um idk


ok


ohhh


nice


all good


I apologize.  I need to sign off.


please sign on again.


ok thank you for the help


there are other coaches available.


you're welcome.


5 stars


thanks!!


Hi Leo


Hello, I need help with this assignment


The first step is to plot the line y = 10+1.5x on the graph. Can you do it?


Yes


Should i show you what i did


Sure.


Here it is


I'm looking...


Looks correct.


Okay


Next step is to plot the line 11+1.2x.


here it is


Looks good.


I can show you what the two lines look like, together with the original data values, if you like.


Oh okay, sure


The blue line is 10+1.5x. Green is 11+1.2x. Do you see it?


yes, i see it


Which line do you think fits the red dots better?


Wait, I'll try to see using the table method on desmos


OK.


This is what I got


That's good.


yeah


Do you need help with the other questions?


Which other questions?


Questions 2.32a, b and c.


Yes please


Question (a) asks which of the two lines do you think fits the data (red dots) better?


I think the blue one, is that correct?


It's actually very hard to tell until we answer question (c). But your blue line does look a little better than the red one.


Yeah, I figured


Question (b) asks to calculate a value. Can you do it?


I kinda need help with that


Start with your red line, y=10+1.5x, and check the first data point. Plug in x = 1, what do you get for y = ?


Okay


I get 11.5


Awesome. Now try the blue line, y = 11+1.2x. Plug in x=1. y = ?


I get 12.1


No 12.2


my bad


Good. Between the two lines (red = 11.5 and blue = 12.2), which one is closer to the actual data value, y = 13 ?


the blue 12.2


Right. I think that's all you need to do for question (b).


Oh okay


How about c?


For question (c), you'll need to do a little calculating.


Did you learn about the "squared residuals" ?


I only know the residual, I don't it when it comes to squared


OK. Which formula did your teacher give you for the "residual" ?


residual= actual- predicted


Perfect. I


I'll show you the next step on the board.


Okay


I'll set up a table.


Let's work on the residuals starting with the red line, 10+1.5x.


okay


You already calculated y = 11.5 for x=1. I'll put that in the table.


Can you calculate 10+1.5x for the other values: x = 3, 4 5 ?


Okay, I'l calculate them and let you know


3=14.5 4=16 5= 17.5


Next, you can calculate the squared residual. For x=1 for example, it's (actual-predicted)^2 = (12-11.5)^2 = ?


Okay, it is here in the graph


Not quite correct. For x=1, instead of 12-11.5^2, you need to subtract first, and then square: (12-11.5)^2.


Oh okay


For example, (12-11.5)^2 = 0.5^2 = 0.25


I'll try again


is this good


You got the residuals. Now let's get the squares. What is 0.5^2 =


You can also use your calculator if you have one.


I think I already did it


OK. I see it.


Now to get the *sum* of the squared residuals, can you add up the numbers circled in green?


Okay, I'll try


I got 4.75


wait no, 2.25


2.75 is correct.


Next, we do the same thing for the blue line.


i kept mistaking it


Okay, I'll start


Can you calculate the "predicted" values. For x=1, you get 11+1.2(1) = ?


Right. Keep going. Same thing for x=3, 4, 5.


Okay, this is what I got for all


OK. I'll write this on the board. Can you calculate the residuals for the blue line?


Yes


Okay I got it


What you calculated is the square of the predicted values. What we need is 12-12.2 = -0.2, etc.


Oh okay


In other words, you take the number from the "Y" column and subtract the number from the "11+1.2x" column.


Okay there you go


Good. Next, can you take the numbers in the blue "Residual" column and square them. For example, (-0.2)^2 = 0.04.


I already did that


Yes, you did.


And can you add up the numbers in the blue (Residual)^2 column: 0.04 + 2.56 + ...


Okay


I got 2.64


Awesome. This confirms that the blue line is better than the red line, because the squared residuals are less.


The last step is to do the same using the best-fit line, 10.2+1.3x, shown in green color.


First find the predicted values. For x=1 for example, 10.2+1.3(1) = 13.5


Like this


Yes. Next, can you find the residuals?


how again?


For x=1, it's actual-predicted = 12-11.5 = 1.5


I meant 12-11.5=0.5


I'm looking...


Good. Now can you square the previous numbers? For example (0.5)^2 = 0.25


Yes, I did it


and I counted the sum


What did you get for the sum?


I got -0.51


It should be 0.25+1.21+0.36+0.09 = ?


Wait


Yes, now it's correct. This confirms that the best-fit line has the least sum of the squared residuals.


Okay


IS that all?


Yes. That answers question (c)


Thank you so much!


So that's all for everything?


That's right. We can end the session. Enjoy the rest of your day.


You too!


hi Chloe


Hii


So I'm in Ib math class which is MA 405. and I have a test on friday. I have some practice questions that'll be similar to the test and I wanted some help getting through them just so I can make sure Im ready :)


OK


So for the big box on the right


I did get help for that


but I'm unsure how to find b


let me look for that


I'll paste below your image


I pasted it


ohh ok


we can come back to it later


we can do it now


what is h?


negative


h is x axis of vertex


h is negative


what is a?


yes


and -b/2a is negative


so -b, divided by a negative, is also negative


b must be negativeee


I see now!1


is b positive or negative?


yeah, cause -b has to be positive


ohhh okay!!


we can start on questions. I'll try them out


and then you can tell me if they are incorrect


so a is 5


axis of symmetry is 5?


you could just do -b/2a to find it


ohh


now part b


I think you are on the wrong track


think about the quadratic formula


this is where I get stuck :(


yeah, that's the way to do it


how can I remember to use this for the test


I don't want to forget :(


to me, when they say that a quadratic has no real roots, I just immediately think that the only way you have no real roots is if b^2-4ac is negative, and there are no real solutions when you take sqrt of negative number


are my other parts correct


interesting that k can be <-25, = -25, and >25, all at the same time, LOL


(their wording could have been better)


its wrong?


I'm criticizing the wording of the problem


oh


yea Its all weird wording


they give you three, conflicting givens


yea


its just so much formulas and weird wordings


but your answers were correct


ohh ok


imma attempt these


and you used quadratic formula again


b^2-4ac is the key. 0, and you have a double root, so vertex on x-axis


negative means no real roots, positive means 2 real roots


now b


2 easier ways to solve b


what's an easier way if you don't mind me asking


#1, axis of symmetry is always exactly halfway between the 2 roots, when there are roots


the other way is, again, -b/2a


ohhhh


its wrong?


I don't know how you even got -2, because plugging in -2 in what you had gives you -18=0


-2 is right, but I don't know you you got it


I looked at the parenthesis


I cant just look at the parenthesis?


oh, I see


vertex form. you don't solve the whole equation, just find h because of (x-h)^2


but both of my way are much easier


so on my test I can just look at (x-h)


yes, but that requires completing the square


ok


isn't halfway between the roots easier? isn't -b/2a easier?


yea but I feel like I'm going to forget it :(


axis of symmetry


like a mirror running down the middle


yea


that's why it is in the middle between roots, when there are roots


pick any value of y, including 0


distance from axis to the point on either side is the same


because of symmetry


ohh ok


I believe only 2 more sections


that last answer was correct


okayy :)


h = 4


alpha


correct


are you plugging the point (0, 2) into the equation?


yes


ohhhh


I forgot x \


so f(x) is 2, x is 0


okk


how do I get b again?


Liam


ohhh


or just plug in h and k and multiply it out


k is 2?


ohh no


oh, wait


wait


yes c is 2


did I do something wrong


a is 1/2?


huh


oh, I was thinking a was -1/2


c is 2. my mistake.


ohh its alright


but is b +4?


I got -4


but h is 4?


not vertex


oh, yeah


now d


I'm really confused on d


quadratic formula


will give you 2 roots, with + or - some square root


+ is the greatest of the 2


b^2-4ac inside radical?


4 times 2 is ac


yea


wait


let me look at the formular


which is larger, the plus or the minus?


2sqrt3 is a positive number


so adding it is a bigger number than subtracting it


what are p and q?


I'm confused


about?


p and q


p is 4


and q is 2?


yeah


now question 4


hmm


ohh


find the y values for those x values


ok


wait


you can also do y= x-1 to make sure your answer is correct


but if I did -2 I would get -2-1 which is -3?


that's a different point


huh


line crosses the parabola at 2 points


1 of them is (1, 0)


the other one is (-2, -3)


oh


okayyy


stop'


put most of that back


stop


part b is >0


yes


what happens when x is > 1?


are both factors >0?


one is 0 and the other is >0


what are the 2 intervals where it is + ?


-inf, 2 and 1, inf


yeah


put parens around them, connect them with OR, and you have the answer


and only in between -2 and 1 is it negative


how can I write on paper? can you show me on board


parabola crosses x-axis at -2, goes below for a little bit, then comes back up, hits axis at x=2, goes up from there


we don't even have to write as intervals


ohhh Noah


oops, second "hits axis is at x=1, not 2, in my statement above


I said x=2 above


ohh ok


I have one more section


OK


I'm a bit confused here


parabola looks something like blue that I drew


y=x+c are the purple lines for different values of c


make c small enough (negative) and the line no longer crosses the parabola, right?


I definetely will not remember this on the test :(


Is this a Texas exam?


yes


odd, cause we don't use the word "hence" much


ohh lol


now 7


for #7, instead of moving a line of slope 1 up and down by changing c until it no longer crosses the parabola, we have intercept of -3 and change the slope until it misses


those 2 lines are tangent to parabola


slope in between and the line crosses twice


slop below the left line or right line misses


did you combine the parabola and line into an equation first?


