Ok, what did I tell you earlier about getting x alone when it is being multiplied my something?


Would it be -4 on both sides?


No, that would be if it was x+4, but right now, it is 4 times x


I’m confused


Ok, let me explain


You always have to do the opposite thing to get rid of something.


For example, to get rid of +4, you have to do -4


and to get rid of times 4, you have to divide by 4


Ohh i understand now


Good job! It can seem a bit complicated, but once you understand, it's really easy!


Would it be 3?


YES! great job!!!


Is there any more problems?


No that was it


Thank you


Nice! Good job today


Working through complicated problems!


Well, have a nice day!


I wish you good luck on the SAT!


You to thank you so much bye


ok


slope and intercept graph


hi


Hello


How can I help


Graphing lines and slope


Ok?


For this lemme draw you how it could look like.


So for slope


It stabds for m


Negative is a downward line like this one.


For positive it would stand upward.


For y intercept


That is end part of equation


And for x intrrcept


It is if y is 0 and x is of higher lower or even 0 value


And for y intercept


It is if x is 0 value and y is of possibly different or equally 0 value


So I hope this explains.


Ok bye


Hi how may I help you today?


hello


I think there is a slight mistake in your work since we are not using e even though it says exponential, we are actually using (1+r) instead for part A, but your work seems correct other than that


well


isnt this e


because


population growth


is always exponential


true but e is used for continues we would use 1 + r because population isn't growing at a continues rate


sometimes it can dip and stuff


what type of poopulation doesnt grow continiously


Every type of population doesn't grow continuesly


really


Yes for example


I will try to make this simplified, but for like animals their populations change a lot since they get eaten they also have to produce more to stay alive otherwise they will go extinct, so that is how population stabilizes and doesn'ty continuesly increase


Or like e is more popularly used with derivatives when you get to calculus and its used for compounding interest in business


But don't worry you had all the right steps


yes


is dis all right


Yup


My teacher in when I took precalc shpowed me this trick as well for logarithms


She called it the alligator


But I think you understand so its fine


All Correct


my trick doesnt rly work


causr anything divided by 0 is undefined


true but


I think just remember that log 1 is 0


same for ln 1 = 0


wats answer


since anything to the 0th power = 1


Remember that okay?


pretty sure the range of logs is always -infinity to finitiniy


unless theres something werid going on


Sorry you are right


my mistake


continue


hmm


rewrite the radical in terms of fractional exponents


Alex do b i


i wanan see how u do it


Ok sure thing


We know ln and e can cancel so


dam


Double check continues on because it refers to the x axis


or like x coordinate


huh


nice


Hello! I could really use some help right now. I just learned this topic today, and while I somewhat understand it, I’m still a bit confused. Could you please go over the original problem with me and then create a similar one for extra practice? Here’s the link to the PDF: https://docs.google.com/document/d/1a2b3c4d5e6f7g8h9i0j/


ok


https://docs.google.com/document/d/1a2b3c4d5e6f7g8h9i0j/ file not found


Holdon


Try again


same thing happened


sorry I have to drop


bye


Ok, one moment


kk


hi


can we use voice


Hi Ben, how can I help?


Yes, we can, one second


Brooklyn


Hi. Uh, can you hear me?


Yeah, I can hear


you


OK


OK.


So, uh, what are we working on?


Um, angle of elevation. I was just confused when some.


OK. Um


Yeah


do you have a specific problem or something that you were working on?


yeah


Uh, can I see it


Um, yeah, I was just like confused on this.


um


I'm gonna make it a little bigger so that I can see.


Uh, DME is a standard avionic equipment on a commercial airplane. It's just the distance from a plane to a radar station.


the distance from a plane to a radar station 160 miles. The angle of depression is 33 degrees. Find the number of ground miles from a point directly below the plane to the radar station.


Uh, yeah, that looks good to me. Uh, let's see.


I was just confused on where to put 160 in like the angle, like that we would be finding X, but I would, would X be here?


Yeah, that's correct


Yeah, but like I was confused on where to put 160.


I be here.


OK. So what do we know about 160?


um that


it's at the distance from the plane to the radar station.


Good. Uh


just so that we're on the same page. Can you mark the plane and the radar station on the


on the triangle


Yeah


Wouldn't it be here and then this is the plane when the Raiders see from here.


Exactly


Oh, 160 would be here.


Perfect


OK, so then if we do


um, so then opposite over


wait, do we know this is a hypotenuse, right?


Yeah, 160 is the hypotenuse, exactly.


So it'd be opposite over hippotenus would be sign.


So it would be


Uh, I don't know if a calculator on me. Is 160 times sin 33?


Yeah.


um


OK, good. Uh, then you're correct.


as far as I can go


um, I have another question.


OK?


I was going to get a picture of this.


Mm


Um, I just had another.


on this.


Mhm


wait


over preparing to land. OK, so this would just be 13.


and then you would find like.


what angles does the approach make with the runway, so it would be


this, right


Yeah


Where's the runway


You're close


Um, the runway


is down here


There you go


Over your breaks back


What angle does the? Oh yeah, you're right. It would just be.


Nice


Perfect


Um, and then you would do opposite over hypotenuse, so it'd be a sign.


Um, and then you do


3 5.025 degrees.


Uh, looks good to me if, if that's what your calculator gave you.


OK. Seems like you've got it.


um


hm


um, I was confused on this one too.


So it would be Iosceles triangle.


The altitude is


80 ft


What are the measures of the base angle.


base is 58.


Mm.


So this should be 20, I mean, sorry.


58 divided by 2 is 29.


and it's asking what are the names?


Wait, what are the measures of the base angles.


Wait, how would you


do that?


The, so the measures of the base, the base angles are the angles that the triangle forms with the base, so it's going to be these guys


uh right


here, uh, I'll, I'll mark them so you can see.


How would you, um, find the measures of them?


Well, um,


Hm


you have the 29 and you have the 80, right? Uh, what do you know about the altitude relative to the base. There's a


um, it's 90 degrees.


there you go. Perfect.


Oh, so it's


um.


so it'll be 30 degree, I mean, sorry.


this would be um


60 degrees


How did you get 60 degrees?


