today?


okay so this is my question that i need help on


Given the function F(x)=X^2 write the equation of the function g whose graph is the graph of f translated 4 units to the left and 2 units down


Ok! Let's start with what you know about this topic (It's okay if it's not much, we all start somewhere!)


so im confused bc would i use the x^2


Yes!


F(x) is the parent function, yes?


right


F(x)=(x^2) [I'm putting the parenthesis around x^2 bc it helps me keep them together in my head]


okay


yea


So lets pretend x^2 = y, correct?


actually forget what I just said


yes


If I have a normal f(x) = x equation, how would I move it 2 units down?


would i do + 2


i lowkey forgot the rules


ccould ou just remind me


Ok!


The transformation equation would look like f(x)=a(x-h)+k


Confusing right? Let's break it down!


a = amplitude, this is going to stretch or compress the function


Think of it like a rubber band, if you pull more then you were [a is greater than1] the rubber band stretches more, but if you pull less [a is less than 1] the rubber band is less stretched than before


sorry ill brb


Okay!


I'll finish typing this out and you let me know when you're ready to continue


sorry im back


It's okay!


You don't need amplitude in this transformation, so we will take it out. Now we have f(x) = (x - h) +k. Still a bit tricky, but we’re getting there!


Next let’s focus on h!


okay


h = horizontial, it’s actually pretty simple, but you need to remember that it is subtracted from x.
   If h is positive (meaning it is subtracted from x in the equation) the function shifts to the right by h units.
   If h is negative (meaning it is added to x in the equation) the function shifts to the left by h units.


I sometimes get this one mixed up myself, so sometimes it helps to just graph something like f(x)=2x and f(x)=2(x-1) to visualize how it changes.


My advice is to use something like Desmos when graphing, especially because you can color code the different equations.


ohh okay


go ahead and graph f(x)=2(x) (by hand or online, either one works!)


alrigh


now lets try finding a few points to help us plot f(x)=2(x-1) on the same graph! If you're doing it by hand and have another color available, I would definitely use it!


In the meantime, let's come up with 5 x-values to plug into our equation!


okay i will


what values do you think we should use?


question fro h right would be - and left ould be +?


or what are the signs


Let's find out! This will help you visualize and understand what and how exactly h affects the function


Lets start by graphing this equation by finding some of the points!


but i don think i would have to graph


for this we will make a chart


i would jus thave to make the equation


Ok! that's fine, but the reason I' trying to show you this is it is a good way to understand and learn how h affects it


oh okay yes i see


Alright! We are going to choose 3-5 x-values to plug into the equation f(x)=2(x-1).


Let's do 0, 1, 2, -1, and -2!


We will plug each value into x, starting with 0.


f(x) = 2( [0] - 1)


so y= 2 (0-1) or just 2(-1)


When x = 0, y = -2.


Go ahead and plot that point.


okay


Now, if x = 1, we will have the equation y= 2 (1-1)


ill brb so sorry


Ok! I think I have to go to another class now, but I can follow up later if you would like!


Keep plotting those points and draw the line connecting them to see the new function! Hopefully this helped and I'm sorry we ran out of time!


heyyyyyy


hello


Hello


Sorry I'm lagging


Hi


it okkkkkk


I need help


Ok could you tell me like what problem or topic you need help with?


with this problem


I think you were writing on the screen, was it that one


factor out


yes


wait


no problem


is that the full problem?


yessss


ok so to factor this out you have to consider the greatest common factor


like multiply?


You have to find out the factors or numbers that multiply to the terms


so like 9 can be broken down into 3 and 3


Sarah


And so for terms with x, you can just treat x like a factor


oh 6x5


for 30


yes you're on the right track


ok,so


You want to find as many factors in common as possible


but notice 6 can be broken down again to 2x3


do I need to add the X in the parentheses


which parentheses


for the final answer


lol


Oh, if you're done factoring and there is still an x in the parentheses, then you just leave it there.


So for this one, you can only factor out one x because 9x only has one x


ohhh ok


Oh sorry forgot the negative hold on


since they both have a negative you can kind of assume its a factor of -1


yes good the gcf is -3x


no


well ok so what next??


then you drop down whatever is left after you factored the -3x out from each of the terms


so -1 ??


Well lets look at the first term


So -9x was the first term


yes


and you took out -3x


and?


So it's kind of like dividing by -3x


When you divide -9x by -3x what do you get


wait


Yeah good, so you can do the same thing for the other term


umm


Be careful, since you had two terms originally, they should still be separate in the parentheses


So you were on the right track


you got 3 when you factored -3x out of -9x


right


But you don't need to put an x next to the 3


ohh


Think about it, when you divide -9x by -3x, the x's cancel out


I think you were on the right track, but where did you get the squared from?


I don't know


since the problem gives you two terms you need to work with them separately


So lets slow down a bit.


Our first step was finding the greatest common factor


that was -3x


So once you get the greatest common factor, you divide that from both the original terms


which were -9x and -30x^2


Michael


then?


so dividing -9x by -3x gives you 3


how about dividing -30x^2 by -3x


Close but that would be subtraction not division


Whats 30 divided by 3?


Yes, good


and since -30x^2 and -3x are both negative, the negatives cancel out


how about x squared divided by x


huh I don't get it ?


x times x, divided by x


think of x squared as x times x


Yes, x^2 , but you divide that by x


Adding a 1 actually keeps it the same; how about this, think of any random number and plug it in for x


So lets say x = 4


what would be 4^2, divided by 4?


Yes, or 4


4^2 is 16, and 16 divided by 4 is 4


oh ok


So we get 4 after dividing


but isnt 4 what we set x equal to?


I don't know


Yes, thats what i set it equal to earlier


The point it, x^2 divided by x is just x


So back to the original question, we had -30x^2 divided by -3x


we figured out that 30/3 is 10


and we have that x^2 divided by x is x


so combine those, you would get 10x


so yes or no


am I right


I think your answer is almost there but there are some parts that are not right


So our greatest common factor was -3x so that should go on the outside


aw man


Its ok, let me guide you through


So -3x goes outside the parentheses


ok


and we got that -9x divided by -3x is 3


so that goes inside the parentheses


by itself


+ or no plus


no plus needs to be in front of the 3


since it's already assumed to be positive


next we take a look at -30x^2


since we divided that by -3x, we got 10x


positive 10x


ooooooohohooooooo


oh my God


Does this make more sense now?


what the heck guys


yes thank you


No problem, any more questions?