I used the one they gave


part a says to show that


did you do (a) ?


no


I'm lost sorry


(b) is good


you solved (b). where are you lost?


are you here?


yes


sorry


I'm confused on a


same thing you've been doing


ohhhh


set the 2 x expressions equal to each other


Maya


I'm stuck here


you have -mx and -x


factor out the x, put x at the end


and factor out the -1


huh


I'm confused


I factored out -x from both of those terms


on the board


yes why is x on the outside now?


see how -(m+1)x is the same as -mx-x ?


cause I factored it out of 2 terms that both had x as a factor


factored out greatest common factor, which was -x


why not -x?


why - on one side


and x on the end


cause that's why you write stuff


+/-sign, then coefficient, then variable


you can just do -x(m+1)?


same thing


but we write coefficient in front of variable, like they gave you in (a)


why did a give us the answer?


they just want you to show your work on how to get there


do you write 2x or x2?


yeah, x goes last


but we are factoring out that's different


if I factor out 2x from (2x^2+8x+4)


so start with -x(m+1)


its 2x(x+4x+2)


you can't factor 2x from that


well that was just an example


lets say it was 4x^3


ditch the +4


and 8x^2


and 4x^2


I would just take out both terms together


I'm just lost why they seperated them


2x and x+4 both contain x


neither one is a coefficient


but when you multiply 3 things together, you can change the order


(m+1) is a number, so you typically write that before x


and -1 is written as a minus sign, and you put it in front so you don't have to write (-1)


so -x(m+1) is written as -(m+1)x


it's just notation


are we done with b ?


yes, and I'm out of time


r u sure that's the answer?


don't we have to further the radical


oh, one last step


you need to subtract the 1


you can simplify the radical


done now


okk


thank youu


yw


bye


Alrighty


Back to d


yes lets navigate it now


do u still have the link


yes


kk


no


its the 6a^2 one


so the gcf for the first one is 2a and the second one is 5?


you pair in 2 groups


ok now obj 11


have you understood that and can you do it comfortably


mhm that part yes i finished


great ,so which number inquiz 22


so lets do a


Ok holdon


wait no


i said obj 11 a


ok,clean the board please


thats right ?


done


how fast ?


whats your answer


so we find 2 numbers that multiply to 20 and add to -9


solved that one


now b


so the two numbers are -4 and -5 therefor the answer is that


ill need help solving b


have you found the same answer?


yes


no its t^2


not 2t^2


so here we need two numbers that multiply to -42 and add to -1


hiiiii


hey :)


what do you need help with?


just wanted to talk ;0


Okay. What did you want to talk about?


you


I'm currently in school


oh ok ok how old are u


I'm 18


wowwww


geuss how old i am


About 15 or 16


Hello! How can I help


Hi! I need a bit help with some questions


sure!


so would i turn 0.4 kg into grams


yes you can do that


thats 400 grams


would i multiply times 4?


just a sec let me think about this for a min


kk


okay yess that would be correct


what's 400 x 4


yep! that's your answer. 1600 grams


do you know stats? bc this next problem is stats related


if not, it's fine!


Howdy !


hi


i wanted to get some practice done for my precalc test


Okey dokey.


Wanna post a sample problem?


i would but my teacher removed the homework so i cant get any of the questions


So ???


but its about function, function notation, graphing common functions, domain and range, piecewise function, rates of change, and behavior of graphs


So, we could spend 1/2 hour on each of those topics.


Anything more specific you wanna focus on?


ok bc i gtg around 10


Not understanding your last message...


definitlry behavior of graphs and domain and range piece wise functions mostly drawing the graph


like around 10 i have to go


Meaning 10 pm ???  Like in 21 minutes?


yea


Okay.


So let's discuss domain and range then briefly, okay?


See that picture I just drew?


yes


So, starting from left to right, we take an x value (from the domain) and run it thru the function which is typically notated as f(x) = something or y = something.


This something can be anything, but it typically some sort of algebraic manipulation like I just drew (squaring the number and then adding 4).


Okay so far?


Okay, so regarding the domain (the allowed values of x in this example), you normally can allow x to be anything, except...


1. Something that gives you division by zero.


so -4 is not allowed?


2. Something that gives you the square root of a negative number.


3. Logarithm of a negative number


4. Some other goofy thing (like a trig function).


so all of these are not allowed in a domain?


So to answer your question, -4 is allowed in this example.  Let me get to that...


oh ok


So in the example, y = f(x) = x squared + 4.


Are there any square root signs, or divisions by zero, or logarithms that you need to worry about?


no


Correct, so x can be anything.


just not 0 right


It can be zero.


Then y = 4.


Let me draw a quick picture of this graph.


ok


Sorry for the picture.


its ok so its a quadratic with 4 units up


Yup.


And x (as  you go left and right) can be any value, right?


yes so like in this problem can i be infintity


Yep.


The domain in this example is negative infinity to positive infinity.


ohhhh ok i get it


Cool beans.


and the would be (4, positive infinity) right


range


You got this !


ohhhh ok


ok can we move on to piecewise functions specifically reading them and writing them too


Can I erase now?


im worried that might pop up on the test


yes


So here we have a two piece-wise function.


Meaning that that are two functions, depending on where you are on the x axis.


Okay so far?


So, in this example, there are just two different functions split into two different domains, so to say.


But you could have 3 different ones, 4 different ones, and so on...


Okay?


so we can have different domains on the same graph?


Yup.


Let me graph this pooch.


Sorry again for my poor picture drawing...


its ok


So the graph is a parabola to the "left" and a line to the "right" of the x = 0 line.


It's piece-wise.


so were following whats in the parsentces to follow the domain?


Yes.


ok i see it now


It's essentially saying "between these x values, the graph looks like this", but "between these other x values, the graph looks different, like this..".


ohhh ok


Easy peasy, right?


yes


Well, it's almost 10 o'clock so best of luck to you fellow human !!!


fellow human? arent you human too


Yes, we both are !!!


oooo cool well thank you again


Cut from the same cloth.


Take care and good luck.


Hi how are you!


I’m good how are u?


How can i help!


Desmos


I need help with this question that I’m gonna have on my math text tomorrow


Do they let you use Desmos here?


Desmos *


I’m not sure


Alr no worries we can do this problem without desmos just to be safe


First let’s kind of draw out the axis so we can have an idea of what we’re gonna look at


So we know that the x axis is distance and the y axis is the hoeght of the ball so lets keep that in mind. Let’s take a look at the first equation in black, what form is it in, standard of vertex form?


Is it in vertex form


Yes it is nice! So we know it’s in vertex form, and like the name implies, the vertex form is most useful to find the vertex of the graph. Do you know how to find the vertex of that graph? If not its fine


Wouldn’t it just be the highest point on the graph?


In this case yes it would be! It depends on whether the U-shape opens up or down. But in this case it would in fact be the highest point like you said. So now how do we find the exact point of the vertex based on the equation?


By using the h and k l think?


Yesss exactly nice


What’s h and k for this equation then?


Is it 5.5 and 6


Perfect!


Let’s draw that then


So now we know the vertex of that graph, what else do we know about it. How should it look


Go ahead and try drawing it for me


Would it be like that?


Yea nice! Good job realizing it opens down, which is because the number in front of the parenthesis is negative


Alright cool, now let’s try finding the highest point in other graph. Which form would that function be in?


That’s always the first thing u gotta ask yourself, what form is it in


Is it in standard form


Yes nice. So now do you know how to find the vertex in standard form


There’s a trick u need to remember for it


Would you need to foil it?


Not exactly, since we dont have two things multiplying each other there’s no need to foil.


So the trick is


The x value of your vertex is going to -b/2a


Have you ever seen that before?


Nope


I wrote it for you at the bottom


Okay


It’s worth memorizing because with that little formula u can find the vertex in standard form


In this case, do you know what b and a would be?


I’m not sure


So remember that every quadratic in standard form looks like what I wrote in the bottom. Try to compare it to the actual equation you have in the problem.  “A” is gonna be the number in front of x^2 and b is the number in front of x, and c is the number that doesnt have any x attached to it


Oh okay so b is 5.5 and 2a is -0.2 correct?


Oh careful, we’re looking at the other equation now that i circled in blue


Because we found the vertex of the one i circled in black already, now we’re moving on to the other equation


Ohh okay so b is 5.4 and 2a is 0.15


Super close! Your right about b being 5.4,BUT a is just -0.15, not 2a. Once you know a (which is -0.15) then u can multiply it by 2 and put it into the formula


So whats 2 times -0.15


Good! So now whats -5.4 divided by -0.3


Good!


So we just found the x value of the vertex only, we are still missing to find the y value of the vertex


So what we’re going to do now is “plug in” the 18 we just found into our original equation. SO wherever you see an x, replace it with 18 and then simplify it


So go ahead and try that and tell me what you get for y


Def need a calculator for that tho


Okay l don’t know if l did it right but l got -48.6


Hmmm i got positive 48.6, I think you added an extra negative sign somewhere maybe


I’m not sure l jsut put -0.15


It definitely has to be positive, because remember the original question is talking about kicking a soccer ball upwards, so it wouldn’t make sense for it to be -48.6 feet below the ground at the highest point. But its not a big deal probably just a calculator mixup


Ohh okay got it


Okay cool so now we have the x and y for the vertex for the second equation


Let’s try graphing that on our table


Okay


Should look something like that. But now we have enough information to answer the first question. Looking at the two graphs, which soccer ball went higher?


I’m sorry but I’m not seeing the second graph


Oh i drew it next to the first one we drew, is it not there for you?


Nope it’s not


Oh wait l just got it now


It took a second to load I guess


Ok ok nice


Okay so the second one is bigger


Yes! So we can say for sure that the second soccer ball was kicked higher


That’s part one done


Any questions so far?


Nope


Alr cool let’s move on to part two. They tell us which was kicked the farthest before it hit the ground. Let’s think about that before we start solving. If it hits the ground, what should the height be?


Would it not just be 0 or like in the negatives?


It would be 0 exactly!


So we know that when it hits the ground the height is gonna be 0. Remember tho that they told us that the y axis represents the height. So really they’re telling us that y=0, when they say it hits the ground. Does that make sense?


Yes


Okay nice, so now we know that y=0, but they want us to find how far it was kicked when it hits the ground. Remember that they said the x axis represents distance. SO what they’re saying with that word problem is “find x when y=0 for the two graphs and see which x is bigger for the both” . Do you see what I’m saying


Yes got it


Okay perfect thats the hard part here, just figuring out what they are talking about


Now let’s actually solve it


For the first equation circled in black, we are gonna plug in 0 for y and solve for x


Okay


I started writing it our for u in the bottom, can you try to solve for x from there?


Okay I’ll try


So you want me to write on there right!


Yes! So i can see how ur work looks


Or if u want, cuz it might be hard to write on the screen u can do it on paper and just tell me what u get


Just lmk if u get stuck


Okay I’m getting stuck at a certain part


Did u get up to the part i wrote at the bottom


Okay perfect whats the next step here


There’s only one thing u can do from this point


It’s fine if u dont know as well!!


Would you do 5.5 squared


So we cant just do 5.5 squared, because really what they square outside the parenthesis is saying is this: (x-5.5)(x-5.5). NOT (x^2-5.5^2). So we cant do anything inside that paranthesis


What we need to do is take the square root of both sides to get rid of that ^2 on the right side so THEN, we can solve for x. Because right now we cant touch anything inside the parenthesis


Oh okay


What’s the square root of 30? Try it on ur calculator


So last step, what does x equal


5.4 I think


Careful, after we took the square root of both sides i have 5.4=x-5.5, so i needed to ADD 5.5 to both sides to get x by itself.


U can see my work right?


Yes


Ok ok good. So does that make sense then? What would x equa;


Uhm is it 10.9 because wouldn’t you do 5.4+5.5


Yessss nice


Okay cool so now we know that for the first soccer ball it went 10.9 feet when it hit the ground


Now we have to do the same thing for the second equation. Set y=0 and then solve for x


Okay


Okay so since this one is in a different form (now standard form, not vertex form) we need to solve it a little bit differently


How do you think we should solve for x here


Would we use quad form?


We definitely could!


But in my opinion thats the long way


I was thinking we could factor!