Mm, cause there are 69 triangle.


Wait, why is that a 30, 60, 90 triangle.


Oh wait, that doesn't make sense.


Hm, oh wait, oops, you would just do Pythagorean theorem for the


lengths of the legs


right.


Yeah, so


Pythagorean theorem would give you the hypotenuse, and it would work fine for that. But you don't need the hypotenuse for this.


so we, but doesn't it say


what are the lengths of the legs?


Oh


you're right, it does say what are the lengths, what are the lengths of the legs? Yes, that would.


that would work for that


So 29 2 + 802.


So the answer, so this would just be


Sounds about right


If that's what your calculator said.


Yeah, you know I'll open a calculator and plug it in.


What are the measures of the base angles, so


hm


wait, uh, how would you do that?


Oh wait


It's another trigonometry platform.


Oh wait, yeah, so you do, you could just do


opposite over adjacent, which is


Hm


So it'd be 70.


degrees


Sounds good to me


Uh 70.07, right?


Oh yeah


Mm


the


Oh wait, this is the last question I have.


trouble on


So you're just trying to find x


Right


How far? Yeah.


Yeah, that's the, that's the first question. Then there's a second.


And then you may find why, just how long is the wire after.


Exactly


So then


adjacent


Perfect


feet


and then why just.


um


it


adjacent overhead cottons, so the line.


um, 193


Little bit of her


Yeah, 02. Uh, yeah, that's correct. Good job.


OK, that's all.


OK. Uh, do you have anything I should clarify or anything like that?


That's it.


OK, bye then


Bye. Thank you


Hi Alex, how can I help you?


hi


solve a polynomial function


find all real solutions of the polynomial equation.


i hate writing this board lol


but i know i can do synthetic division here


Yes, this white board is hard.


so true


Great start.  Why did you first try -2?


i tested all of them


and they gave too much remainders except -2


i know -2 is a possible zero so far


And -2 gave a zero remainder?


Yes!!


yes


OK, so now what?


the thing is should i continue doing sythetic


thats where i am stuck


i dont think i can use the quadratic formula as yet


Why not use the quadratic formula?


its a square root function


It might be messy, but it WILL work. Right?


i think so


And you have a quadratic function.


ohhh


Yes, it will work.


ok


lemme me do this


good so far?


Let's review your quadratic formula equation.


i see whats wrong


hold on


Careful, should be (-6)^2


good?


What is the square root of 132.25?


Still all over 16?


yea


The square root of 132.25 is 11.5.  You don't need to take the square root again?


um


maybe


So 2 roots ;


yes


(6+11.5)/16 and (6-11.5)/16


ohhhh


thank you


Do you use DESMOS?


You can check your answers by graphing the original polynomial.


okay


This can be kind of tricky.


It helps to stay very focused to avoid careless mistakes.  :)


definitely


Great job!!


thanks


Anything else?


yea


OK, how do you find potential solutions?


list the possible rational zeros of ,

sketch the graph of  so that some of the possible zeros in part (a) can be disregarded, and then

determine all real zeros of .


sorry my thing is freezing


You can start by testing the factors of +-15/factors of +-4


Don't forget to divide by the factors of the leading coefficient, 4


how would i do that?


factors of 15/factors of 4, +or -


soo


DESMOS graph shows the roots clearly.


the original one right?


Yes, is it OK with your teacher to use
DESMOS
?


i just did


yes hes good with that


What roots/zeroes did you see with DESMOS?


What are their values?


the points?


i mean 4 roots


Yes, I got -1, 1.5 and 2.5


yes


How did you get 4 roots from a cubic polynomial?


oh sorry


i put the wrong number but its three


Yes, 3 roots.


yeah


If you use DESMOS to graph, the roots or zeroes are (-1,0), (1.5,0) and (2.5,0).


exactly that


Those values of X result in a value of 0 for Y


ohh


And those values of x correspond to potential roots by using the factors of 15/factors of 4


okay


how would we determine the all real zeros though


Graphing?


for c


The graph will show all real crossings of the X-axis.


ohok


thank you


Sure, you're welcome.


Hello! I got my test back, and I saw that the “R” means revise, so it’s partially correct. I’d like to know what my mistake was so I can fix it, and then I’d like to try a similar problem with different numbers for extra practice before I retake the test and redo those sections. Here’s the link to the PDF: https://example.com/math_test.pdf


perfect! let me load the page and I can see what we can do from there :)


Ok!


ok, I see that on the first one, a, you distributed, and then just mixed up adding and subtracting the constant terms.


do you know what I mean by that?


umm no


i added a negative 1


infront of the "-"


you just added the 3 instead of subtracting it


bc i thought that means its a 1 infront of it


at the very last step.


everything else is perfect


it is a neg 3


she circled the -8


yes, but the 5 is positive, so it would take away from 5, not add to it


-3+5 = 2


ohhh


ok


ok let me rewrite this


everything else on there looks great!


on a, I mean, we can move onto b when you're ready :)


so the answer is -3x+2


yep!! it was just a sign mix-up, I do that all the time


Can u give me another problem like this one just for practice


I wanna do that for each problem


of course!


you can use chatgpt to generate one


thanks!


ok, let's try (4x+7)-2(x-1)


solving on paper


ok! I'll work it out too and we can see if we get the same answer :)


perfect!!


do you want to move onto b?


yes


what did i do wrong


I have a trick that I like to show students, can I teach it to you? it makes distribution a lot easier.


the first thing you do it draw a square, and divide it based on how many terms you have in each part.


ok


but what did i do wrong?


was it the calculation?


i believe it's a distribution error, which is why i'm showing this to you.


ohh i didn't write -5x


there should be two terms with "x", not just 1.


i get it now


ok! do you still want me to show you the trick or do you want a practice problem?


so its


yes, and then the final should be 4x^2-17x+15


does that make sense?