YES


Sure, go on


Wow ok, this one looks a bit tougher, but we can use the same process


We first need to find the greatest common factor again


nnnngh3bfeufn34dn4f ahhhhhhhh


ok


um


For this, I recommend writing all the factors out


Let me write it below


I've listed out all the factors for both terms


umm


so now you circle anything that both lists have in common


including the x's


lol


Close, but since they only have 2 x's in common, you only circle 2 x's for each one


umm ok


Remember only the things they both have


So now you have -1, 2, x, and x in common


yes


Then you multiply them together


the x court as ones


each x counts as one x


so if you multiply 2 x's together, you get x^2


ok


Yes, and then -1 times 2 is -2


so combining those gives -2x^2


Yes, so now we have the greatest common factor, we can start writing it out


Now, we have to worry about what goes in the parentheses


what ok


So like before, you divide the original numbers by the -2x^2


no


Since we took -2x^2 out of -20x^2, we must divide to find what's left


x^2 cancels, so we are left with 10


rfight


Good


then?


Then do the same thing but for -6x^5


Close, but you did the opposite


you multiplied instead of divided


whats -6 divided by -2


Yes


whats x^5 divided by x^2?


ok yay


For this one, a fast way to do it is by subtracting the exponents


x^7 would be if you multiplied


oh but I sum it


summing the exponents is how you do multiplication


But subtracting exponents is division


I don;t know\


It's ok


So just to clarify, When you multiply, you can add the exponents, but when you divide, you subtract the exponents


so x^5 divided by x^2, you do 5-2 and get 3


so x^3


Then, combine that with what we got earlier, which was 3


so 3x^3


Once we get out result, we plug that into our final answer


Any questions?


If not then I'll call it a day


Thanks for joining!


ok let me try this, give me a min please


Hi.


Okay.


okay I got an answer


Okay thank you.


Alright well I'm not supposed to just do it for you.


Do you have an idea of what to do?


Yes I do.


ok.


Do you want to show me your answer?


Wait can you set it up please?


I can- it's just like a long division problem.


I’ve been doing too much synthetic division I forgot how to do this one.


ok It's just very similar to long division.


I set it up initially


if you see it


OK so far?


Yeah I guess.


ok can you try the next step?


Close.  It would be -2x


on top


Oh okay.


ok. Then you multiply that to -2x^2 -2x


? Like how?


(-2x)(-2x^2-2x)  distribute


ohh sorry


It's -2x times x+3


my bad


It’s fine.


ok so I multiplied it.


Then subtract


I don't know if you changed the negatives.  But it should have come out to 4x


Sorry. I accidentally erased it it’s not -6.


Sorry it’s not -2.


It should be (-2x) - (-6x) = 4x


ok


aright so bring down the 14


Make it 4 on top


4(x+3) = 4x+12


subtract.


You end up with 2, which is the remainder.


Now it's done.


Hi


How can I help you?


Hi.


Please post your question on the canvas


I need help I forgot to ask the previous tutor about before it ended.


Okay.


Sure. let me try


I need to figure out the answer for Part B.


D: sum of squares


Square of Sum


Oh okay thank you.


any more?


Um no not for right now thank you.


welcome


Have a nice night.


you too.


hello]


Hello!


Do you have a question?


Yes, I do. Can I upload it on the board?


sure


Can you read it okay?


Yes


Your answer is correct. It is not one to one


Just to understand better, it is not one-to-one if it fails the horizontal line test, correct?


Correct.  If it fails the horizontal line test, that means that there are two x values for the same y value, so it is not one to one


Make sense?


Yes, thank you :)


I had a hard time solving that one


do you know how to do that?


I was taught but it didn't really click for me


for f(g(x)), you take the expression for g and plug it in for x in f(x)


So 3(x/3+4)-12?


right


I also wrote it on the board.


What does that equal?


Would I have to distribute the 3?


yes


Would this be the answer?


the 3's cancel


no


what about the x?


ok?


I'm a bit confused as what to do next for solving this problem


it's done


f(g(x)) =x


I don't have to write any numbers at all?


that's it.


Oh, alright then.


Well, thank you for walking me through those problems.


If f(g(x)) =x and g(f(x))=x, then f and g are inverses of each other.


And you are very welcome.


Have a good evening


You as well


bye


central angles and arc measures


hello


Hi! So you’re working with angles. What do you know so far?


the measure of the arc formed by the endpoints of central angle is equal to the degree of the central angle


Right, so if the central angle, facing JL 105, what is the amount of degrees that the arc is?


Correct!


And how many degrees is an entire circle?


So if you take the amount of JL, and take it out of the total degrees, that would be the angle measurement for JML


Of the total degrees?


is line AB linear?


Is there a picture of the question you’re referring to?


yes, does it show now?


Nothing is showing up for me, but how about you explain the line?


Is it like a straight line that looks like the edge of a ruler?


Hello Alex!


how are you today? :)


hello!


Just letting you know, I have to leave this session after about 30 min... :( I'm sorry


i just wanted to study/do homework on derivatives of exps


its fine i have only like 12 questions to do


ap classroom


okay good


is there a specific problem you are struggling?


no i just wanna do all 12 with you


is this sledge hammer??


I'm not sure what you mean by sledge hammer


like


f(x) - f(x+h)/x


or was the top the other way


oh the limit definition?


yea


and yes


it's actually


and h not x on the bottom


f(x+h)-f(x) / h


yes


do you think you can solve this problem?


now you know how to approach this problem?


for sure for now im just gonna plug in


oh you actually need to find your original equation first


then you plug it in


oh wait is it already plugged in


yes sort of


so uh


so you need to find your original equation


well you just said that it should be f(x+h)


right?


so the original equation should be?


just e^2, thats what f(x)


is


is that what your asking


you answered what Alex) is


I was asking you what f(x) should be


but you got the answer to the problem :)


i did??


no actually


oh wait


im silly


we should look for the derivative


its e^x


yes that's our original function


and we are looking for x) right?


cant i just use normal exp formula?


yea


like normal derivative rules not the original one


yea it worked


great :)


is there a way for you to check answer for problems?


or does it tell you the answer at the end when you submit it?


i mean i can run it through AI


thats it


I also recommend doing a check with AI


I don't know if your teacher allows it


but that's what I do if it's not a test :) to make sure I'm correct


yea its just homework


yea it got the same answer


good!


is there other problems you wanted to work on?