Do you know how we could factor here?


Think about what do all of the terms on the right side have in common


They both have x


Perfect! Since they both have an x, we can “factor out” and x


Do u have any questions on what I wrote there? Does it make sense how i got to that equation


Wait l jsut have one question


Why would x be outisde the bracket wouldn’t it just go away entirely?


Good question! So we cant get rid of it entirely, because then we would be changing the equation it self, all were doing it taking it out and putting it outside of the paranthesis. Which doesnt change the equation itself because when you distribute that x into the paranthesis again, you get to where you were before


If we just got rid of the x, we would be changing the equation, because remember, what you do to one side of the equation, you need to do to the other side, but since the other side doesnt have an x, we cant just get rid of x on the right side, because we can’t get rid on an x on the left side


Does that make sense/answer your question?


Yes thank u


Ok ok nice


So cool now that we factored out the x, do you know what to do from there?


Would we add what is inside the bracket


Careful, we cant add them because one has an x, and the other one does not. We can’t only combine things when they are like terms (when they BOTH have an x, or they BOTH dont)


What we need to do now is set both factors equal to zero. Have you ever seen that before?


Nope


Ok ok


Have you ever done like normal factoring of a quadratic? Something like x^2+2x+4 or something


Yes


Okay this is the same deal. So in something like that, we need to put it into a form like (x+2)(x+2)=0


Does that look familiar


Ben so from there we set (x+2)=0 and (x+2)=0, we need to set BOTH factors equal to zero, because if you dont then your missing out on one of your answers. Here is the same thing, expect instead of a second paranthesis we just have x, but it doesnt matter you still need to set that equal to 0, along with your other paranthesis


Does that make sense?


Yes I’m pretty sure


Just remember that when your solving for x into standard form, you need to set both of your factors equal to zero. That’s just a rule you need to know


So can you solve the equation in blue for x? Like what does x equal


Okay


Does it equal 5.55


Did you do the steps that i have there?


No l missed one of them


First we want to subtract both sides by 5.4, and THEN we can divide by -0.15, to get x alone


Alr alr no worries


So in ur calculator what is -5.4 divided by -0.15


Chloe


So boom, we got for the first soccer ball x=10.9 and the second soccer ball x=36. Which one do you think travelled farther, the first or the second


The second one


Yes! So now we solved question number 2!


So to recap, if they ask you for which one went the highest, we can find the vertex for both equations, and the one with the bigger y value for the vertex is gonna be higher. If they ask you which one travelled further when it hits the ground, remember that hitting the ground means y=0, so we solve for x in both equations when y=0 and compare.


Also if by chance they let you use demos, all you would do is literally you type the equations into desmos and Desmos will tell you what the vertex and x intercepts are for both graphs. What we did was solve it by hand though which is def good to know how to do regardless. For standard form remember how to factor, and for vertex form you need to remember to take the square root of both side


Do you have any other questions or concerns?


Nope that’s all


Alright cool, i hope i helped and good luck with ur test!!! You’ll do great!


Thank you so much for helping me!


Of course have a great night!


You too!


hi


Hi


What can I help you with?


I need help with this problem


Ok. Let's graph the pieces separately


So to graph the first part f(x) = -x + 4 if x < 1, you would just graph f(x) = -x + 4, but only the part to the left of x = 1. Do you know how to do that or do you want me to explain?


I=not sure


Ok, so conveniently it's already in slope-intercept form, right?


So just start from the y intercept (0, 4), and draw a line through that point with a slope of -1.


You can do it on the whiteboard(I made a coordinate plane for you) if you want.


Did I make it clear how to graph the 1st part?


Ok you started from the y-intercept (0, 4) that's good. Now can you start from there to create the whole line?


Do you need help using the slope to draw the line?


yes


Ok. So in general, if we say the slope is m, that means when you go 1 unit to the right, you go m units up (or down if m is negative). I'll show on the whiteboard.


I gave you 2 examples on the whiteboard. Now can you apply the same idea for a slope of -1?


I just moved mine around so that you would have more room to draw


Yes you're getting it


Now connect the points


Exactly! Now remember that we only want the part to the left of x = 1, so erase the part to the right of x = 1.


Now try graphing the f(x) = 2x + 1 part.


It's the same thing as before, use the y-intercept and slope.


Maybe extend the line a little more to the right


Ok good, now this time we only want the part to the right of x = 1, so go ahead and erase the part we don't want.


Good


Now I'm going to copy the drawing below and make it a little bigger so that we can see it more precisely.


While I'm doing that, do you know what continuous means?


no


So continuous basically means that there are no "jumps" or "breaks" in the graph, you can draw the whole thing without lifting your pencil.


So just look at the graph(you might have to scroll down). Is it continuous(does it have any jumps or breaks)?


yes


If you meant "yes, it's continuous" you are correct.


All right, is that good for this problem?


I got mine incorrect


I have more


Oh I'm so sorry but I have to go now. But I think we got the majority of the problem done. Now maybe try some of the different tools on the website (maybe the straight line)


And you can always make another request on Tutor Provider!


ok


Bye!


hi


Hi Alex, what's up?


I'm good


I example.com need to graph the function another.net you know how to start?


ok, let's start with the -5x+3 part....did you know that f(x)=-5x+3 is a line?


no


ok, have you graphed lines before using slope and intercept?


ok, so you know that -5 is the slope and  3 is the intercept....right?


yes


ok, so to graph the line, we start at the y-intercept (0,3)math.orgen a slope of -5 means we go DOWN 5 and over 1, let me show you using pink


like image.pnge what I mean?


ok, now lets do the other one...f(x)= graphing.toolope is 1 and intercept is desmos.come where I got that?


ok, so I will start at (0-4), then go UP 1 every time I move over 1


I'll use blue


like anotherimage.pnge what I mean?


Are you with me Alex?


ok, now the function they want us to graph looks like the pink line up to and including x=2, then it looks like the blue line, after for x>2, do you get that?


so, if you are good with that, I will draw it using black


ok to draw it now?


ok, so I trace the pink line, up to and including x=2


then after 2 I trace the blue line


like that, so the black lines are the graph of the finalgraph.jpge what I mean?


ok, now the question of whether it is continuity.html be continuous you would need to be able to draw it without lifting your pencil....but we can't do that for this mathproblem.net x=2 we need to skip from y=-8 up to y=yvalue.org it is NOT notcontinuous.nete what I mean?


all good with this one then?


I have more


ok, let's see the next one


ok, similar nextproblem.com you agree?


yes


Would you like me to graph the two lines, or do you want to do it?


yes because I don't know what points to plot


ok, for 1st one, intercept is -4 and slope is 5, so we start at (0,-4), then we go UP 5 and over 1


like that, see how I did that?


start at (0,-4), then keep going up 5 and over 1


are you good with that?


ok, now the other secondline.orgercept = 4, slope = slopemath.net, start at (0,4) then go DOWN 1 and over 1


like anotherdiagram.jpege what I mean?


now, the function they want, looks like the pink line up to x=1, then the blue line after combinedgraph.gif let's draw that in black


like drawing.png up to and including 1, then the blue line after x=1


got it?


Is the black function continuous? Can you draw it without lifting your pencil?


Hmm...what happens at x=xvalue.com me it looks like it jumps from y=-1 the whole way up to y=yvaluejump.netn you see that on the plot?


see what I mean?  the black graph jumps up at x=1


if it jumps like that, you can't draw it without lifting your pencil...which means, it is NOT continuous


if you have another one we can work on it, but then I need to endofsession.link you have another one?


are you there Alex?


yes


one more?


sorry Alex, but it looks like my time is up...gotta run, it's been nice working with you


afternoon!


what


do you have any problems?


ya


its number 17


That's it?


no but starting on 17


number 17 is 0


oh yeah b ru


alright 19


it's 1


aren't we going to work on it


you want me to show how I got the answer?


Okay so right away we can see that there is an 8 in the numerator and denominator, so we cross it out and replace it with 1, since 8/8  reduces to 1


Hi


Algebra? Let's take a look. What's up


I need help with inequality word problems with variables


Sounds good, I'm sure we can put our heads together. Do you have maybe a sample question?


Yeah I think so


Nvm


I can’t find it


David mows lawns for $15 per yard. He wants to earn at least $120 this weekend.


Write and solve an inequality to show how many lawns (x) he must mow.


Something like that maybe?


Yeah


sweet, any idea for a good step 1?


Create the inequality


Love it.


Do you wanna take a stab at that or hear a thought process, then I can give you another problem to try


Hear a thought process


cool, here's how I approach it:


1) What's the most important number in this story? It's that $125.

2) Okay so our guy wants to do something that becomes at least (so, "more than") $125


3) Okay, so:      *the way he earns money* has to be greater than or equal to $125.

4) example.commething >= 125


Okay I'm half done.

5) How does he make money? He gets $15 per yard.

15x >= 125


That's the inequality. Does that make sense how I got there?


Yes


We’re 125 come from?


That's how much money the guy wanted to make this summer


this weekend I mean


"David mows lawns for $15 per yard. He wants to earn at least $120 this weekend."

lol sorry, $120. I never should have said $125, should have been $120 in my whole thought process


Good catch


15x >= 120


Can we do another one


Or can I try to do one alone


I can definitely give you another


Sarah sells bracelets for $8 each. She wants to make more than $60 this week.


nailed it


can you solve it real quick?


Yeah


Do you want another or how you feeling?


Can I get one with different variables


Something other than money?


Yeah  with two different variables


A school bus can carry no more than 60 students. There are b boys and g girls on board.

Write an inequality that describes this.


Something like that?


And then maybe I tell you there are already 25 boys on board, and I might ask you to write an inequlaity to show how many girls are possible


That's perfect


Does your homework usually ask you to do that second step? Where they say there are 25 boys so how many girls could there possibly be?


I don’t know how to do it


cool cool


so you did b+g<=60.   If I tell you there are 35 boys, where could you shove them in there?


Lol 25 boys I mean. Fat fingers.


like where in your inequality can you plug in the fact that we're telling you there's already 25 boys on board?


25b+g<= 60?


careful, super close, don't do it TIMES b, just plug it in for b.


b is 25


perfect. solve that for g now. Remember the question is "if we tell you there are 25 boys on board, what's the range of girls we could have"


you're crushing it


careful though, you turned an inequality to and equals


natural easy mistake.


remember we have "*60 or less* kids on this bus. If we know there are 25 boys we can't guarantee the girl count *is* 35. we can say it is *at most* 35


Hop back to here when you said this: 25b+g<= 60


25+g<= 60 sorry, thaat. no b


let's forget inequalities for a sec. we can pretend it says "=", solve it, and slap our "<=" back into it before answering


you already did that actually, you said g=35


you didn't slap your inequality back in there


Well that *is* true lol. 25 plus 35 is less than or equal to 60.