4
𝑥
2
−
17
𝑥
+
15
4x2−17x+15


Yeah I get it now, can u give me a problem just like that one then we'll move on to the next pae


page


of course! how about (3x-2)(x+7)?


mhm


answer is 3x^2+19x-14


it looks like I only have enough time to do one more, do you want to do 3?


sure


and yes, that's perfect!


why is it wrong


what's the second term?


is it just ab^4?


no, the 16ab^4


i did the smallest exponents


if that's the case, then it's because that term only has one "a", and your equation has "a^2" as the smallest exponent.


yeah


i just noticed lol


4 is a factor of all 3, so that makes sense, and then it should be 4ab^3.


other than that, you did everything right!


thanks for your help!


unfortunately I do have to go. if you need more help, you can request another coach. it was a pleasure to be able to help you!! :)


is there any available


how long is it going to find a tutor


hey there


how are you


good


would you be able to check my homework if I did it right?


Sure, are your answers the ones in blue?


yes


sure


questions 1 and 2 look right


okay


Question 3 You correctly identified similar right triangles and then You explained why they’re similar and how to use proportions to find the height


so far so good


Question 4, you’re correctly identifying why the triangles are similar and how to set up the proportion


okay so far so good


5 is good too


Ethan: Correctly set up proportion (Ethan’s height / his mirror distance = peak height / mirror-to-peak distance


Arithmetic looks good


great job


okay sounds good is there anything that you think I might need to change ?


No, I like what you did and can follow your thought process


okay does this match with he peak a a nd b and c just making sure I didn't make a mistake
and for question 2 is it right. averting


yes, your logic for both peak A and peak B matches the problem setup and is correct


okay thank you so much


I need help with Unit 2 two variable data specifically


Hello


Hey, I'm Sarah, how are you?


Im good thanks how are you?


I'm good, what can I help you with today?


I have a practice test to go over and prepare for my test which is tomorrow


Alright, whenever you are ready, you could put up a practice problem problem and we could look it over


That's the first question


Okay, what does the correlation tell us about two variables?


I have no idea


is correlation like the relationship


Yes, exactly! The correlation between two variables how related, or how correlated they are together


Except, always know, the correlation only represents the linear relationship between two variables


Let's say I throw a tennis ball up in the air right


If I graph the time vs height


It should look like that probably right?


yes


Because the ball goes up quickly and then starts falling down.


Now, what our correlation tells us is the LINEAR relationship between this height and time


But clearly, these two are not linear


Which is why our correlation is 0,

but we know there is a relationship between time and height right?


So, based on the correlation being 0, we know there is no LINEAR relationship between time and height


so option B


Yes, a good bit of students would get caught by a here, but always try to put things into a realistic perspective.


You know time and height have a relationship, if you were a physicist you could probably figure it out. So it couldn't be choice A


Especially for AP Stats, if you don't know something, try to think of it in real life standards. Majority of the curriculum is pretty intuitive if you see things like that


So whenever  a question is asking or talking about the correlation of a graph or something its asking whether it is or it is not linear ?


The only curriculum knowledge here really, is that correlation is the LINEAR relationship between variables


Yes, correlation compares the linear relationship


Ok


Should we move to the next question


Yes, whenever you are ready!


Is there a choice for this question?


Is there a choice E I meant*


How can I remove that picture


Thanks


That's choice E right?


yes


Okay, these questions will come up quite a bit for this unit. The best way to answer is to go down and cross them off one by one.


Does choice A seem correct?


Yes


since for both New and Old property it says thousands of dollars for the value


I think


Hmmm, check the values again


When old property is 250 thousand


The new property is a little lower right?


250 thousand for old, the new is a little lower right


oh ye since 225<250


which makes that statement false


is that correct


Yes, so you can just examine the graph and see for yourself, how the values change based on one another.


But, we could also look at this numerically, which you may need for FRQs.

Do you know what the slope of our line of best fit is here?


nope


Alright, here is a pretty important you do have to know about the curriculum, is how to read your computer output graphs.


For these graphs, for this unit at least, jsut visualize them like this


None of that matters, you don't need to know what it means


Especially for this unit.


ok


I think I know the slope is it the 0.95597


Yes! And what is the y intercept?


So, our slope is 0.95597


Do you know what this means? How would you interpret this value?


no


I don't


Okay, our slope is the amount that y changes when we increase x right?


yes


If I have y = 2x, for the every 1 increase in x, my y will increase by 2 right?


Here, my x values represent the Old Property Value

y values represent New Property Value right?


So, it is the same thing here,

For every 1 thousand dollar increase in Old Property value, the estimated New Property Value increases by 0.95597 thousand dollars right?


is x the 1 thousand dollar


Yes, and our slope represents the y value increase


so the 0.95597 is the y here


Yes, exactly


Do you see why choice D is correct?


So choice D is not the appropriate description of the sample


No, choice D is appropriate.


Oh yes sorry


Option A was the one that isn't appropriate right?


Yes, why is choice D valid though?


Recall, what does the slope tell us?


it tells is the amount that y changes when we increase x


Also if at any point you want some more clarification on anything, please let me know.

Especially for a class like AP Stats, it's very concept based.


Great, so what does the slope being 0.95597 tell us in this situation regarding the property values


It tells us that for every 1 thousand dollar increase in Old Property  value the new property value increases by 0.95597


0.95597 thousand right?


yes


So, it's saying for every $1000 increase, the new property value will increase $955.97


Which is exactly what choice D is saying


Yes so it's an  appropriate  description of the data in the sample


Yes, would you like to go over the other answer choices or just do the next question?


I kinda don't understand option E


But I get the rest


Okay, another thing you will need from this computer output is the S in the bottom left corner.


This S is the standard deviation of the residuals.


Which basically means, how far did the observed values differ from the expected values.


Because the line of best fit lets us predict values right?


what's the line of best fit


The line of best fit, is the line that represents all the points together


Look at the graph, the line of best fit is drawn there for you


oh ok I see


In the question, they took a sample of 25 properties right


Each dot point on the graph represents on of the properties that they took data from


So, right after getting this data


They put it all on one graph


And now, they wanted to know,

How could I guess the approximate value of something at this point?