I don't think I'll be able to go through every problem with you because of time


just letting you know :)


C


its fine!


great job!


quick elimination since others didnt chain rule


yes that's correct :)


c


correct!


how does that look??


well


i used product rule here


not quotient


like our first problem, we should first start with finding our original equation


right?


is this not the origonal equation


its not in f(x+h) form


no it's not


it's in


f(x)+f(a) / x


form


do you think you can find the original equation?


well seems like its just


then?


yes!


and it seems like you know how to find the derivative of 5^x :)


sorry its been like a month since ive done this is like the start of deriviatives


don't be sorry!


why would I be here if you have a perfect understanding of every concept?


rightt


v


b


that's correct :)


great job!


i got this one


i think


f(x)-f(x+h)


so it seems like 7e^x is the og


i dont see an answer id get


you are heading in the right direction


oh wait


its looking for the origonal equation


would you like a few hints?


also i think its 7/4


and negative since the signs are swapped here


yes :)


so its that


so what option do you think is the answer?


C


yes you are correct :)


great job!


I think I'll have to leave in a few minutes


do you have any last minute question before I go?


or last minute problem you want to work on?


yes lets try one more!


sure! :)


how does this look so far


could you tell me what rule you are using here?


chain rule


ohh I see


do you remember all the properties for derivatives for trig?


oh wait


do i make the uh csc-1


x


yes


y


woops


and you solve it using the derivatives of inverse trigonometric functions


so the arccsc goes on the other side right


what do you mean the other side?


like move it


i kinda forgot


or is it just equivilent


wait so how does it work


I'm trying to share an image with you


but I can't find any way to share it :(


so let me just write it in the white board


try searching derivatives of trig and inverse trig into google


and it will show you like all these trig rules


i remember all the inverse formuals


the one that I wrote in the white board?


its just that where i put the arccsc after changing it


yea


like once i chance csc-1 to z


do i move it


that was my question


the derivative of acrcsc x becomes what I wrote below


and now you just need to plug in the x


which is e^x for this case


oh thats it


yes :)


it should be


d


i think


that's what I am thinking as well


i thought ex would go on top


to be honest


based on the formula


there answer should be


based on my calculation


and there will be no e^x outside of the root as there is e^x on the denominator as well as numerator


due to chain rule


yea i got that too


so neither make sense honestly


to be honest, yes


I recommend asking your teacher in this case


even ai agrees


because I searched this problem through online and got that answer


I know....


oh


so the AI is showing that d is the answer?


it used a different identity i guess


I think d is the answer and it's just a matter of how you are writing the answer


but I recommend checking in with your teacher


especially if this is not a test to check your knowledge


yea i definitly will


okay


good


well, I hope that was a little bit of help


thanks for the help!!


of course :)


hey


hi


how u doing


show me ur question whever u ready


ood how r u


im good im good thanks for asking


damn they making u do this in Grade 8


its not hard tho


heyy


omg im so sorry my laptop turned off


hii


Hi Mia.


How's it going?


i need to do b


Scientific notation.


First write it in scientific notation, right?


so what is 4,600,000?


do you understand scientific notation?


Are you still there?


yea


Good. 4.6 times what power of 10?


Six. There are six places after the 4. Right 😀


mhm


OK, so 4.6 x 10⁶


What is the 23 one?


2.3 x  10^10?


Great. There are three groups of 3 zeroes plus one more place for the three, so 10


We can also write it as 2.3e10 for convenience.


Now divide 4.6 x 10⁶/(2.3x10¹0)


h,,


Hold on


It's not that hard


What is 4.6/2.3?


What is 6-10?


Maya.


So that is the answer. In scientific notation, 2.0 x 10⁻⁴


Do you know the rules for exponents, like
xᵃ/xᵇ = xᵃ⁻ᵇ


yeah


lets do c


OK.


What are the two numbers in scientific notation?


idk


How many places are there in the first one including the 5?


Count them ...


5.6 x 10^-12


Yes! But I'm wondering, why did you first say you didn't know how to do it?


Is something confusing you?


oh


do i do 80,000


Yes.


8 x 1^5


ALmost


how


how many places to the right of 8?


I only see 4


Now you can do it with a calculator 5.6/8, but do you know what 5.6 divided by 8 is?


Fine. I was just saying that you could do it in your head by knowing 56/8 is 7


So 0.7 x 10^what?


-12 minus 4


Yes. So 0.7 x 10⁻¹⁶. But that's not proper scientific notation


What is the right answer then?


so how


It's not right because you need to have one digit before the decimal point.


so 0.7 x 10⁻¹⁶ is 7.0 x 10⁻¹⁷


Does that make sense?


oh


nextt


Let's have you do it and then I'll check it.


idk


What part don't you know?


i do know but im a hurry


But you're practicing for a test so you need to do the work. Just getting an answer is useless to you.


Just write down the scientific notation and divide 8.4 by 4 (in your head), and subtract the exponents.


idkk i need to hurry


OK, I told you the steps.


k


thats the bext question


this one


OK, the exponents are:
3 - thousand
6 - million
9  - billion
12 - trillion


So 35 billion is 35x10⁹


But you have to change it to 3.5 x 10¹⁰ for scientific notation


okk


Do you need any more help?


yes


OK. What do you need next?


OK, since we're not doing anything right now, you can close this session and then come back later when you need more help. OK? 😀


im here


But we're not doing anything


thee


So you need to draw a region model. Can you draw one for 3/4 and one half?


OK, I need to go. Have a good day! :-)


hello


Hi


okay i need help


uh its just two questiosn


what is your question?


so ill show you the problems and is it okay if we work through them together


ok


okay so i can set it up and then like we can go thorugh it


that's correct


okay so now i would just do 1/2x10 sqaured which is 50


I think it would be a good idea to include the units


like that?


it's not inches


no yea sorry i looked at the wrong prblem


go ahead and do the calculation


ok i got this im gonna write it


boom


Good


okay next one


That's right


are you all set now?


no i dont know where to go from there


Do the calculations.


how


i dont know how


Any questions about that?


It's just like multiplying fractions


nope i got it. can you explain why we wouldnt use 1/2


we did


okay wait


also


yes i see that


so when the 1/2 turns the sqaured number into a decimal we go back and leave it as a fraction correct?


There is no decimal here.