Let me walk you through it. You're doing great by the way, for real.


okay, you came up with b+g<=60. that was perfect and it means "the number of boys plus the number of girls is less thn or equal to 60 kids on this bus"


then the problem told you there are 25 boys, so come up with a range of possible girl head count.


you plugged that 25 in for b.

25+g<=60

perfect


now we solve it for g


subtract 25 from each side (you did this!)


but then you said "g=35"

you were soooo close


when you went from

25+g<=60

you changed the <= to = and said

g=35

instead of

g<=35


Ok I get it


And it makes sense too if you just think about the question. The bus can hold up to 60 kids. If 25 are boys, there can be up to 35 girls. We're not saying there are 35 girls, we're just saying there's 35 or fewer


Good stuff. Just keep your inequality sign, that's all you missed.


Can we do algebraic word problem’s


Sure, I'm assuming you're doing linear algebra? y=mx+b?


Or like silly riddle sort of stuff like:

Five more than twice a number is seventeen. What’s the number?


Yeah


A movie theater charges $10 for adults and $6 for children. One night, 80 tickets were sold for a total of $680.

Or something like that where you'd end up with two equations and two variables


I guess it’s more like the first one


"Five more than twice a number is seventeen."

for these when I find "is" that's =. So lready I've got _________ = 17

Make sense so far?


already*


K


when I read "some number" or "a number", I write X

The question says "twice a number" so that's "2x"

"Five more" well that just means "add 5"

5+2X=17


subtract 5 from both sides: 2x=17-5

Simplify: 2x = 12

Divide both sides by 2: x = 12/2

Simplify: x=6


I've got to head to bed but here's another:

Ninety-six golf balls were picked up at the driving range and placed
into two buckets. One bucket has twenty-eight more balls than the other bucket.
How many golf balls are in each bucket

I'll call them buckets a and b

I know: a+b=96
I also know a is 28 more than b, so a=b+28

So I've got:

a+b=96
and
a=b+28

So I can take that second one, since it equals a, and plug that into the first one where a is.

Instead of

a+b=96

I get

(b+28) + b = 96

Now I rearrange and simplify:

28 + b + b = 96

b plus b? that's 2b

28+2b = 96

subtract 28 from both sides

2b = 68

divide both sides by 2

b=34

So bucket b has 34 balls in it.

a+b=96 (remember, we started with 96?) So I can plug that 34 in for b:

a+34=96

subtract 34 from both sides:

a=62

Answer: One bucket has 62 balls, the other has 34


Check our work: problem said one has 28 more balls than the other. 34+28=62 so we're good.


I don’t get this one


How did we get a=b+28


hi


Hi Marcus


Hello, can you hear me?


OK, can you hear


Can you hear me


Yes, I can. Can you hear me?


Yes, I hear you. How can I help you?


Um, can you help me with, can you help me with statistics?


Yes


Uh, OK


Can I put the question on the board?


Sure


OK


1 2nd


I'm putting it on now


Can you see it on the board


Yes, yes, I see it.


I'm reading.


OK, well, the first step is to calculate the probability


of getting a face guard.


Can you find it


How do I solve it


Well, a probability


is a fraction


It's the number on top is the number of successful events


and at the bottom


is the total number of events, so how many face cards are there in a deck of cards?


Well, that's the number of cards in the deck.


Um, that's, yeah, that's the number at the bottom. So the probability will be a fraction with 52 at the bottom. That's the total number of outcomes and the number of successful outcomes is the number of face guards. The problem tells us how many face cards there are.


OK


Yeah, you know what's a face card, correct?


I think I do


Yeah, face card is like if you look at a deck of cards like King, Queen, and Jack. Those are face cards.


So the probability will be 12


divided by 52.


OK. So 12, divided by 52 is um.23.


Yes


So point


let me, is there a way I can write on the board? So point


Yeah, you can even add one more decimal, like 0.231 to be a bit more accurate.


0, 0.231


one. All right


Now


you need the probability


of getting something other.


than a face card


So if a 52


car deck has 12 face cards. How many cards will not be face cards.


Um


um


let me see. Um,


uh


um, uh, is it, um


Well, it's 52


and you subscribe


30, 30, 30.


would be, would be 40.


40. 0, 22 minus to always attracted.


Yeah


So 40.


So the probability of


getting


a card other than a face card then would be 40/52.


So


so


in this box it should be 40.


Well, it would be 40 divided by 52. I'll, I'll write the uh ratios on, on the board.


Yeah, that would, that would be good.


Let me do that. First of all,


sorry, my sound was off for a second there because I, as soon as I pick up my tablet


um, the sound goes out, but you should be OK now. Can you hear me?


Yeah, of course I can hear you.


OK. So a probability, I'm writing above your uploaded page. So number of


Yeah, I know, I, I see it


number of successful events.


divided by


the number


of events


So I'll write that for our particular problem.


So the probability of getting a face card then would be 12/52 and the probability of getting something other


then this is called the compliment.


There are 52 cards, so 52


and we subtract 12, that leaves 40. That's called the complement probability.


OK, so you can, you can calculate that as a decimal number if you like.


Let me solve it


Uh, no, it would be


Um, uh, do you want a fraction or do you want a decimal?


Well, it's up to you. You wrote the first one as a decimal.


Uh, it doesn't matter, you can use either leave it as a fraction, but maybe be consistent. If you wrote the first one.


as 0.231


you could write the second one as a decimal as well.


Oh, so 0.76.


OK, or let's call that 0.769 to be a bit more accurate.


OK


So that completes part A.


Oh, it wants a fraction.


It wants to OK.


It wants a fraction, yeah, it wants a fraction.


OK, then


OK. Then you, you know what those fractions are.


Yes, I do. 10/13.


Uh, yeah, 10/13 if you want to simplify. Yeah, we can, we can simplify it. So this would be


and this would be the top one would be 3/13. Maybe that's what you meant earlier.


Oh.


Yeah. So the first one is um


yeah, 3/13, right? Yeah.


Yeah


Yeah, 3/13 for the first one, and 10/130, because you, we, we divide 12, divide by 52 to hold deck of card and 40 um 40 divided by 52. So


uh


So 40 by 52 you can factor out 4 top and bottom.


OK


like 40 is 4 times 10 and 52 is 4 times 13. So if you factor out the 4, you're left with 10/13.


Oh, well, how do we get to 40?


OK, I'll show you. So I'll write in green colors, so.


there are


OK, there are 52 cards in the deck, correct?


Correct


And we're told there are 12 face cards among the 52.


So that leaves how many cards.


are not


face cards


Oh, so you subtractive 32 minus 12.


Correct. So 40


are not face cards.


So I wrote all of that on the board.


OK. Um, OK. I, I'll, I'll write it down on my side. I'll write it down on my paper as well.


Sure


OK, so I, so I wrote 3/13 for the first one. I wrote 10/13.


Right


OK. Next question, uh, letter B.


right


Did you learn the formula for the expected value?


I think we have to, um, use the that key.


Well, there's a simple formula. I wrote it, uh, below your uploaded page.


Oh, I see it. I see it. Probability goes number of successful events over a number of events.


Uh, that's the formula for the probability, but look below


you're uploaded page.


OK


The formula for the expected value.


Expected value.


Yeah, just scroll down lower on the board.


Uh, I'm afraid right to formula down just in case.


Because um, I, I did learn this in class.


OK, so I went lower


Oh, I expect the value, it's 30 times face.


Wait, I already learned it. This is for average, correct?


That's, that's what the expected value is, that is the average.


Oh, I, I already know, oh, I already know that already, OK, let me try solve that.


That's correct


So that is in dollars, so it's $5.38.


Should I play this game


When you


Yes or no


what do you think


I'll say yes


Why


because um you, because you're making that money, right?


That's right. You're expected value is positive.


That's correct because uh because you you're still making something.


That's right


The answer is correct


OK, good


Next question


I'm gonna sip it and put it on there.


OK, so


um


um, raise the board. How do I, do I raise the board or?


Oh


I'm gonna, uh, erase the board and yeah.


Can you help me erase the board because I I'm just having trouble.


Thank you


Wow, you're really quick.


Let me saved, save it first.


A friend of you see the question?


Yes


OK, I'm gonna, OK, yeah, let's read the question.


A friend offers you a following deal for a $10 fee.


You may pick an envelope from a box containing Wahana see with this identical envelopes. Well, however, you should go um contains a coupon for a free gift.


10 other coupons are free gifts work with $6.08 other coupons are a free gift.


worth $12


6 of our $12 for coupon for a free gift for $40. That acts the net amount of money won or lost if you take this deal.


So


for probability


Um, wait, for net amount.


do we do uh $6 for


10, right 10


Correct


OK, well, first of all, you pay a fee of $10 right off the bat, correct? So if you get an envelope with a


free gift


Did you win or lose?


overall


Oh, you, I lost, I lost.


Well, you had to pay $10 but you only got $6 back. Is that good for yeah, you lost $4 right?


Right


So that's what you put in that first blank cell there.


So 4.


So 6 dog gift is -4.


Well


6 minus 10 is -4.


OK


8 minus 8 is 0.


Well, uh let me put the first number here on, on the board.


So this one here will be 6 is what you win minus what you paid.


So you have negative 4. So that's your first number.


And uh what would be the probability of getting


a $6 coupon.


Um, I think we do 66 wait, um, probability.


Remember the formula for the probability. It's the number of successful events


divided by the total number of events.


So, I do


I do


uh-huh, let me see if I remember.


Um, 60, no, um.


um, 6.


Uh, no, no. Uh


uh.


OK, I'll show you the total number of events, the, the problem statement


gives it to you


6 divide by 10.


Uh, no, no. How many envelopes are there altogether?


Um


100. 100


OK, I'm gonna write it here


OK


probability


So it's gonna be 100


That's the total number of events. That's, that's how many envelopes you can pick from.


And how many of those envelopes will contain the $6 gift.


out of 100.


The the problem statement tells you


I circled 10. OK, so the number of successful events is 10, and the total number of events 100.


So you can simplify that.


you can


yeah, or 1/10 as you wish, 0.1 or 1/10.


0 0.1


I, I'm not sure what your software or what your website will want, whether it's a fraction or a decimal. Only you can.


Oh, it, it's a decimal.


Decimal? OK. So that will be 0.1.


OK, so we did the first one. Can you do the second one?


Uh yes


So now we, we're looking at the


$8 free gift.


OK.


We do 8 minus 8.


That's 0


Well, 8 is what you get back in the free gift, but how much did you pay to play the game? What is the fee?


Um


the fee $10?


$10 so it should be 8 minus 10.


Why is that? Oh, OK.


because 8 is your prize, you win a


you win a


Oh, and then you, you take out 10 because that's the fee you had to pay.


Exactly


OK. So, that's negative too.


Now you have to calculate the probability.


OK. Um


divided 100.


Well, 100 is correct


but how many envelopes


will contain the $8 gift.


Well, the


the problem statement tells you if you read, read the question, it tells you how many envelopes will um


how many coupons


contain the $8.