Which they do, by finding the line of best fit, which REPRESENTS all of the points ALTOGETHER


So, now if I want to estimate how much my y value is at a certain x value


I can just use this line of best fit


For example, If I want to estimate the y value at x=50 on this line of best fit


I can just find the y value on the line


Just to make sure, do you want any clarification on that? This isn't exactly too big and is more of just a deeper understanding thing


Is that line called the least square regression line


I think I get it


Yes, that is another name for it


But, now recall


Initially we only took a sample of data right?


yes


So, if I draw this line


Some of the ACTUAL data that I got from my sample will probably not be EXACTLY on the line right?


Because my line is an estimation of all the points altogether, which means not all of them fall directly on it.


So, my standard deviation of the residuals tells me on average, approximately, how far was the data I GOT from the value I can ESTIMATE it to be using my line of best fit


Ok


So, here our standard deviation is 7.53867 right?


It is saying on average, the new property values they DOCUMENTED FROM THE SAMPLE were about $7,539 from what the line of best fit told them it would be.


Ok it makes much more sense now thanks


Alright, is there any question of the entire practice test you really wanted to look over, in case we aren't able to do all of it?


Yes the FRQs


Alright, whenever you are ready, you can put it up


It has part c d and e too


First, what did the newspaper claim about the number of semesters and starting salary?


The newspaper claims that the more semesters needed to complete an academic program the greater the starting salary of the first year  job will be


So, in simple terms, as semesters increased, starting salary did too right?


So, what does the graph show us?


The graph shows us a positive linear relationship ?


Could you draw directly on the graph, what you think the line of best fit looks like


Exactly! So there is a positive linear relationship, and based on the data points as the number of semesters increased the starting salary increased right?


ye


This was something you picked up on immediately basically with the line of best fit.


The line goes up and tells us how they relate


So, we say the scatterplot does support the newspaper's claim.
Why?


The scatter plot supports the newspapers claim because the data shows a positive association between the two variables


Perfect! You actually got it right on.


This is another really important thing about the AP Stats curriculum, in the explanations it is mainly vocabulary based, because you have use the right statistical words in your answer.

Here you just had to talk about there being a positive association.


However, one thing, is you should ALWAYS put thing into context


Never say anything like "between the two variables."


ok


You will lose a point for this on some questions in the FRQ, and you likely have or will see the FRQ rubric, but losing a SINGLE FRQ point is crucial because of how they grade.


So, here, you would say "between the number of semesters and starting salary."


what does a perfect answer would look like then


The scatter plot supports the newspapers claim because the data shows a positive association between the number of semesters and starting salary.


On the rubric, they will literally have a bullet point that say "Student explained in the proper context" for these explanation questions


Though your teacher may or may not be extremely strict about it, this is something that is on the AP exam, so just always know to do this for FRQ questions in this class


Ok  thanks I actually had no idea about the rubric and  how the AP exam works since this is the first AP class ive ever taken


But I will try to pay attention to those details


Yes, sometimes they will occasionally say to explain it in the context, but sometimes they won't but they still expect you to.


For part b, what is the slope?


Great, I just realized too, notice it says to explain in context, you will definitely lose a point here if you don't use the right language.


So, going back to how we interpreted the slope before, how would you interpret the slope here?


Remember, follow the basis "As x increase by 1, y increase by this."
But you have to explain using the words from the situation


The slope is 1.1594, for every additional semester needed to complete an academic program the starting salary is expected to increase


Almost, you want to include the numbers in there as well.


So, you'd want to say something like

The slope is 1.1594. For every additional semester needed to complete an academic program the starting salary is expected to increase 1.1594 thousand dollars.


would it be thousand dollars or euros


Euros, I didn't read the actual scale, you're right though


These are very slight nitpicks, but this skill of interpretation is EXTREMELY important for the exam.


Do we have to say what the slope is at the start of our sentence


You just have to identify somewhere in your answer, since it tells you to identify it.


ok


But, you already did, but when it tells you to interpret slope, you HAVE TO say

"the y value is expected to increase"

"the y value increased on average by"

you CANNOT SAY "the y value will increase by"


Remember, the line of best fit is an ESTIMATE of the y value. It DOES NOT TELL us the y value we ACTUALLY documented from our sample.
It tells us the EXPECTED VALUE


okk


Very annoyingly, if you accidentally forget to include that one part about the slope they will also take a point off on the exam, because it is technically wrong


If you'd like to do the other parts, you could put those up too now.


I think my teacher took my points off because of a few small mistakes like that in my last test


Where can I put it the board is full


Yes, it's because a lot of the things in AP stats do not DEFINITIVELY tell you something, so you always have to be explicit with your language because the numbers you get in this class tell you one specific thing, not about everything


I'm going to get rid of question 2 is that alright?


Since, it's so similar to the FRQ


yes


Alright, what on the graph is it telling you to focus on here?


What group of people?


people who have business majors ?


Exactly! Could you circle on the graph where those points are?


Great, so what the association between those points look like?


Remember to use proper context and sentence structure


The lesser the number of semesters the higher the starting salary..?


Yes, but to put it in clearer terms, first, could you draw the approximate line of best fit for the business majors


would it be like that


Exactly, just draw something that looks like it represents all the points.


But now we can see, as they took more semesters, their starting salary decreased right?


And remember, association is about how closely the points are to each other.


So are they very close or very far?


very close


And the line of best fit is aimed downwards,

So, we can say, there is a strong negative association between them right?


Now, try framing this in the context of the problem for full credit


Remember, you need vocabulary + context.

Here your vocabulary is just to mention association, its direction, its strength.

And the context is the situation being asked about


There is a  strong negative  association between starting salary and number of semesters for the business major


Great!


direction  is about whether its positive or negative right


Yes, that all I meant by it


Now, for part d, what is the median of a data set?


I actually dont know


That's alright! The median is just the middle number of a data set.


So if I give you a data set like,

1, 2, 2, 3, 4


What number is in the middle?


Great, so 2 is the median of the data set.


If I give you a data set like

1, 2, 3, 4, 5, 8


There is no middle number so right?


yeah


But, 3 and 4 are in the middle together, so instead we just add them together and divide by two


So (3+4)/2 will be 3.5


Which is our median for that data set.