I will show the steps


no


its okay


look


there is


because 7^2 is 49 and then 49 x 1/2 is a decimal


so i go back and just leave as 49


49 times 1/2 is 49/2


brotato chip🥀


if you multiply


It is important to know that


multiplying something by 1/2 is exactly the same thing as dividing it by 2


is it because 49 is an odd number


yes it is


okay i got


it


thank you


yes because you cannot half 49


thats what im trying to say


It has nothing to do with 49 being an odd number


however, because 49 is odd, 49/2 does not come out to be a whole number\


which is why it equals 49/2


but 49/2 is a perfectly good number


yes


ok


thank you for your help sir


goodbye


You are very welcome


have a great rest of the day!  good work, by the way


bye


Thank you! have a good day as well.


Hi!


hi


What do you need help with?


im sharing my scrren


Can't see


it


give me a few minutes


I'll be right back


gonna get a pen and paper


Hi what do you need help with


I am looking over question on my calc test I got wrong and I was stuck on figuring out how to solve them


Oh ok I can help you with that


I have a problem on the board I was stuck on


Do you know what a derivative is?


yes!


So what is it?


a derivative would be like the rate of change/slope of a tangent line


Yes! That's right


So what is the slope for the graph you provided?


Like I know that basing on the graph the derivative would be a parabola because the original function is a cubic


Thats right


but I don't know how to narrow down like I dont know if its going to be concave up or down


The slope in the beginning is positive so the derivate has to be above the y axis


would it be okay if we move to the board and use mic if possible


sorry!


Sorry, I am not available to use the mic right now


oh ok no worries!


At the max and min the derivative is zero because the tangent line is 0


ok


So which graph has the derivative at 0 at the max and min of the original graph


a


thank you for your help today!


No problem


bye!


Howdy !


Hi


So what's going on today in your math class?


righting equations from this


Okey dokey.


So you're doing trig transformations (just kinda in reverse) right?


ya


like righting equations from this graph


sin and cos


Yep.


So I wrote in blue the standard equation of a sine curve (with transformations).


So based on what you're writing.


a = 2.


d = 0


And you can either assume that this is a sine curve (with phase shift) or a cosine curve (with a different phase shift).


Period = 2pi/B


What is the period based on the picture?


So b = 1


Again, I'm assuming a sine graph...


is this right too?


So that's the phase shift


So c = 3pi/8


So function is y = 2sine(x + 3Pi/8) + 0


its minus


Oops - that's a x - 3pi/8


Yes, correct.


so we find the phase shift for cos by seeing the closest max or min and seeing how much its close to 0?


Hmmm...


how do we find phase shift for cos


Yes, you're right!


oh okay yeah


This is a cosine graph shifted right by 3pi/8


Or a sine graph shifted right by a bit more than that.


yaaa


Either would be fine - you just gotta start from the right spot.


ohhh okay yeah


thats all


Great - so best of luck to you and take care !!!


Texas


hello


i did a  through c, but i need to do the rest


hi


lets do d


yeah sure


0.52 can be taken as 0.5 that is half half a value


ohh


yeah great


now for e 23% is close to 25% and 81 is close to 80


oh


so u need to find 25% of 80


yeah well done


okk


now for f we have 35% of 22 here 22 is close to 20


ok


so we find 35% of 20


Well done!


U need any more help feel free to ask


yeha i do need mroe help


Ok tell me


there


so for a whenever there is multiplication the powers add up


so it will be 6.12*10^7*3


no i find a better way to solve


No thats wrong u can't divide them


it is multiplication


ohh


for b and c u can try this method


so how would do that in this type of format or idk


for a u just add the powers


oh


whereas for the other two u can use this method


so how would that look like on the board


but we have solve it


or ?


idk


is that the full answer for a


wait i am solving


this is the way u solve


if u want i can get u the final ans


yeha for a


whats the final answer for a


Hope u understood


i dont get it a


how did you how did you calculate


how did you get that for a


Now u got it


yea


do we solve after solving 10^7/


no that becomes complicated u can keep it this way itself


oh


Liam i have to show my work


hope u understood the process


no


it is simple multiplication division


what u didn't understood


im on c


ok so now u show me how u solve


ok there


i understand it now


u sure!


this one


explain why


Scientific notation requires the first number to be:
between 1 and 10 (1 ≤ number < 10)
But here 12 is greater than 10, so we must adjust it.


so the adjustment will be 1.2*10^11 and this is the scientific notation


hmm


hi! im on 11


Great, how do you think we should start this problem


I think its ASA


It can also be SAA because QT is congruent to RT


For it to be ASA, QT would have to be congruent to RS. Since the problem does not say that it is a rectangle, we can't prove that


Does that make sense?


yes


Do you have any other questions?


And #3 is QRT=STR


SSA


SAA


not for 11


Do you want to work on 12 or 10?


i already did 10


What about 12?


im not sure


Do you have any other problems you need help with?


I can also pull some up for extra practice


i need to do the last 3


which is 12 13 and 14


Ok, for 12, we are already given 2 angles. Which side would need to be congruent to make ASA true


AC and DF


AC and DF are actually not directly between the two angles


What about BC and EF?


Do you see how they are directly next to both angles?


yes


Can you write the congruency statement?


IN order for ASA to be congruent, angles BC and EF has to be congruent


Lets try the second one.


What angles have to be congruent for AAS to be true


GH and JK has to be congruent


They have already given us an angle and a side. So, we have to find one more angle that is congruent


KG andn JH


Those are sides. We are trying to find congruent angles


K and H


GKH has to be congruent to JHK or HGK can be congruent to KJH


Do you want to try the next one?


We have to find a congruent side and a congruent angle


LMN and QNP


That would be these two angles.


That does not look right


How about QNP and LMN?


isnt that the same thing?


typo meant to write LNM


yes


What other angle would make this ASA


hello!


Hello! What can I help you with today?


i need help with a homework problem… i will post it on the board :)


alright!


i need help with number 7 :(


No worries!


We are solving for h, and we have to be careful because it's an inequality


First, we can subtract 8 from both sides


yes which is 6


sorry -6


Yes!


Since we have a negative sign on both sides, we can divide the entire equation by -1 to make it positive


however, if we multiply or divide by a negative number, the sign of the inequality flips


Does that part make sense?


Awesome!


Now, to get rid of the 3 on both sides, should we multiply or divide it?