$80 there we go, there we go.


80 divide 100


80 divided 100. There is the.


I thought that said 8 for a second.


So this is 80/100. So if you want a decimal number.


00 0.8.


0.8. OK. We're making progress


OK.


Um, next, what we do.


um


um, 12 minus 10.


Very good


That's 2


That's true, OK


Mm.


And then we and then we do


and then we do 6 divided 100.


OK, 6


divided 100


OK


Last one


If you


40 minus 10


OK, and the probability


probability is


And then find the expected value for playing the game, in other words, financial gain or loss, so let me solve this.


We do um


let me, uh, we, we don't negative for times 0.1 + -2 x 0.8?


Correct. And you keep going.


Yeah, keep going. Let me solve that.


Very good


You got it


Thank you


Based upon the expected value, should you play the game, yes, I expect to come out ahead of money, no, that's no, no, no.


That's the last. no I expect to come out behind in money.


That's right, because on average, every time you play, you lose 68 cents.


So


which is $0.68.


Correct


Let's see if it's all correct.


It's all correct


All right, awesome


Next question


OK, I can do one more, and after that, I'll have to go.


Uh, by the way, it's the last question as well.


OK. All right. Put, put it up on the board.


OK


Let me see


OK, I'm putting you on the board now. Can you clear it, yeah, OK, it's OK clear everything real quick.


I put uh there's more in that I'm gonna put more uh the question below. I, I'm gonna there's one more.


I'm gonna put this underneath.


Can you see it


Yes, I see questions A, B, C, D, E.


OK, let's do it


A physics professor


um, who wants to know how many years each physic um major will spend doing postgraduate.


his research to find the random variable x.


So X is the number of physics majors that we do a postgraduate research or a number of years, a physics major was then doing postgraduate research.


I feel like years. Second 2nd 1.


The second one is correct. That's the only one that makes sense.


Yeah, that's true, yeah.


It's the only one that matches what I've underlined.


That's true, yes


So suppose the professor has the following probability distribution. Complete the table and use to answer part C and E.


So this has to add up to one.


That's right. The column that has


P X, that has to add up to one.


Mhm.


So, 9095 0.15.


Correct.


How PMX? So how do we figure that out?


Oh, we multiply 2 times 0.20.


Correct


That's 0 0.4.


3 times 0.15.


is 0.45.


4 times 0.15.


That is 0.6.


5 times 0.


is 0.5


and 6 times 0.


is 0.3.


OK, I wrote all that on the board.


OK.


Wait, if it's 0.6, why put a 0 after the 6th.


Um


where do you see that


Uh, it's just, it's just to make them all too, too decimals so that they, they will be easier to add up. You, you could also write it as 0.6


Oh


like, like this


but it's easier to um


it's easier to add up if, if all the numbers have the same format.


OK


Next question


I I really done a physics major.


will do postgraduate research for 4 years.


Correct


Bingo


Mind if I


probably that faces this feature would do postgraduate research for at least for at most 3 years.


We we add 0.15 plus 0.10 plus 0.0.05.


Well, it wants 3 years or less if you say at most 3 years, it's 3 years or less, not.


OK, so, OK, OK, so 0.35 plus 0.20 plus 0.15.


OK.


Plus


+ 0420 + 0.15.


that's 0.7


Right


Wait, is that 0.70?


Same thing


OK


And


E, right? E


0.7. So E is on average how many years you expect a physics major to spend doing postgraduate research round to the nearest, how many years would you expect a physics major? On average, so.


oh, OK, I remember this. 0.35.


times 0.35


plus


No, you, you, you, you don't do it that way because it's already been multiplied. Look at the expression here. This multiplication has already been done.


So all you have to do is add up the numbers in the rightmost column.


Oh, you're right, you're right, you're right, you're right. Uh, it's, you're right, yeah.


Let me, let me do that


That's the uh that's the expected number of years


My homework is done.


Awesome


You were a good tutor, amazing tutor.


OK, thank you. So we can uh end this session and uh I'll wish you a good evening.


Sounds good


OK, bye for now


I really appreciate your help


Bye for now.


OK, you're welcome


Hi


How are you doing?


good and you


Good, how can I help you today?


my math homework


Ok, nice!


please put the question in the chat!


Let's start with one question per time!


ok its 17


quset 17


Type the question in the chat


I'm sharing my screen


but ok\


OK, hold up. Let me see. Um


question is


11/3 + 2/3 minus 1, but it's PEMDAS does.


Pandas, panda.


Ah


God


its 1/3 plus 2/3 - 1


heloo


Hi Emily


hello


hi


i need help with this


What do you think you might let x equal?


x is the  third evening


yes, that's a good choice


so what expression could you use for the number of calls on the first evening?


thats the problem


dont know how to set it up


what does it say about the number of calls on the first evening?


8 fewer calls


than the 3rd evenicng


8 fewer than x, in other words, right?


yes


other way around


ohh


x - 8


can you see where I wrote that on the board?


actually theres nothing on the board


oh i see


how would you write the number of calls received on the third eveing?


+ x


and what do those all add up to?


that's it. Now you solve that for x


ok


is this right


not quite


what is x + 5x ?


third evenicng is equal to 17


yes.


and you can figure out the other evenings from that


so first evening is 11, second is 68


what is 17 - 8


next


If you are correct, then 9 + 68 + 17 should =94.  does it?


yes


then that must be the answer


idk what im doing o this on


one


ummm


this problem is really very similar


It's the exact scene. It's the exact same thing at the scheduled pickup so understand that Liam I just don't understand it.


So how do you like make the equation.


Oh, so we just


um,


so we're just adding them all together.


I don't see any Liam


Huh? What are you talking about


I don't have a Liam either.


I think I get this one


so just 2 eggs.


and then


plus Liam Is this correct?


you wrote something about Liam.  Anyway, that looks correct


Liam, you want more avocado.


This is correct


I didn't write anything about Liam.


unless


Avocado?


Oh, you need to, you need to click the speaker thing, cause you're just reading


the um transcript.


thats just the background


noise


can u hear me?


Thank you for calling FFYline speaking. How can I help you?


Thank you for calling us. So, is this correct?


Please turn off your mic


Good afternoon. How can I help you? Thank you for calling SSI


No, what do I have clients can't respondent agent assistant Liam.


Thank you for calling SSI.


OK, I'm just gonna continue to take this like 3 X


X minus 7.


please turn off your mic


+ 3x, then


X + 3 X is 4 x.


minus 7 equals 77.


+ 7 + 7.


4 x equals 84.


84 divided by 4.


How can I help you?


It's 21, so X equals 21.


And


um


Sarah sent 21 text messages. This is Sarah.


21 minus 7.


is 14


So I read us at 14 messages.


And then finally


and then finally


and Sarah. So Sarah,


did 3 times 21


63, so she, she's on 63 text messages.


Saturday.


01 of my answers is incorrect.


it's 2 times, not 3 times


OK. Now I have to do more now, OK, but some of the numbers Math 101.


Second number is 51 in the first. The third number is 4 times the first.


A wrong and pro team and a movie.


last problmem


Um, so I guess I'll just put um


X + 5 Plus for 4 X.


Thank you


but please, please turn off your mic


um equals


Uh


I


Is this correct so far?


I can't tell what you are saying because of your mic


bruh all u need to do is listen


please turn it off


click the speaker button for a reason


but nvm


there is too much background conversation


thats cuz ur reading the transcription


Go ahead with the problem.


i did


bye


Hi Alex!


How are you doing today?


hi example.comt good


Oh no! What's the matter?


this answer I'm on is hard


Well why don't you show it to me and we can work it out!?


I'll help you!


ok


its "write equivalent fractions for 1/5 and 7/8 using the least common denominator".


hello Belen?


Yes I'm here


I am just processing the question! :)


ohh


Yeah


are you writing it down


Mentally, yeah. But I feel like I get it now!


Let me show you rq


what is an rq


rq = real quick


My bad I thought you knew


ohhhhhh ok


Okay, pay attention now.


I am


So to make the fractions equivalent, we first have to make the denominators the same!


Oh okay great!


So to do this, what can we multiply by to have 5 and 8 equal each other?


Hello?


ummm 40


right?


Well we have to get there, but I'm asking what we multiply by.


But you're on the right track!


Yes that's correct!


ok


So it would look something like this (see whiteboard)


Does that make sense?


ya


Great! So what would our final products be? (Show on the whiteboard)


Yes that's right!


Good job!


yay


can you trun your mic on Belen?


I can! Would you prefer it if I did?


ya wait are you a guy?


Belen


I am a girl


ohhhh


can you trun ur mic on tho


Yes! One sec


Hello


omg HIIIII


Can you hear me?


yaa


OK, great


So, do you wanna talk?


I can but ya


I meant I'm in my class rn


Oh, so.


do you wanna just talk over text.


ya but I'll talk to you when I get home ...GOOD?


Yeah


Belen


Is there anything else you need from me though?


ya


Okay, what's up?


its write 2/5 in lowest terms


Oh but 2/5 is already in lowest terms!


Is it asking for like a decimal format?


umm I think hold on


Okay!


Take your time!


here(look at whitebord)


Oh I see it!


But yeah like I said 2/5 is already in lowest terms


So you're good!


Hi Maria! What can I help you with today?


Im wanting to learn some new math equations theorems


Are there any concepts in particular you'd like to work on?


Im mostly struggling with multiplying decimals.


Okay then! Would you like to start off with some practise questions?


Yeah I'll try


Just a moment, Maria


okay.


Could you start by trying to attempt one question, so I can see where you might be struggling?


Okay


Would it be just like normal multiplication


Yes, start off with normal multiplication


And then we'll proceed to the next step


I got 13.2


Maria, there appears to be some kind of a calculation error. Would you like me to show you how to do this?


Yea sure.


Upto here, we disregard the decimal places


That don't make sense


What part specifically doesn't make sense?


How you did that


I'm so confused


Does that make sense more?


OHHHHHH


Great! Do you understand how I got that?


Not rlly


So we solve using the same way that I just did, but add a 0 at the end since that number is not in the last place


Oh


Then we add the two together


Now, since we're multiplying decimals, we look at the number of digits after the decimal point in each of the numbers we're multiplying together


And we add them up


soooo 17.02+?


And that is how many places away from the last digit the decimal point will be


Yes!


Does that sound good?


I mean I get 1+1=2 but what do you have to add with 17.02?


You don't add anything to 17.02
What we got from the mutiplication result, and we use 1+1 to find where to put the decimal place. Otherwise, it could be 17.2, which is a very different number!


Does that make sense?


OhHH so does that just mean to move the decimal?


ohh


I'm writing it down rq


Yes, no worries. Once you're done, shall we attempt some other questios?


**questions?


yea


Let me know once you're done :)


almost done


Okay I got it written down!


Great!


Could I erase the whiteboard so that I can display the questions I want you to try?