You don't really need to know that for this question, but you just need to know, the median is the middle number.


ok


Great! I was actually just about to tell you to do that


So, this question is quite simple isn't it?


yes


Clearly, the Chemistry one is higher than the physics one, and the business one is lower than physics


Getting this question right is all about vocabulary and context


For vocabulary, always remember, if it tells you to compare some values, ALWAYS use comparative language. You have to EXPLICITLY use words like "greater than," "less than," "equal to."


Ok, so for the answer do we just say which median is higher for which major  or is there supposed to be numbers


You just say which is higher than which.


You can't really calculate the numbers exactly, since you just have a graph.


I was confused because when we were going over  this in class today my teacher had values for the median for each major


Perhaps your teacher guessed a random value. Here we could approximate the median though.


Let's look at the graph then, if you're teacher probably approximated it


The median will be the middle number right?


How many chemistry data points are there?


So, let's think if I give you a set of 8 numbers
1, 2, 3, 4, 5, 6, 7, 8


To find the median, you have to average the 4th and 5th largest values right?


You would add (4+5)/2, which is equal to 4.5


So, here what data points look like they have the 4th and 5th highest base salary


that one?


Remember, we have 8 data points, so we need to find the 4th AND 5th largest


So we should have two points in mind, not just one


those two ?


Great, so the median will be the average of those two points right?


yes


And it looks like it is going to be about 55,000 euros


Which is probably how your teacher did it.


But, although this skill of figuring out data from a graph is kinda important, we don't need it for this question.


Just say, this median is higher than this, and this one is lower than this, and this one is in between.


ok


So, try to frame your answer for full credit here.


At least, on the AP exam, you would never need exact values like this, perhaps if your teacher taught it this way, maybe she specifically wants to see you approximate it.


Business majors have the lowest median followed by physics major  and chemistry being the one with the highest.


Ok


would it be something like this


Yes, that would likely get full credit, the hardest thing about a question like this honestly is trying to make it sound decent.

But, if you are ever low on time, just know, you don't need to write in proper English to get full points.


Well you do need proper English, I mean you don't need to make it sound nice by trying to not use the same exact words and using "and" a lot of times


Ok I will try to keep that in mind thanks!


Now for part e, what did the newspaper report say initally?


Look at the initial graph, do you remember what the line of best fit you drew for it looked like?


If not, go back to the original graph and graph the approximate line of best fit


Great! Do you see how different these graphs are when they present their data.


Is it that basically the more number of semesters that you take the more starting salary you will have


Exactly, this first graph makes you think taking more semesters led to a higher starting salary right?


Yes


For e I have like a hard time understanding what the question is asking me just by reading it


It's basically saying,

"What's wrong with the newspaper's claim?" And it wants you to explain the data more accurately.


Do you see how it's asking you to do that?


ye


Alright, now look at your second graph


For each major, draw a line of best fit


If you want as well, there should be a shape icon on the bottom of the whiteboard where you could just put a straight line on the graph


Oh I see I didn't know that


Thanks


But, can you immediately see how different these graphs are?


Now, our line of best fit is saying the exact opposite is it not?


They are all saying as you take more semesters, the starting salary actually decreases.


But, what made it look like it increased?


yes


was it looking at the whole data together


Exactly, but what did we split the data into?


3 majors


Exactly!


And after splitting the data, we can see that actually


All the data points from the original graph that made the most money were Chemistry majors


All the data points from the original graph that made the least money were business majors


But, without categorizing them by major, we couldn't tell them apart, and it looked like as you took more semesters you had a higher starting salary.


Because clearly, based on the second, more detailed graph, the more semesters you take, the less your starting salary.

The thing that increased your starting salary the most, was the major you were in right>?


So, what could you say about the number of semesters and starting salary?

(Include something about how major affects starting salary)


Also, I understand this is a lot probably, the analysis question of the FRQs is always the hardest because you have to put it all together,

So, if there is something you want to go over, let me know


The newspaper report should be modified to account majors, since overall the majors that tend to take a long time to complete have higher starting salaries


I don't know if that makes sense or answers the question


I'm gonna be honest, I would have written an extremely long response to this and I thought you had it wrong, but it seems like you summarized it all perfectly.


However, I think you could get full credit for that response, because it does answer everything, but I would just elaborate and call back to the data that they gave you


Actually wait, not necessarily.


Make sure you do call back explicitly to the graph.


By explaining all 3 majors, business, chemistry, and Physics, all showed that as the number of semesters taken increased in their major, their starting salary decreased.


would I include that in my answer


oh ook I see


i'll take note for that part


Yes, for the analysis question try to always explain your answer, this question is intended to be the hardest because it wants you to show you are thorough and fully understand


Then you'd mention how the major in general led to a higher starting salary.


For these analysis questions, they want to see a deep, thorough analysis, so when going through your answer, just think to yourself,
"Did I give a thorough analysis"


okk


I will combine all that and include it in my answer for this part of the question


Yes, it would be a pretty long response, but that is exactly what they expect for this question.


ok


Do you perhaps have time for one more question this one is on the shorter side


But overall, this FRQ question is really simple actually isn't it? Maybe except part E.

In part A you just had to look at the graph and see that as the x value increased, the y value did too

In part B, you just had to read the number from the graph and talk about it

In part C, you had to isolate each major and look and see, in this group, did y increase or decrease as x increased?

In part D, you just had to compare three numbers where you could easily determine which was bigger or smaller

In part E, you had to combine all the concepts together and think about the situation in a realistic standard.

The majority of the difficulty in this FRQ was the writing and getting full points for each response though, otherwise, the curriculum knowledge needed is really standard.


Yes, we could definitely do one more question.


Ok thank u so much


I would likely have to go after as I have a lot of homework in some other AP classes


I'm going to remove question 1 to make room, is that alright>?


yes


Whenever you are ready, you can put it up


Okay, here you want to make sure you have a ruler


What is the equation for the line of best fit


Did you approximate that line?


I don't know how to do that


As in, did you just look at the points and guess what the line would look like?


oh ye


Here, you have to do it differently as it actually tells you he equation for the line of best fit


What is the equation for the line of best fit here?