Which one sill get rid of the 3 on the h's side?


so what do we do we divide but we kcc?


kcc?


keep change change


I'm actually not familiar with the term, but I know that we have to multiply 3 on both sides in order to isolate h


sorry could i put it on the board?


Sure!


Perfect!


That's perfect!


I just broke mine up a bit, but doing it all in one go works too


Since we didn't multiply or divide by a negative number, the sign stays the same


yes


Now, just multiply the two fractions together!


i got 18/4 but thats improper


Yep! That's my answer too. Do you want to write it as a mixed fraction?


sure :)


Do you know how to do it?


i got 4 1/2


yes :)


Yep! nice!


You seem to already know how to solve inequalities pretty well, but let me know if you need help with anything!


okay :)


i am going to do the next problem but is it okahy if i put it ont he boar?


Sure!


sorry my keyboard is not working


No worries!


Based off the circled problems, I'm going to start with 11


To find the error in the inequality, you can also solve it yourself and compare answers with the textbook


oh sorry we are oing 12-16


Gotcha!


For 12, what would you do as your first step?


distribute :)


Yep! But another way would be to divide out 5 immediately


That way you get a nice clean inequality to solve!


After dividing out 5, you can immediately subtract 4 and get an answer


Let me know what you get!


sorry i did this,


so im stuck if we flip the sign or not


i dont think so since we are subtracting


You would be correct!


We only flip the sign if we multiply or divide by a negative number


Adding or subtracting doesn't change it :)


ohh okay thank you so much


No problem!


so i got g>-1


Yep! Nice!


we kept the sign even though we did -5/5


don’t*


right


Yes, if you're just dividing by 5, then the sign is the same


As long as the number that is doing the dividing is positive, the sign doesn't change


oh so the denominator is doing the dividing right


Yes, the number in the denominator determines the signs fate


ohh okay


So if it is 20 divided by -4, the sign would change


If it is -20 divided by 4, the sign wouldn't change, because the thing doing the dividing is positive


ohhh that makes so much sense now


Glad to hear it!


i was confuse on that thank you so much for solving my confusion!


If you have anymore questions, feel free to ask! If not, and if you feel confident, feel free to end the session!


okay :)


i think i am confident :)


Fantastic!


thank you so much :)


No problem!


Have a great day!


bye! You too :)


hello


how may I help you this afternoon?


nvm


Sorry?


my teacher said i cant us u


use


oh, I see.


ya thx for ur helpppppppp


you are welcome


bye


bye Sam


hello, can you help me with my ixl's?


Hi, Sure I am happy to try to help


can i tell u my answer and then maybe u can help me by showing me the right answer?


sounds good?


Sure, that's fine.


Do you have it to put on the screen?


is it C for this one


Sorry I'm not sure what the answer is,


But I wouldn't say C


because those segments are the same length..


I think it's B


B?


Think so


Why isnt it A


I'm not sure about this question, sorry.


You can switch to another tutor, that might be better.


oh ok


Ok I'll end the session.  Sorry, thank you for having me try.


Ok


hello


Hi


how can I help?


Algebra 1


Algebra 1aolving inequalities


ok


I put something on the whiteboard


we need the exam scores


the variable is set to x, which represents the points Sarah got on her exam


Okay


her score, x, is greater 100-27


so, x is greater than 73


So that would 100>27?


So I write down what you put at the top


yes


if she lose less than 27 points, it means she got at least a 73, right?


Yes!


now we need to see the rest of the table


Ok


can you tell us what is written on the right side of the table?


The box?


It's the grade and points


right, I cannot see the point


what is to the right of the A?


Ok I updated the image


ok, so what grade could Sarah get?


Something less than 27???


she lost less than 27 points out 100, she got less than 27 off


100 minus 27?


so, she has more than 73


which grades represent higher than 73?


A c


A, B and C


Oops my bad


do you understand that?


Yes my bad I wasn't looking at the others


so, for b. it would be that she got a C or above on the exam


Yes


should we do another problem, or that is it?


What do I write down


for a, write what I put on top of the page


Yes I put that


for b, Sarah got a C or above on the exam


that's it


The next one says find the error but it's hard to see


I think I'm ok for tonoght


Thank you for the help


you're welcome


I have a few questions I need help completing


I am unable of speaking and listening on voice


Hello


Hi im glad to help you


Hello, so I have these few questions for my precalc class and I'm a bit confused on how to apprach it. How can I do this?


Oh just send to me


I had sent a picture in the whiteboard area


But if you cannot see it, I can read them out to you


Im sorry I can’t see that could you type it in


Yes, I will


Question: Find the exact value.


33: 315 degrees


315 is a quadrant 4 is the same value=360-45 -sin45


So there is calculator work?


yes


Or you can answer


uh huh?


root 2 over 2


Right


Does it help to get your answers?


Yes


So, if I were to start on the next one, 34: csc 9pi/4


Sure


would I convert to degrees first?


Or is there a way without converting?


You dont need to convert degrees it is alot easier if you use Radian


Radian


How can I do that?


So 9pi/4 is bigger that 2pi so substract 2pi 9pi/4-8pi/4=pi/4


pi/4 is 60 degrees


Isn't it?


Or am I wrong


So it will be 45degrees


Oh yeah, sorry


so then, csc(45) in my calculator


and that is the answer?


oh shoot, I have a Texas Instruments TI-30XIIS, but it doesn't seem to show any of the reciprocals


I only see sin, cos, tan, and sin^-1, cos^-1, and tan^-1


But the exacst value means nodecimals so just root 2


You don’t have to use calculator


How do you know how to make it a root?


The final conclusion was csc(45), how do I know this concludes in root(2)?


Because sin 45° = √2/2.
csc = 1/sin, so 1 / (√2/2) = √2.


uh huh


Okay, I see


for tan(-135) how could I go about that?


Just 45 degrees and Tangent is positive in Quadrant 3 so the answer is 1


Is this helping you?


I'm partially a bit confused


My apologies


Is there any help  i can do?


I understand using the astc rule for the positive tangent, but how come it results in 1?


45° triangles always give tan = 1 because sin and cos are equal.
Since 225° has a 45° reference angle and tangent is positive there, the answer is 1


So, if tangent were in another quadrant, and was negative


It would be negative 1?


Yes exactly


if it were to be cotangent, what would it be?


Cotangent is 1/tangent.
Since tan(–135°) = 1, cot(–135°) = 1 as well


I see


Going back to Sin and Cosecant, how come the roots come into play?