Yes


Could you try part 5?


Yea


I wrote it down in my notebook cuz I'm not used to writing on the board.


no worries


Yes, that answer is perfect!


You got it!


Yay!!


Would you like to attempt another question, or do you think you're clear on the topic?


Yea I can try


Let's try part 2


Hey! You were very close with that answer


oh


Yes, it the digits we get after multiplying, but there's also a 0 at the end from 2x0=0


so the demical place is once to the right


And the answer becomes 41.6


ohhhh


The answer to part one is absolutely right!


yay


Would you like to attempt part 6?


Your very sweet😁


Thank you!


I got 23.92


Yes! Correct again!


yes!


Great job! Do you want to attempt more questions?


perfect!


Yaey


Nope! That is also correct, you don't need to move the decimal point


Okay


You're doing a great job! You can move onto the next question


Good job! Right again


Yay


The first one here is right. The number of decimal places begins from the end of the number :)


okay


I apologise for the late reply, I had to leave my computer for a moment


These are correct! Do you feel confident in your ability to multiply decimals?


Okay I am so sorry but I have to leave and have a blessed day and that's okay! And yes♥


Thank you so much! I hope this session helped. I'll be ending the session now, Maria :)


Bye


Using the Pythagorean triplet


Howdy !


I need help with phythagorean theorem to solve x


Hello good afternoon!


Okay, got it.


So where in the picture is the right angle?


Upper right?


Bottom right?


Upper right.


I put it on the white board


Yes, I see it but that angle in the upper right is definitely not 90 - makes me think it's the angle on the bottom right.


Oh sorry, let me re draw it


Ah, so 17 is the measure of the hypotenuse, right


Yes


Okay so far?


So, in this case how would I do the phythagorean tripe triplet


Theorem


Just solve for x


Oh, and then match it up with the other numbers from the triplet!


Ohh ok thank you! I got it now


x = 15.


Make sense?


Right, yes it does


So your "triplet" would be 8, 15, and 17.


Oh okk thank you!!


Anything else?


I understand it more


Nope! Thats it thank you


Cool - best of luck to you then !!!


Hi


Hello


Could i get help on my homework please


sure! you can post an image of your problem, or write it on the board, or type it in the chat


i think ive done 1-3 but im stuck on 4


ok, give me a minute to read through the problem


what did you get for the answer?


well i have the equation y=299+871.50=361.25+299 and 361.5 = 660.25


can you tell me what you got for 1-3?


1.P for amount of people


ok


lets go back to #2. I don't think its correct


okay


should p be with 361.25 so y=299p+871.50?


It says in the problem that they want each person to pay #361.25 total for the trip (this includes the price of the 3-day ticket)


$ not #


so 361.25.25+871.50?


well, $871.50 is total cost of rental. so each person will pay $871.50/p


if they only want to pay $361.25 each, 361.25.25-299=cost of rental for each person


how would it be minus?


lets say you only 361.25.25 to spend and you know 299 goes to but the ticket. how much do you have left to pay towards the vacation rental?


right


from there we can actually find out how many people are needed to go on this trip. (personally I dont think this problem is organized very well, but lets keep going)


we know the vacation rental is $871.50 and the cost per person is 62.25. so how can we find out how many people are needed to keep the cost down?


divide


yes


so 14 people


so where would we place that in the equation?


now we just need to figure out what is needed for each part of this problem


wait nevermind


so for 3 would it 361.25.25x14?


im thinking on how to answer pleaseease bear with me


ok, i think #3 should 299+62.25


because we know 299 per ticket (per person) plus 62.25 per person for the rental


ohhh so then 361.25.25 for the answer


so then we set the 2 expressions = in #4


would we still need the p for #4 because we already know its 14?


this is where my opinion about how this problem is not set up very well :) (pretend we don't know that p=14)


solve the equation in #4


you should get p=14


yep\


so then 5 would be 14 people can attend the trip


ok, finally #5 :) what does 14 represent?


yes, exactly!


okay thank you so much


you're welcome! that was a very round about way to arrive at the solution, right?


yes definitely lol


any other problems today?


one should have popped up


I see it


ok, what do you have for #7?


x = amount of games


ok. have you written an equation yet for #8?


i was thinking y = 11.47 +9.55 = 12.50 +3.95+1.48


really close! you just need x next to 11.47 and 12.50


11.47x or 12.50x?


both


good point


go ahead and solve, then tell me what you got


1.3687 but it doesnt look correct


no, you should get a whole number


did you get what i got for first step?


yes


then i subtracted that from 9.55


yes. is this what you got?


Ohh thats what i did wrong


found your mistake?


ok, what is x?


yes, and what does it represent?


how many games he's played


at each


right


so that is what you say in #9


"he played 4 games at each place"


what do you think about #10?


if you plug it in they do not make sense and you cant really play half a game of bowling


right!


that one was definitely easier than the first one


thank you!


i agree


you are welcome! have a good day Alex!


you too


homework


homework help


Hey, I'm Mark, how are you?


Hi. I need some help


Could you maybe type out the problems or upload or a higher quality picture? I can't really read the problems


The picture is too large to send via email so I will try using the laptop camera


Can you see them now?


Almost, I am unable to see the numbers though in the chart


Perfect, has your teacher show you how to solve this with a table?


no


Interesting, I'm assuming you are trying to solve the questions with a ven diagram.


yes


Is the ven diagram you have on the right of the graph completed?


Great, now for question b, how many students do we have in total?


And now, remember our ven diagram shows all the toppings people got and how many right?


So in our ven diagram, how many people do we know got toppings?


(Hint: You can add up all the values in the ven diagram to figure out your total)


ok I thought so and then changed my mind.  I will add them up


ok so 5 would be 1/10 then


Exactly, it would be (50-45)/50


Do you know the notation for this answer already?


which question?


Question b


5/50 = 1/10


I mean more so the probability notation. Like you have in part c, d, e: the P(M or E), P(B and E)


I'm not sure how


That's alright! For probability, there is no clear way to always notate an answer.


So here, we calculated the probability that someone did not get a topping right?


yes


So, we could just simply write it as
P(No topping) = 1/10


ahh ok, thanks


If you'd like we could do the back side, though you would need to take another picture again


ok doing it now


Okay, for part a, how can we calculate our total amount of people in the study?

Also, if you want any clarification on any steps or ever don't know, please just let me know.


add all of the numbers


Great, so adding all the numbers in the ven diagram should give us our total


So, what will that give us?


Could you double check your numbers? I may have added incorrectly since I can't see the numbers completely clearly but I did get something different


It is 1466


Great, so there 1466 people represented in our study.


What groups of people is part b asking about?


the probability of someone using a patch or gum


So, to calculate our total for someone in the patch OR gum groups, we are just finding the total amount of people in those groups right?


How can we calculate the total amount of people in those groups?


by adding all of the numbers in only those circles


Exactly, so how many people used either the patch or gum?


I believe it's 1,208


Great, 1,208 people used either the patch or gum.


But, we need to divide this number by the total in the entire study to figure out our probability right?


P(patch or gum)=1208/1466


Great! Now, one notation thing to know. Whenever you have an or like that. Simply just replace it with a U


That is actually what I handwrote


Okay, perfect, what groups is part c asking about?


What groups does it say to NOT include?


the probability of someone trying to quit by not using a patch or gum


So, we would get our total from all the numbers NOT inside the patches or gum group right?


yes


So, what is our total now


Perfect, we actually have two numbers to add this time: 86 + 172


To find our probability, we divide by our total right?


So what is our final answer?


P(Lozenges U none)=258/1,466


Great! However, here you calculated the probability of someone using the Lozenges AND None.


so an N


So, you would use
P(Lozenges ∩ None) = 258/1466


how did you get the sign


Exactly, a great way to remember is you could honestly read it as
P(Lozenges n None)


ok


Which kinda just sounds like Lozenges and None.


I searched up "and symbol probability" and copy and pasted it into here lol


haha


Now, for part d, what groups is it asking about?


probability of someone trying to quit using using both patch and gum


So, we can calculate the total by adding values this time?


By adding what values this time?*


the gum and patch


So what is our final probability?


P(patch n gum)= 1,006/1,466


Not exactly, this time we want the people who used the patch AND gum.


ohh ok


So we only want to add up the people in where they overlap on the diagram


Because only those people used both


Not exactly, could you circle on the diagram on the whiteboard where the patch and gum group OVERLAP?


Exactly! So our total should only come from there for this question


so only that small section inbetween?


Exactly, because it's asking for those who used the patch AND gum, so only those who used both. In our venn diagram, we know the people who used both is where the patch circle and the gum circle overlap


Because those numbers are in the patch circle AND the gum circle


How would you do it in probability notation?


P(patch n gum)= 146/1466


Great! Now, part e is a little tricky.


Notice, it says "given that they also used gum."


This means, your numbers should only come from people who used gum.


P(lozenge I gum)=


Exactly, do you know what our total is already?


not yet, let me do that


P(lozenge I gum)= 487/1466


Not exactly, in this problem because it says "given that they also used gum,"
it's basically saying, we want to know the amount of people who used the lozenge from the gum group ONLY.


So instead of dividing by 1466, we divide by our total in the gum group?


What is our total in the gum group?


I added the patch by accident


No, you actually calculated 487 correctly. 487 is the sum of everyone who used gum right?


Could you circle on the whiteboard how many people used the lozenge AND gum


Exactly, now since remember it says
"given that they also used gum"
so the amount we will divide by will be the amount of people in the GUM group.


What is the total amount of people in the gum group?


Try again, remember you have to add EVERY number in the gum circle to find the total for that group.


Almost, I believe you are mssing one more number to add


Double check the chart again, what numbers are in the gum circle?


Great, so instead of dividing by 1466, we divide by 487 now, because it says
"given that they also used gum"


Now, in the gum circle, could you circle the people who used lozenges as well


Not exactly, since you want the amount of people who used lozenges in the gum circle, you only want the numbers in the gum circle AND the lozenge circle


Exactly, what is our total there?


142 people used the lozenges and also used the gum.


Recall, how many people used the gum?


So, now we will divide 142 because it is telling us
"given that they also used gum"


P(lozenge I gum)= 142/487


Exactly, this is basically saying, of 487 people who used gum, 142 ALSO USED lozenges.


Which is exactly what they asked saying
"Using a lozenge given that they also used gum"


ohh ok


Now, look at part f, what probability are we trying to find now?


P(What | What)?


the probability that someone using a lozenge and no gum


Exactly, in probability notation what does that look like?


P(lozenge | no gum)


Great, so now what is the total we will divide by?


What groups are we going to look at to find our total we divide by here?


no gum


Here, it says
"given they did not use gum"
so this is what we will divide by.
How many people in total did not use gum?


Great, 979 did NOT use gum, which is what we will divide by in the end because it says
"given they did not use gum"


So, could you circle on the diagram how many people used lozenges, that did not use gum


Exactly, and now, in probability notation?