So, our equation is y = 35.1 + 0.427x


Could you plug in two values from the graph here and give me two
x,y coordinates


What two values would I use


Any value you see on the x-axis, you can plug into the equation


Then take another value from the x-axis and plug it into the equation


You maybe want to use a calculator for this


ok


can I use 50


Ye, it just needs to be on the x-axis


So we have the coordinate (50, 56.45)


Now we need a second coordinate to help us draw our line


would whatever coordinate u used be y and what u got from the equation be x


Actually, it would be the other way around. Remember, in an equation, you plug in an x value and the equation will return you a y value


ohh ok


so if there is an equation with the question do you automatically find the x and  y coordinates


Did you use another coordinate to help you draw that line?


Say I want you to graph a line right


I can find two coordinate from the line


Say, I find them and they are there and there right?


Now, to graph my line


I can just draw a line through them both


so I should find two coordinates before drawing my line


yes


And plot them somewhere on your graph


Then, when you are taking your exam on paper probably, you can use a ruler to draw a straight line through them both


would that work


Yes, now you would have to plot that point on the graph


I have absolutely no idea how you just drew a perfect line like that on the whiteboard


But you would do exactly that on paper


I was literally just about to type "it's probably gonna be hard to draw a perfect line through those points on here but it'll be easier on paper"


Anyways, that is exactly how you graph this line


Ye


So that would be it for drawing the least squares regression line


Yes, you just need to find two points and draw a straight line through them


For this question that was the only part I was confused about for part b and c it was pretty easy


Unfortunately, I understand this is an FRQ, but this session has been going on for really long... and I have a lot of homework due tonight.


Yes that was the last part


Thank you so much for your time


I really appreciate it


I learned a lot and will definitely use those tips


That sounds great! I hope our session helped out, most of AP Stats is concept based so don't get too caught by actual number knowledge, because it's mainly just knowing what's happening in the situation.

Make sure to include proper vocabulary and context in your FRQ responses as well, especially for this unit.


I will most definitely do that thanks again!!


Have a great rest of your day


Goodbye!


hello


hi


problems, now please


I need help on my homework


there


Which problems


can you do 26 questions with me 5-30


are you able to


I'll see what I can do


ok


number 5


subtract 9.18 from 20


You keep the decimal point in line


since there a 4 decimal places


No there are 2


that's what I learned today


by my teacher


or is that just in sales tax


No your teacher is wrong


this problem has 2 decimals


can we go on to the next probelm


oh


ya


For number 6, divide 288 by 16


so 18?


yes


ok next


question 6 actually


its


Number 7 Number 7


were on question 6


it's 18


oh nevermind


hold up


ok


I gave you the next few answers


um I did it


For number 10, a prime number is a number that is only divisible by itself and 1


you got everything?


can you show work again for 8


reallyy quick


up


press Ctrl z


rlq


oh its 5


just making sure


ok so I did the work and is it d?


#11? Yes


yesss


Want me to explain


wait was it wrong


No, I want to explain it to you


oh ok


go over this for a few minutes


I'm getting water


ok


The kitchen


Let's continue


that's 11


That's actually #12


i mean 12


its right?


Im sure


Yessir


number 13


I'm sure it's 56


got that to


15 is is 90


no


B) 45


oh ok


got it


let me read 18


read it


is that 80.90


is that = 80.90


oh yeah it is


oh


ok


hold on


alright


hello


hey


number 19 is


first part is 0.09 second part is $0.90


right?


eys


yes


perfect


is the reciprocal 3/2


number 21


divide both sides by 7


can you show the equation


pls


can you do it with me


oh ok


number 22


let me read it


I read it


I got 6.15


ya I see it


got it


got that


next question


hello


oh sorry


its alright


is that a +


oh ya


number 27 is 0


oh


wait is 26 6 1/2


yes


ok


alright 28 is 1/2 right


two more


number 29 is 36


now last one


lets right the equation


down together


lets do 30 now


How should we go about this?


ooh I'm kinda confused


can you help


maybe


Ohh


we got this


you got this


wooo


that's the final answe


r


Yay!!


wait can you check two questions I did by myself rlq


hurr y up cos I gotta sleep


that's it


just see rlq


you don't have to do the problem


for 1 is it 20% for to is it 0.69 cents


which one?


number 1 20%


number2 0.69 cents


is it right


written plractice? #1 is 16


no homework


those two


1 and two


#1 and #2


Yeah, #1 is 16


For #2, Im putting it on the board


#2 is 68 cents


ok well good night to you


bye


Hi Leo! My name is Ava. What can I help with today? :)


the picture on the graph


Can you enlarge the picture, please?


I did


Okay! How do you think we should start?


I don't understand it


Can you put the picture back please?


do you see the picture


No, I do not.


do you see the picture now


Yes!


ok


So the two triangles would be related by a postulate or theorem, correct?


yes


So we have one angle that is congruent. There are also two different sides that are congruent to the same side on the other triangle.


What postulate or theorem would this be?


I think theo0


think theorem


Which theorem?


Like SAS, SSS, SSA?


would it be sss


Good try! But there is a congruent angle in between the two sides! Which theorem would it be then?


SSA


would it be SSA?


Give me one moment.


Good try! But it's actually SAS!


The angle is in between the two congruent sides, so it's SAS!


Okay okay I get it


Do you need help with anything else? :)


I need help on this one


Okay! Try using the knowledge I gave you with the last problem to try to figure it out!


k


What postulate or theorem are you thinking it is?


The angle is in between the two congruent sides so...


Leo?


Hi


Happy Friday!


Happy friday


So what help do you need


I need help determining if a point goes through the origin


Hello?


That depends. What's the full problem


The expression y=5x


That's it?


And y=3x


That’s the equations


In that case, yes, it's more than safe to say that both lines go through the origin. Want an explanation?


Yes how?


I can’t tell


Okay, so the slope of a line is y=mx+b. A line goes through the origin if it has a b-value of 0.


What’s b?


It's the y-intercept.


You can also determine this by substituting the origin's coordinates (0, 0) into the original equation. If equation fits, then the line passes through the origin.