The roots come from the special triangles.
A 45° triangle has sides 1, 1, and √2, so sin(45°) = 1/√2 = √2/2, and csc(45°) becomes √2


Wait, the second part where sin(45)=1/root(2) changes into root(2)/2, what's that about?


1/√2 becomes √2/2 because we multiply top and bottom by √2 to remove the root in the denominator


and root(2) * root(2) = 2


Yes thats correct


and you told me earlier that csc(45)= 2root(2)


But I'm confused


csc(45°) simplifies to √2, not 2√2. The 2 cancels out when simplifying


uh huh


So basically, sin and csc(45) are the same answer?


Yes


Is there are any help i could do


Just 2 more please


Sorry to use your time


No im glad to help you


for 36: cos 5pi/6


I should not reduce it by anything, otherwise it's negative, right?


So going off that, it's less than pi, which is in quadrant II


quadrant II is for +sin


But it's cosine, so it's going to be negative, correct?


the ref angle is 45


so, cos(45)


cos(5π/6) is in Quadrant 2, reference angle 30°, so the value is –√3/2.


reference angle is 30?


oopsie


Where did you get rad(3)/2?


√3/2 is the cosine of 30°.
5π/6 has a 30° reference angle, and cosine is negative in Quadrant 2, so the value is –√3/2


when I'm looking at a 45-45-90 triangle


the sides are x and xroot(2)


but where do you get the rad(3)?


√3 comes from the 30–60–90 special triangle.
Its sides are 1, √3, and 2.
The 45–45–90 triangle only has x, x, and x√2 — no √3 there


oh yeah, my apologies


1 is the side opposite of 30, right?


Yes, the side opposite 30° is 1.
Opposite 60° is √3.
Those come from the 30–60–90 special triangle ratios


I see


Okay, I understand


So, two more


I would start with the quadrant and ref angle


so, I would -4pi?


(2pi but twice)


I'll probably need to do it more


Reduce –22π/3 → 2π/3.
Reference angle 60°.
cot(60°)= √3/3 and cot is negative in Quadrant 2, so the answer is –√3/3


Is there are any help you with


No, I think that's it


It has been a pleasure to learn from you, thank you so much


Have a great rest of your day


My apologies that I cannot wait for you come back, I am running short on time


hi whats up


I need help with my homework


ok give me a moment


ok


ok so for the first problem


the equation is saying that for each number in th series, u multiply the previous term by n


because it n times (a n-1) right


a n-1 represents the previous term


dose n stays constant


so n is the number next to the a


let me show u


okay


so in the first line, n = 1


because we are caluclating for a_1


in the second line, n = 2 because we're calculating for a_2


a_5= 5 times a_4


almost but not quite


the n is multiplied by the previous term


so if we want to solve a_5, we would multiple n times a_4


bc 5-1 = 4


so what would a_3 be


if we're solving for a_9, we would multiply the n value (9) times a_8


well you have to go through and solve a_1 first


do u see what i wrote


do u see the pattern


a_5 would be 5 times a_4?


yes


and to solve a_5 u have to go through and solve a_3 and a_4


because they all depend on each other


ok


why dont you try solving a_3


since a_1=1


4 times 3 - 12


so 12


for a_3?


what did u get for a_1


the answer is 24 so im trying to find ur mistake


thats right for a_1


what did u get got a_2


for


but a_2 is 2


so a_3 would be 3 times 2


so whats a_3 then


yes


and then whats a_4


12 4 times 3


why?


wait no no no


a_4 = 4 times a_3


is 24


yess good job


ok now do the same for a_5


4 times 6


= 24


now a_5 is the same pattern but the n is different because now its 5


5 times 20


why 20


we said a_4 is 24 right?


so where did u get 20 from


5 times 24


yup


yes good job


u have ur answer!


yes


can we move faster though I have 7 more and I have to be somewhere


yeah


ok so u have to find the pattern between the numbers


what can u add to each to get the next number


yeah so i wrote the formula


d is the difference between them


so 15 as u said


and a_1 is the value given


it says that in the problem


so u just plug in the values


u keep the n because thats a variable


n+27 times 15


which gves


hmm


wait can you write on the screen


and substitute in a_1 and d


-27 for a_1 and 15 for d


cant


ok ok


no problem


but if u did u basically have the answer


405 n


no wait


-27n +15


ur not multiplying n and -27


your adding -27


ok


but what i wrote matches one of the answer options


so


you understand the formula we're using right


anytime u have a_1 and the difference between the numbers, u can j plug it in


yes 4 is right


yes


anything else?


oh sorry


ok for #4


u know that the domain is all the possible x values right?


so if you look at the list of coordinates given, you just need to find all the x values there are


I can use desmos


u rly dont need to


but if u want sure


wait sorry have to go bye


ok bye


hi


Hey sorry for the late response my laptop gets very buggy while using this site


Hello


hello


Um


I apologize for the late response. My laptop


doesn't work well on this website, so it tends to freeze a lot.


no rush


But if I do go quiet for a certain amount of time, the laptop just froze. I'm, I'm like still here. I'll put the um problem on the board.


take your time


There is the problem


okay


those z-scores should be the same


except one negative and one positive


Oh I did not solve this, so I would appreciate it if you went through everything with me


I just know that its wrong


do you have a z-table handy?


Yes


do you see my sketch?


yes


I see a key word at the very top of the screen


Okay


Middle


Ah yes, I shaded it on my end


if we are covering 95% what is left uncovered?


-2 - 3 and 2 - 3


what percentage is left uncovered?


percent


in each tail, good


and that as decimal is?


are you sure?


no


good


can you find that in the z-table?


Would I be looking for the number cloeset o 0.025 internally, or should I look externally?


the closest or split the difference if it falls that way


okay


you might need to add a trailing zero


Alex on the z-score table


do we need to look up the other decimal?


So would 0.025 be the first number that we read the probability of?


that would give us the left z-score


do we need to look up anything else?


Why do we need to find that in the context of the problem?


we are asked for these z-scores


Okay


do we need to look for the right boundary?


So for the right z-score score, this would be whatever's left from 2.5?


And yes


we could


could we use the z-score you just found?


no?


isn't the normal curve symmetrical?


Yes


aren't the tails the same area?


Is this unrelated to the range?


don't we need the positive z-score?