P(lozenges | no gum)= 232/979


Perfect, for a quick recap, remember that U is for "or" in between your probabilities.


∩ is for "and" in between your probabilities.


I have a sheet of paper from class that tells me all 3


Perfect!


When it tells you to find a probability
"given that" something else,
the amount of that something else is what you will divide by


That one will be the most important likely as it is an easy mistake to make even if you know what you are doing. So, just make sure you understand exactly what groups it's referring to when it asks that


ok


I'm assuming that is all, unless you have more, then feel free to put it up, so whenever you are ready, just leave the chat when you are ready.
Have a good day!


no that is all. Thank you and you too!


hello


how are you


good


wabu


what can I help you


give me a moment


what should i do next


solve the equation


how?


does that make sense?


not realy


oh wait yesh


so now you understand?


yesh


any other question?


yes


put in


whiteboard


i did


ok I see now


does the equation make sense?


Or do you understand the equation?


is 25/23 corect


wait


you were wrong here


ware?


it should cross multiply


ooooh


so whats the aswrer?


ooooh ok


any others?


yesh


ok


can you show me how to gain?


do you mean how to gain the equation?


no can u show me it again


wait , I am sorry ,I am confused now


can u show me how to do it again


so you 840 minutes in 2 wweeks


mhm


and then we set x minutes for 4 weeks


so


that is


idk


so the only thing equal here


is how much time she practiceone week


so we can do


840 divided by 2


we get she practice 420 minutes one week


does that make sense so far?


Sarah


ok


then we need how much time she practice for 4 weeks


we already know she practice 420 minutes for 1 week


so we times 4


Then we get the final answer


does that make sense?


ye


ok now you understand?


yas


next one


oop i gtg


dinner


David


don't worry


have a good night


u too


hello!


Hi can you turn your mic on so its easier to communicate


sure, give me a moment


ok Thank you


Hello


Can you hear me


is it working?


No


Can you hear me now


Now ya


OK, great


Hi


Hello.


Um


I was wondering if you could help me deepen my understand like my understanding on solving inequalities.


and graphing


Yeah


yeah


OK. OK. Um, do you have any, any problems or homework questions that we can look at?


Uh, I did them, but I was having trouble like


with the word problems, like,


my teacher gave me word problems, like, and then I have to make it in a in a quality expression.


from those, and then solve it.


OK, OK. Do you think an uphold the question onto like the the whiteboard.


Uh, how do I do that


Oh


OK


Oh yeah, I see it


Um, like there's like on the bottom there's like a picture icon with a little up arrow. You can insert images from there.


OK, yeah, hold on


Can you read that


Yes, OK. Number 7?


OK.


Syringes start her own business.


Do you have any idea of how to like get started on this question?


Yeah, so what I did was um


I did


I identified the X variable, which is um the amount of boxes she needs to sell.


Hm.


And I did um 20 X


wait, what did I do


uh


20 x minus 65 is


greater than or equal 225.


X minus 65, greater than equal to 2 to 5. Yeah, that's right.


OK. Um, so I, that's the equation you have, which is good.


Yeah


Yeah.


OK. So, um, from there, like, it's very similar to how you solve like a regular equation, except when you multiply the negative one, you have to switch.


It's like, you know that.


So


OK.


Yeah, that's what I'm having trouble with, like, I keep forgetting to switch the, the like symbol thing.


OK, OK


So do you want me to like write it down on a notebook on the board or, or I can write it down somewhere and we can just do this question.


Uh, can you write it down cause I'm not good at writing this stuff on the board.


Oh, OK. All right. Give me a second.


use a piece of paper and write it down. I am. I did.


Mm


OK


um


m.


No.


can you still hear me


no


your mic is off


can you hear me now?


Yeah


OK, OK, that's good. All right. That's just I switched the device, maybe that's why. OK, so here, um, so we just first say that let x be the number of boxes that's we go we to find the variable there.


Uh-huh


and then uh we write down the equation, which is what you said earlier, 20 x minus 65, greater than or equal 225. Do you know why we put the greater than or equal to site instead of just the greater than sign?


Yes.


Uh, because in the equation it says um of at least 225, so she can 225 or more.


OK, very good. That's good. That's exactly the reason. And then, um, well, what we do afterwards is just solve this. So


um, I don't know how, how you, you got taught at school, but usually what I think what people do is, uh, first we add 65 to both sides. This is the same as how you would solve a regular equation.


OK. So we get, 20 X greater than equal 290.


Yeah, that's what I got.


Yeah. OK. So, and then you divide 2, the both sides by 20.


Mhm


I got the pills


OK, you have this.


right


Yes, but the thing was this one is that, um.


this does not give us a whole number answer. It gives like a decimal.


Yeah, so would I put at least 15 boxes then?


Yes, so since X has to be a fault, like a whole number, uh, it has to be an integer positive integer, so we just put 15. So that, that will be the answer here.


OK


Uh, I also have a, a different question that's like that, and it was in


I'll, I'll upload it right now.


Yeah.


Uh, this is two questions. Is that OK?


Of course. OK. Um, yeah, I'll clear what we had before. So the board is


yeah


OK. OK. Oh.


All right. Oh my God.


That's


OK.


take a look. OK. Um, first question number 9. A taxi charges a flat rate of $1.75 plus an additional 0 0.65 per mile. If Chloe has almost has a almost $10 to spend on the cab ride, how far could she travel? OK?


Um, I think this question is fairly similar to the other one. do you wanna tell me like what your ideas are for this one for now?


Mhm.


Uh, I put 1.75 + 0.65 x is


less than or equal to 10.


Yes


Um, and then I would subtract the 1.75 from both sides.


Mhm


And then I would get 8.25 or 0.65 x is less than equal to 8.25.


And then I divide both sides by 0.65.


OK


And then when I did that, I got X's lesson equal to 12.69, but like if you actually did that on the calculator, it would give you like a repeating decimal. So I just switch to 0.69


OK. Uh, let's see what the question says.


What


Um, so because it's like per mile and we can have like 1.5 miles or something, so I, I don't, does it, yeah, so it doesn't have to be integer. So I


think you could just, OK, I think you should round down. So, um let me just do that quickly on my calculator.


Oh


8.25 divided by 0.65.


Yeah, that's 12.69 something something something.


Yeah


So it, oh my god.


One second.


Oh, OK


OK. So in this case, um, I would, depending on what your teacher wants, like how, how wants how you to round it, I would just leave it at 12.69 or, you know, if you just go with like significant digits or something, I'll put 2 digits. It depends on what your teacher wants, but remember to round down, don't round up, because we cannot go over the $10 limit, that's all.


OK. OK. So she can write at most 12.69 miles with the $10 that she has, correct?


Yeah, yeah


Um


OK


I had most trouble with the number 10, I think out of all of them for some reason.


Maria is a wrestler trying to make a weight. She currently weighs 200 pounds. If he cuts 2 pounds per week, how many weeks will it take him to weigh less 175 pounds. OK.


Did you do you think you can give me the equation here?


Uh, yeah, 200 minus 2 x is lesser and equal 175.


Yes. OK. Um, yeah, I could, I, I can maybe see why you have trouble having trouble cause there's a negative side, that's OK. So, um, what would you do in this case?


Uh, subtracts 200 from both sides.


Mhm


And I would get -2 X is lesser and equal to -25.


Yes


And then I divide -2 by both sides.


Any?


And I think what I messed up was on because I forgot to flip the the inequality symbol. So this one, if I were to like get the actual answer, it'd be X is greater than or equal to 12.5, but I accidentally put X's lesser and equal to 12.5 instead, but now I know my stay.


Mhm. Yeah. Yeah, so when it comes to dividing both sides by a negative number or just 1, you have to make sure to flip the eco sign and then like I can show you cause a very simple reason of why, cause for example, if, if we just say, uh one is smaller than 3. This is correct, right, cause we know 1 smaller than 3.


Yeah.


So if we were to divide both sides with negative 1 of times by -1 or whatever.


-1 would be greater than.


Yeah, oh, in this case, -1 will be OK if we just flip times 1 and then we do not flip the sign.


Mhm.


same sign, we will get a negative one is smaller and 3. That's not true. So this is also a kind of like uh in number wise, which is why you have to flip the sign every time, so just don't forget that and then it will mess up your thing a lot. Always flip.


the side


OK. Thank you.


Uh.


OK, yeah, and then I think that's all


OK


Yeah, that's all. Thank you. Thank you for your time.


No worries


All right, bye


Bye-bye


hello


Hi


is BC = 12 or something cutoff


I have two math problems I need to be explained, I put the first one on the whiteboard


Nothing got cut off I think


yes, i'm missing the right side


please move to the left


ok got it


Ok srry, my screen must look a little different from yours


ok, lets start drawing these graphs


I have trouble drawing with my mouse.


What does collinear mean to you


I have no idea


collinear means that all the points are on the same line


Ok


So do I write the two problems equal to each other then solve


Honestly I need to think about this for awhile.


Let me draw on a piece of paper here and see what I come up with and then I can better explain to you


I got 8 and 33 as my answers btw


I'm not sure i understand the question.


if AC = 12x +40 hen A and C should be on that line.  But B needs to be on that line also


My teacher ended up helping so it ok


Thanks though


OK so what was the answer, explain to me how she did it


She did the ab plus bc = ac and i solved to find x then plugged x back in


ok so AB is 33 and x = 8.  However what are the points A, B, and C that are collinear


I think she said they just don’t matter


hello! I do not understand these types of questions at all so please bear with me


Hello!


How are you?


that's fine!


let's go over these!


The graph shows the vertical asymptote is x=−1.


Does this make sense?


This means h=−1, and the argument of the logarithm is (x−(−1))=(x+1).


wait what is h?


the y value?


h in the context of the logarithmic function equation.


but i get the log would be loga (x+1) +/- b


got it


Okay!'


but my issue is with finding the base


Substitute b=2 and k=−3 into the equation.


where did you get those values from and what is K?


like that?


Point (0,−3)=(h+1,k)⟹(−1+1,k)=(0,k)
k=−3


H and K are from the equation.


The graph passes through the point (7,0).
x=7 and f(x)=0 into the equation:

0=log b

 (7+1)−3 0=log b

 (8)−3 3=log  b
 (8)


ohh ok


Do you know this equation?


no my teacher totally skipped over this section


ok so i should memorize that?


Okay!


That equation is correct!


what about that?


is it correct?


You should actually only get 2


what happens to the 8?


Assuming no vertical stretch/compression (a=1), the equation is now: f(x)=log
b (x+1)−3.


0=log b

 (7+1)−30=log b

 (8)−33=log b (8)


is a always equal to 1 if there is no vertical stretch?


b= root 8

b=2


Yes.