What’s m and x


m=slope
x=x-coordinate


Ok


Well in the original equation, y=3x = 9 and y=10x equals 10


That doesn’t make sense


Wait what


Or does the equation have to follow a logical path?


I tried solving the equation and I got 9


And 10


You gave me y=3x, right?


Yes


Well then it should go through the origin. The only way y=9, is if x=3.


Check the board


Oh


The problem says 3 pizzas and the number of pizzas is 32


Yeah, the Gonzalez family's graph would be represented by y=8x


because 24 divided by 3 equally is 8


8x3=24 so it is proportional


ye


And 10x3=30 slices


So it is proportional


Yes!


Hey, are you there? Cause if not, I'll end our session


Bye


Emily


hey


And how are you doing today, Emily?


I’m doing good , and you ?


Thank you


That's very kind


And do you have some maths homework, geometry homework for us to do today.


you’re welcome!


yes , geometry is kicking my butt !!😭😭😭


You'll be OK


we’re working on translate right now and special right triangle ,45-45-90 and 30-60-90


Working on translating


yeah, vectors, translation of vectors


and special right-angled triangles


Amazing


Yep


Good. Can you draw us a right-angle triangle, please, on the board.


sure!


You can use the shapes button to help you.


Can you see my triangle


ok!


I'm going to adjust my triangle.


so


yes!


it looks like a right-angled one.


Then I got to rotate it so it sits.


on the base


Can you try that as well for me? Use your shakes to to help you out with this. neat drawing.


Have you found the triangle button?


ok


Good


yes


i’m on my phone


OK. We'll take that as a good example of a right angle triangle. Could you put a little square in the corner where the right angle is.


Yes, they're lovely


And have you got a ruler with you?


no 😭


Ah, that's all right.


So I'd like you to use the


grid lines to help you work out the distances.


So


make a triangle


using the shapes


menu for me


Can you click on the Shapes menu?


That's it


And then rotate your triangle.


Yeah, you have to try and adjust the lengths


using the handles when you select it, you should see some dots that will help you.


what sort of triangle have you got at the moment, Emily?


Is it a right-angled or an acute angle?


Are there any right angles in your triangle at the moment?


it’s kinda hard


It's kind of hard. I, I understand.


sorta😭😭


So we'll use my one then as an example for now.


my green triangle


ok!


and will use some


axis as well to help us out? Do you know about the Y axis and the X axis.


I forgot 😭


That's OK


I do not like math 😭😭


So the X axis is horizontal one. Can you see after all you?


an X and a Y axis at the moment.


And along the x-axis,


we have a certain side, we can call them, yeah, but certain letters if you want. So of course at the crossover point we have what's known as the origin.


of the graph.


Let's put that in. That's normally.


00 mark, where the two axes cross over.


That's the origin. And then we can call the other two corners.


A


corner A and corner B.


Can you label your triangle as well, somehow?


Put letter O at the corner at the right-angled corner.


and A and B on the other two corners.


ok


Yeah, so the right angle corner is the one with that little square that I've put in on the green triangle. Put an Oix so that little square.


Yeah, and then put


A and B opposite


on the long side


both ?


Yeah, you need to put, yeah, 3 corners in for your triangle. The corner O


which is the right angle corner.


and the other two corners you can label A and B.


That's it


And put in the third corner, call it letter O.


Like I've done on my triangle.


That's good. So we have got


33 sides, and the three sides are what sides? Side


OA


Can you tell me the other two


This side OB and they form


the right angle


And of course, opposite the right angle corner we have side


What do we have? Side.


A B


OK


I'll be back in about half an hour, Emily. So do look out for me when I come back online.


can we do with the letters like 4 on the hypotenuse and find the short side


and practice measuring your sides, cause my sides measure


phhh


ok


9.5 on this side.


9.5 units, and the same on the other side, 9.5 units. So I've got a right, a right angle isosceles triangle here.


because it's got two equal sides.


Hi


Hello


How can I help?


this is Emily mom


I have her math assignment that I need you to have her read and answer 15 questions herself please


if she does not get it right please correct and explain


Okay, no problem.


I need to convert the pdf to picture


as you do not support pdf right?


No, we do not.


Can you take a screenshot or type the question?


i will


one sec please


Take your time :)


i shared you 15 questions


please have her do her own


thanks


lets me know when you want me turn on the audio


plesae tell her do not use calculator


Sounds good.


Let's start with the first question.


Hello?


Hello.


Oh, I'll make this to me. I can't hear you.


Can you turn on the button right of you?


um.


Sorry, my mic doesn't work.


she does not know how to type keyboard


we can try a different tutor sorry


Oh


Is there uh then


oh.


then and go and like bingo are big boy.


to


That's okay, feel feel to speak. I will answer using the chat.


sorry we can try a different tutor


as she will need to get explain too


i gotta leave the room


Alright, have a nice day.


thank you for your time


No problem. Good luck :)


Hi!


Hello! nice to meet you


What are we working on today?


So I am currently studying/practicing by doing problems that I've already done on homework but doing them again with different numbers but same format for some extra practice I made it into a pdf so I can see how the problem is solved in case i forget etc


ok sounds great! is there a way you can screen share or take a screen shot of the questions and share that?


sure


your work looks perfect!


Yeah but im saying


I did the homework with how to solve it some written by a past coach to use for practice


But I want the problem rewritten with different numbers but same format, does that make sense?


yes that make sense let me come up with a quick problem.


kk


Is that the kind of problem you wanted?


yes im writing on paper rn


well il solve on board first


this/


can you circle your answer?Im sorry I cant tell which numbers you set as your final answer.


hi there, I'm Alex I can help you with your math!


Hello I need to study for my algebra final


great! I can help you with that! Do you have questions that we can work though?


I will try to upload my study guide


That would be perfect! Feel free to ask any questions you may have:)


I'm sorry but I'm having very much trouble understanding almost everything that's in the packet. So I'm gonna need thorough help and I will be paying attention very well.


I would also appreciate it if we went step by step.


And if you don't mind turning your camera on so I can understand it more, feel free, but if you don't feel comfortable, that's totally fine.