Yeah, but if the z-score scores are the same, how would there be a range?


would the right z-score be negative?


yes


is that negative to the right?


wouldn't it be to my left of the bell curve?


can you mark what you mean?


where the circle is


Honestly, I'm a little bit confused.


with the


with the um negative B


on the left side and the positive on the right side.


can you give me the z-score at the red mark?


in fact do we need the right z-score?


can we find the lower boundary of our range?


Explain?


can we use that hand-written z-score formula?


yea, but don't we need he z scores first?


we have the z-score


we can use that to get the lower boundary


okay


so find the lowest 5 first and then the highest 5?


don't we need that range at the bottom?


yes


can we ignore the figuring on the screen and do it ourselves?


Alex?


using the z-score


may I erase my drawing?


yea


and yea we can plot the numbers from the problem in , make it equal z-score and simplify to find the sample mean correct?


the mean is given up top as 40


ah I see


I will try o solve this on paper, because my laptop freezes when I use the whitebaord


can you solve for the big M?


whiteboard*


Yes give me a seconf


M = 45.88


what is your denominator?


I see what you were saying now, the z-score on the right tail would just be 1.96


and that was my final answer


that is the right boundary


how about the lower?


So now I would use Alex, correct?


perfect


Okay I will do so now


is that the only way?


idk what you mean


Wouldn't it be 40 - 5.88?


that is what I mean


ohhh okay


the symmetry is our friend


Ohhhh I see now, so rather than like redoing it from the beginning, I can just do 40 +5.88 and 40 - 5.88 to find the higher and lower boundary


right


and the z-score for the higher boundary can be found if we know he lower one, because like you said, it's symmetrical


it is the same deviation but in two directions


Ah that makes sense


if we know one we get the other for free


So our range is 34.12 to 45.88?


all because of the word "middle" or    "central"


yes good job


Yea I see it now, I have some other problems I would like to practice with. I just want to take a few notes first


sure


Alright I will put up the next problem


Once again, ignore the work shown. It's not mine, so I would still like to go over it


for any normal problem I have to make a sketch and label things


Np


are you required to use this z-score approach?


Um yea, its been the focus for this unit


okay


does the picture help at all?


If you explained it I think it would help more


can we find the z-score for this problem?


yes


that z-score looks correct?


My only concern is that if we have to find the probability of 16-pound bags that average more than m=14, can we still use m =14?


I will chck it now


No, because this shows the probability of randomly picking a sample of 16-pound bags that averages the same as an M=14 shrimp per bag


we want more that 14


mine is stumbling too


hhh


Hello


Yeah, sorry, my chat is like not working.


at all. It took like 5 minutes for me to be able to like type or message anything.


it is working fine for me


some hiccups


Yea my laptop is a little hot that may be why. This is the first time I am understanding this unit though, so I would like to continue


please


Would we use an inequality symbol to answer this question?


yes the word "more" demands it


that is what the sketch does for me


Honestly even with the explanation the sketch does not help much, but based on the context of he problem would we just change M=14 to M=15 and find the probability through that?


why 15?


do you get that same z-score?


I am rereading it give me a second


Nvm that would not make sense, I was confusing what we were comparing


so for the final answer we would read the probability for 1.67 then use an inequality symbol?


yes but we have to be careful with this one


what area goes with this z-score?


Um wdym?


do you have a z-table available?


yes


ohh


can you mark on the screen which direction that area covers?


okay


Is that correct?


are you starting at our cutoff?


Would we start at 13.5 an then go to 14 for 1.67?


no, we want from 14 to the right


we used 13.5 to help determine the z-score


ah okay


I am a little bit confused on what makes the answer deeper than anything greate than 0.9525


greater*


the 0.9525 covers from the left


but we want to the right


okay so would we find the z-score score for Alex instead?


i mean probability


yes great job


Ohhhhh


our symmetry again


well done


Alright, I will do that right now


so thats the answer?


by the way


yes


also equals that


as it must


huh, I am starting to sort of notice the patterns, but I would need more practice


I would like to move on to the next one


please


I need to take some notes first


sorry


sure


I have a question: Does the placement of 14 on the right side of the bell curve matter?


yes because it is greater that the mean


in the relation to like the eneral numbers at the boom of the bell curve like 1,2 and 3


I am helpless with these problems with the visual


without the visual


It does seem helpful, but I just don't really know how to use it


But the question I am asking, do you get what I mean?


I make the curve with the mean down the middle


I feel like my questions's a little bit confusing. Um, what I'm asking is that like I understand why you put 13.5 in the middle, cause that's the average.


Um, you know how at the bottom of the bell curve, there's z-scores or like 0-1, 2, -3


Does it like


matter where we put 14 in relation to that, or is the line that you drew, is that just like a an estimate is that not something you really have to think about.


those look like z-score numbers


I undesadn 13. and 14 are not


let me draw an an example on the board


like if this was dawn nomally they would e a he op


top*


OK, like what I'm asking


is that like I understand 13.5 and 14, like if this was drawn, I guess like normally they would be at the top, but I guess I wanna see what it looks like with the Z score numbers to, like for myself.


let me clean the board, i know what you mean


Okay ty


using the object eraser is easier


can you remove your image and we can start on a clean board?


Yup


mean=13.5, sd=.3


the SD was 1.2, or are you jus showing an example?


with the sample it became .3


Explain that pls


with a sample we divide the standard deviation by the square root of the sample size


and thats the mean for that sample? So we would ever us the given SD to write out a bell curve?


use*


sure


does this sketch make any sense?


Yes


brb


np


hi


Yea,, im here just finishing up some notes


perfect


or the way you did it before


your marking indicates exactly what we need


Yea its starting to make more sense


I am ready to move on


okay


Alright the question at the bottom


yes


Okay so I can find the z-score score, but o deemine whether this is represenative or extreme idk


sorry I need the picture


what is the shaded area ?


how about the unshaded?


The shaded area is the probability of a sample mean of 57???


and greater


okay that makes sense


Well the Z score I found was 2.5


And the second part idk


can you find that area in the z-table?


ok


you did before for the other problem


for which direction?


going to the right


can you do what you did before with a greater than?


Yea I would do 1-0.9938 ?


yes perfect


and this is to find the probability of a sample mean less than 57


no greater


Ohhh okay I see


well done


Alex, I would like some more practice, bu I have to find some problems first. This will only take a few minutes. I will just get them from my textbook


okay


good work


And question when we find the z-score for a sample mean, the area of that z-score will always represent the probability less than the sample mean?


not the sample mean but whatever cutoff in the question


Okay


Oh wait how do we determine whether this is extreme or typical?