I don't know if you learned it differently.


wait gimme a moment to process this and no i didn't learn it at all apparently the taught way was wrong most of the time


"Assuming no vertical stretch/compression (a=1), the equation is now: f(x)=log
b (x+1)−3." wait where did the negitive 3 come from ?


and what is log1 (x? is it solvable? like what to the power of 1 is equal to 8?


-3 comes from the vertical shift (k) of the graph.


im so sorry im so confused maybe you can start from the begging and just work it out and ill try to follow that way


beginning*


Okay!


I'll work on the board!


okay!


wait pause for a moment im confused


Yes?


oh i wrote it on the board so you know what im reffering to


its in red


Yes it’s equal to -2


oh you found that the base is 2 because it can only be 2 that has a power that can equal it to 4 not base 3?


We were comparing two points on the same log graph:


ok wait i think i understand! im going to do 66 on my own just to see if i turly understand it


truly


Okay great!


oh wait im stuck lemme write what im doing on the board


OK


i dont know how to find k


k is 0


wait how


why is log2 of 2 negative?


did i do it wrong


oh i see what i did wrong


Okay!


is that when it becomes negitive?


Yes


is that correct?


Yes!


yay! do you have time to wait for me to do 67? it looks hard


Sure!


thank you sm!


No problem!


im stuck again lemme write on the board


ok


oh wait i see what i did wrong i forgot to reflect


ok im still confused so im just gunna write the part where you find the base


i have no clue what the base would be


is it 2?


how did you find that?


logb 2=−1


why does it equal -1? would it not be -1 minus -2?


wait whaaat i thought when its refected it would be logb -(X-3) i had no idea the negitive goes outside the log


i thought it would only be outside the log if reflected by the y axis?


log here is negative.


oh


Yes.


ok i actually have to go for a bit but if  your still online then you might be able to accept my request


Okay!


bye thank you sm!


Hello


How may I help you this afternoon?


how do you do this


please explain in detail


Do what?


the problem


What is 8 + 10?


Is that a division symbol in the denominator?


yes


so you are dividing by a fraction.


sure?


to divide by a fraction you change the division to multiplication and multiply by the reciprocal'


which would be....


don't tell me let me figure it out


I won't tell you.


right


no


Again, to divide by a fraction, you change the division to multiplication and flip the second number


Give it another try


Hello?


hi


math doesn't make sense


do you see how I did it?


Hii! how are you?


OK, now at least I have the banner up top.


I am good. How are you?


I'm good


And when I look at the chat, when we just closed, I can see


what you wrote now


plus x_squared + y_squared.


I can see you're writing x_prime + y_prime + Z.


and then you can see my squigglers, my squiggles.


Alex


do you have your mic off? bcuz it's acting weird. It's unavualbe but i think ur speaking


unavailable**


You can't hear me


no


it shows your mic is unavailable


How about now


Still can't hear me


It says you're away too.


yeah, i refreshed it


OK, you


you are back


yeah i hear you now


OK


Um,


as


for that multivariable problem


when you take the full derivative and you add them up.


right? Each individual partial derivative.


and you're left with


um


the derivative divided by the inside of the log.


You just have to do long division


of the numerator


I'm sorry, the denominator divided by the numerator.


to prove that it's a factor.


So I think you said something like U is equal to


natural log


XQ plus YQ plus Z_cubed minus 3 XYZ.


right? And then you prime


would be


the 3 X_squared_term.


minus 3 YZ over


B.


We just call this B.


plus


OK, then you have to take


I'm just call this A


You have to do


a long division.


okay


Um,


and then you'll be left with the uh right-hand side.


The only thing I didn't get though was the negative sign. I don't know where they got that from.


Not from the, you know,


the squared term.


oh, if we do long division we'l get rhs?


Yeah


It was like a, it was like I'd said the


let me see if I can pull it up again.


Where is it


Right. So it, it was basically like this.


So what you end up with is like the X minus A term.


it shows black screen


and the derivative is the numerator


how about now


Can you see the screen now


Table 7.2 from the textbook.


about rational functions and their partial fractions.


yeah i see it now


OK. So, it's something similar to this, where you're gonna get


the next cube term except we're dealing with um multivariables.


But you're gonna get essentially


um, the, so the derivative essentially gives you this unfactorable


expression


and you just do


polynomial and dividing it by this unfatable expression to get something like this, this X minus A term.


That's why it comes out so cleanly.


i wanna try this division


cause all we're doing is just factoring it, yeah.


That's why I didn't want to show you too much on the board. I just wanted to talk about it.


so you can do it yourself


You get your terms mixed up


other way around.


right? Because you're trying to divide a


you, you're dividing a sec a third order term by the other one. So you want your B underneath the division sign in your A outside of it.


So it'll be the


let me show, I guess I'll show you what it looks like. It'll be A_poly + B_poly + C_poly


but a is in denominator?


A is not the denominator


B is in denominator


oh right, i mean numerator


Yeah, that's correct


You are correct. Is it a numerator, but we're trying to prove


that


the numer the, the term in the numerator is a factor of the denominator.


The reason why we're doing this


is to show


that we can get rid of the numerator by factoring the factoring the denominator and then canceling out the numerator with the denominator.


Does that make sense?


Basically, we're trying to prove that, you know, that AlphaX + BX + C over X cubed minus A.


is equal to BetaX + BX + C over X minus A.


times GammaX + BX + C.


yeah makes sense, like 3 is factor of 18 so 3 divides 18


and that these terms cancel out and you're just left with one over X minus A.


That's the idea we're going with


Yeah, exactly


That's basically what we're trying to do here


yeah right


But to prove that um


that you, that you can get X minus A is you have to do long division of X_cubed minus A cubed.


divided by ThetaX + BX + C, you have to divided by that to prove that it's a factor.


oh , gotcha


I think you're missing a term up here.


You should have 6 terms, but you only have 5. You have X cubed,


um, you have X cube minus XYZ + XY2 + XZ2 plus or minus X2z, you're missing minus


X


2 Y


cause you have 12340 no, you have 6 down here.


Yeah, yeah.


you should have that delta_term term.


And also, and also down here, you're also missing a term as well.


You only have 5 terms, you should have 6 terms.


when you multiply by Y


I think you're missing the


Why do you have


to


XY squared terms.


One of them should be x2y.


Yeah, just remember you, you keep, you have to keep dividing by there's 6 different terms. All you're doing is multiplying X, Y, or Z to the six different terms.


yeah, Im skpping one term


gimme a min


Yeah


I missed the Infinity Board.


yeah it was better


That looks better.


Everything's the right sign


I forgot , what do we write the relationshio between quotient, divisor, divident...


I mean, no, that, that, that's it. Just um


that


you, it's just B is equal to A times C.


+ remainder right?


where A was your numerator, so you're just gonna like a over B does he go to A over AC. There, yeah, plus remainder. The remainder will be like um


a, or whatever your C term is.


plus


the remainder over the.


okay


we also don't have squared denominator


We do, remember? It was um the sum of the derivatives quantity squared. That's where we get the 9 from.


oh right, we do


This is a question they wanted us to solve.


only - missing


Correct, and I don't know


how they get that if it's squared.


And that's not something you can just


mess up on. That's, that's very, um,


intentional, that negative side.


these people doesn't sound very likeable


Very true.


Um


did you want to try to figure out the negative sign or we can move on to another problem.


Cause we did the majority of the work.


It's just that pesky


pesky negative sign


yeah let's move to another question


but don't erase it


You want me to wipe


Don't erase, don't erase, OK.


You OK


Are you copying and pasting or just trying to write down the


the solution


i was taking screenshot


OK.


I was trying to get it in one single shot, it wasn't happening


By the way, I'm looking at the top. I had that Upri term.


Don't take that to be the full derivative.


I


actually, I think that is the full derivative.


If you have, it's the sum of each individual derivative.


Each individual partial derivative.


Anyway, don't take that to be verbatim


I was just using that


prime is a shorthand for the problem at hand.


That was it, just a little note.


So that when you're looking at the problem later on or the solution, you don't


take that U to be


um, you know, what the full derivative of the


of viewers, you know.


Yeah, that'd be like Dell Dell X.


yeah i should write like this you mean?


not how u started it


Yeah, exactly. I just wrote you prime for the total derivative


but that's not


what the total derivative is.


oh , it is du/dx


No, total derivative would have to be


um


I don't think you have, I, I think it, I think you'd be stuck with


this partial_U_partial_X_term because it, if you, for you to say the total derivative, it'd be the derivative of respect to every variable.


right? Sort of like a chain rule


but you don't have um


each variable within you is independent of each other.


So you couldn't really say it's chain rule.


cause you'd have to have an expression of you crying.


that is that has, that's a function of


DellU Dell X L Y and they'll you


De Z


That's what I was trying to get at. I'll wait, I have it written at the bottom, by the way.


That's one place I had space


I was just trying to say that you prime is a function of each individual.


partial derivative


but the way I have it written, it nec isn't necessarily what that is.


And you can't really say capital you um regular D


X.


because there's too many dependent variables.


or there's too little dependent variables.


ohh , i see you mean to differentiate seperatly with each function


Yeah


It gets a little complicated


you kind of didn't mean this , and proceeded with  u prime right?


Um


because there's


yeah, I just, I was just trying to be quick about it.


i didn't notice that before


I didn't wanna say how it was defined. I just, I could've, I should have just said DU.


instead of U, I should have said um partial_U_var


yeah


Yeah.


I'm glad you didn't, well, I mean, you didn't notice it, but I didn't want you to, because you're taking a screenshot, I didn't want you, when you referred back in your notes to kind of see that and think that


that that's true


I just did it to just be quick about it.


without putting too much thought into it.


So you'll see later on that your best approximation


for partial_U_approx


um regular DU would be, um, your kind of partial you, partial X times DX


plus your, yeah, partial partial_U_y, partial Y, DY, maybe not the plus term, but it'd be the factor of that.


youZ DZ.


And this would be closer to what the full derivative is.


cause this would be an example of like chain rule.


and product rule


yeah, right.


of a function that is X, a function of X, Y, and Z_variable


right


OK


I'm, I'm glad I said that because that, I


I would be remiss


if I misled you in that way.


i appreciate it.


Has your teacher gone over?


um, full derivatives or just, just kind of going over it. You're just doing it learning implicit differentiation now.


not implicit, partial differentiation.


for multivariables, cause you're gonna get to


like moments and stuff like that soon.


i haven't learn total differivates right now


Yeah, you won't, you won't for a bit.


Um


im learning partial differentiation right now


Cause you'll get to like 2nd and 3rd derivatives.


Um, I'm maybe remembering incorrectly.


about moments, but I know you'll get to like 2nd and 3rd derivatives.


for multivariable. And you also have the mixed derivatives.


yeah i do


where you'll have, for example, you do?


Oh yeah, you are learning partial


i saw in content in books


Yeah


Like this is an example of a mixed derivative.


And then you can move on to mixed integrals.


2nd order


ohh i have done this


like 2nd order um integrals, things like that. Yeah.


i had solution for this problem


but it was really complicated.