.0062 means that with those parameters (mean and sd) we would have a sample mean greater than 57 about 6 times in a thousand


this would be most extreme


Okay so ig describe an extreme value and a typical representative value with examples please


what was our area for question 2 before?


for 14 and greater


in that situation


still rather unlikely if that mean 13.5 were true, but not nearly as extreme as this last question


What is the most obvious defining factor for an extreme like sample size value


or ig most straight forward


a threshold or .05 is the most common that I know of


so anything less than that is extreme?


usually


and anything greater would be considered typical


probably


but I would always want to see this area number and decide for myself


mmm okay, we can go through some more similar questions. If thats okay?


sure


Alright ty


the expected value is just the mean or mu (that Greek letter)


ah okay, give me a second to put two more problems up, and we can go through them


I see them


Alright I would like to start from the questions at the farthest left corner


okay


with the 30 average and SD of 8


I would like to try it by myself


and I will share my answer


please


Alright I will lyk when I am done


Okay, so I did the rest of the work on my laptop. I wanted to check to see if my bell curve was correct, but my final answer is 0.3085


on paper I meant


for part a?


yes


good


Alex for questions b-d idk how to do


c is fine for me


but the positively skewed questions idk, we can go in order tho, so B next


d is the same as c with the large enough sample size


I am stumped with b as well


Hm I don't think it will be on the test, so we can honestly do c and move on to the others


the skewness and small sample size are problems


idk how that would look or be represented honestly


me neither


That's fine, we can move on


I would like to do C to get more practice with questions like it


I will solve it on my own and stype my answer in the chat


okay


is my final answer


Alright lets try question 2


I will try it on my own and I will share my answer


You said expected value is just the sample mean right?


right


Okay


just the mean they give us


Oh? So the only think we have to calculate is the standard error?


so the expected value is 40, and the standard error is 4


for a


good


Alright the rest of thse I am confident about, so is it okay if we move onto chapte 8 questions?


Alright give me a second to pull those up


Alright here are the questions


Hey, is everything okay?


yes i am here


ah okay, whiever one you want to start with, because I honestly neeed hlp with everything


i use my ti-84 for hypothesis testing


do you something like that?


yes


wait is that a graphing calculator?


then no


it has hypothesis testing in it


don't need graphing


hmm the calculators we use just do simple arithmetic


I have never done hypothesis testing on it, but theres not a lot of functions


we can use the  z-score approach


ah okay for which one?


okay


Okay for 7 I don' really know where to start


can we the z-score formula?


Sorry my computer froze, would we just have to use the Z?


then look in the table


Ah okay, i'll try then


Z = 2.5


can you compare that with the 1.96?


I see the 1.96 but where did that come from and what does that sign = .05 mean


the 1.96 comes from reading the z-score table backwards or inverse


it is getting kind of late for me


can we call it  a night?


That's fine, thank you for all the help


Have a good night


good night


Jackson High an hypothesis testing


We are multiplying polynomials using the box method.


hello


yipes!,..ha!


The equation is (b^2-5b+4)(2b^2+6b-7)


ok, you know how to set up?


No.


ok,...lets see


so both poly nomials have the same number of terms


Let me take a picture to show how I think it is.


the box should ...ok


Like that?


yes, same number of rows as columns cuz they have the same number of terms


2b^4 first top box?


how about if I set it up the first time and then we go thru it?


ok so far,https://example.com agree??


Yes


so we start with the 2B^2 https://example.coms!!!


2b^2 times -5b


add exponenet when multiplying


no,...2 +1 =3


no wait.///add exponents when multiplyign!!!!!!!!!!!!


good


dont forget the b^2


wait,https://example.comga times neg is a +


ok, before,https://example.com you see the corrections I made?


and why?


Now what?


dont forget to add exponenets


Right


now combine like terms,https://example.comke the b squarwes together, etc


it might be easier to lay it all out first rather than doing in your head


forgot one!


so all the b cubes : -10b^3 +6b^3=


then all the squared terms


Ok Help me erase. But what is -4b^3


We don't have to solve


oh, just set up??


ok, well there ya go then


just follow other problems the same way


Yes just set up


Thank you for your help


ok, well good luck,https://example.comre!!


Solving inequality and graphing, Compound inequality and graphing and a lot more


Hello, what do you need help with today?


I was just talking with you almost an hour ago


Oh aren't you the one who said they needed to go to bed?


yes my mom told me to go to bed but I couldn't so I just got back on here.


Ok no worries, do you still need help on the same worksheet?


yeus


yes


upload it please


why you up at 10:20


Its pretty normal for me


how


highschool life


I usually go to bed around 1 and wake up at 6


you are in highschool??????///


I would assume most tutors here are


WHAT


thats crazy '


I must be a dumb highschooler than


What grade are you in?


10th grade wbu


I'm a 12th grade


dang


Algebra 10th grade year is fairly normal, you're not dumb at all


I don't know how to do anything that that man says


Haha no worries, sometimes math can get tricky


okay


But based off our last session you're doing great I wouldn't stress about it to much


alright


I don't know how to start number 2


Ok if you remember from our last session, this is the format I changed the answer to


To start this problem, start from the middle and apply that to both sides of the inequality


I'm lost I'm sorry


No worries, let me show you and I'll explain


oka


Now you see how I subtracted 6 and applied to to both sides


would the next step be subracting 2


No because we always work from the middle, and 2 and x have a multiplication relationship


Now using this logic, what should the next step be?


+18 ?


Thats a good guess, but remember, we work from the middle


We need to get the inequality so that there is only an x left in the middle


What do you think the next step should be?


minusing the 2x?


No because if we minus the 2x 0 is left in the middle and that wouldn't be good


We just want a x and there is a times 2


So how do we get rid of the times 2


ok I'm stupid


divide


Yes good, can you write that


I'm slow bruh I cant do this


No worries, you are on the right track, but look when I subtracted the 6, it was applied to both sides to keep the inequality equivalent


You will need to do the same when dividing by 2


okay am I right?


yes thats perfect


thats perfect, now try graphing it


is that right


Did you purposely leave a gap in the line?


no


ok and the two ends are -9 and 1?


yes


then you are good to go


thats perfect


alright


Now try problem 3 by yourself