Sounds good! lets start from the beginning! I'm in a quiet spot so I can't turn on my camera :(


It looks like formulas are going to be really important for this!


Yes, and my teacher did make us, um.


make flashcards for the formula, so I do have them in flash cards. If you would just give me a second to go get them. I can go get them.


Thats great!


yes, we will need to start with the formula for circumference if you can find it :)


Will you have access to the formulas for the final, or do they need to be memorized?


Memorized


to the circumference formula is


pi times diameter


2 times pi times R


or it's 2 pi times are.


thats correct! so can you identify which parts of the first problem will be used for this?


We'd have to figure out that diameter first to multiply it by


pi


That is one good way of doing it:) remember that there are two formulas that you can use, in this case since you already have radius it might be easier to use 2*pi*r


so multiply 2 times pi and then multiply that by 9.


Thats right!!!


times 9


yess!!!


If it was 5652, where would we put the decimal?


Would it still be between 56 and 60.


Oh wait.


between 56 and 60


or would it be between


5 and 6


ahh i see what your saying, you can think of it as 628*9 and then you have to divide 628 by 100 to get the correct answer, basically move the decimal 2 spots


Oh, I see, but what the ending answer Stoy.


5,652 inches.


not quite, if you move it two places, you would get 56.52 :)


great work with the label!!


Well, when you move the


decimal two spots


from 6.28, then there would be no decimal.


sorry, I might have confused you, when you got 5652, that is from multiplying 628*9 which is 100 times bigger than 6.28*9 so 5,652.0   move the decimal twice to get 56.52


sorry if this is confusing by typing


Oh, so it was twice forward, not backwards.


Exactly!!!!


you can think of it as dividing is making the number smaller


We can work on #2.


Formula for area of a circle is pi times R


ooo this is a good problem


yes! great work with the formula


So we have to figure out the area based on the diameter.


yes!!!


remember that the formula for area usually requires the radius, so it will be helpful to quickly convert that


So we have to figure out the area first, for I meant the radius.


yes! do you remember how to convert between them?


no i am sorry


no worries, I'm going to try to find a good picture quick


I think this helps see that the radius is 1/2 the diameter and the diameter is 2 times the radius


yes


Do you have any questions about getting the radius?


can you just go step by step with me


Yeah, I can help get you started, I want to make sure you know what the steps are:)


So radius equals 4.


and then 4 times 4 is 16, so the area 16.


Wait, but we'd still have to do something with pie, right?


16 times 3.14 is.


c square.


I think you might have made a mistake in that multiplication, we can work through it if you need


Yes, please. Thank you.


Oh, I forgot to put the 2 on top of the 1 and I was multiplying.


so you understand it from here?


So the answer would then be 50.24 cm squared.


The weird thing about me is


it's kind of sad because my teachers won't be able to do this in the finals, but


my mind doesn't work like that because I feel like someone needs to lay it out for me and then I go on from there, but I need to learn how to do it all myself.


Can I do number 3 by myself.


and then when I'm done, maybe you could, we could go over it together and see what I did, write what I did wrong, what I didn't understand, and what I could do better on.


yes, you will need to know for the final, but working through these problems is a great way of learning!


Of course, that is a great idea


diameter is


I think it's


well, radius is half of that diameter


and diameter is


from the right side to the left side of the shape and radius is the middle of the shape to the right side of the shape.


yesss!!! great work:)


Formula for trapezoid is base times height


um or base one plus base 2 times height.


the only thing that I will add is that the radius does not have to be to the right of the circle, but it can be to any point


Oh, OK, thank you


Oh, I see. But


would it be the same thing like if there was point A and point.


D, and they were all the way across equally from the shape, would that then be the diameter


yes, as long as it is all of the way across, like the furthest distance, I will try to draw it the best I can


for example, the black line is diameter that goes through the center, while the red line is not because it does not pass through the center


do you have any questions?


Oh, I see


I'm having a little trouble understanding the fourth question.


ahh I see, that one can be a little tricky because of the way that it is worded.


Drawing the picture will help, ill try to import a picture


Is the image in red a trapezoid?


Yes!!


I believe the definition is exactly one set of parallel lines


So what we do both of the bases, add them together, then multiply them by 3 because the the


the formula for a trapezoid is


base times height, but then you would do basic


plus base 2 times the height.


I think that you were very close, but remember the strategy is to add the bases together and divide by 2


it might be helpful to think of that as turning the shape into a rectangle of sorts


Why would we divide by 2.


Is it because there


bases


two bases.


so if you look at just the part that I put into parentheses, what it is essentially doing is making the bases the same length so that we can use the A=b*h formula. Sorry if this is confusing to read


What do you mean make the two bases the same? Like how would we do that?


They're different numbers. They can both be divided by 2, but how would that make them the same number.


my picture of it is very bad, but adding and dividing by two gives an average length of the sides, so you can think of it as taking the extra from the bottom and transforming it to the top that turns it into a parallellagram


So we're taking 2 from 6


wait


I'm so sorry. I don't really understand.


okay, don't worry!!!!


lets try a different strategy that might make it make more sense


ok


we normally think of a trapezoid like the one in the red, but we can also write it like the teal version, and think of it as a rectangle and a square


xfcxfxxxxxxxxx


Oh, sorry, I did not mean to do that.


sorry rectangle and triangle


are you familiar with area of rectangles and triangles?


Yes, area of triangle is base times height divided by 2, and area of rectangle is the length times width.


PERFECT!!!!!!!


Does my diagram make sense, or would you like me to explain it further?


How did you get the 2?


on the left, we know that the whole base is equal to six, and the top base is equal to 4. So when we turn it into a rectangle, we know that side must equal 4 (because it needs to be equal to its opposite side) and the remaining length is 2


Oh, so you split it up


yes!!! that way we can find the area of the rectangle and the triangle, and then we can add them together


Um, if we were to do, um, 3 times 2 divided by


2, it would just go back to 3. So with the triangle be 3?


yes!!!!!


And then for the rectangle, the formula is length times width, so


would we just do 3 times


which is 12


perfect :)


and then dont forget to add them together!


3 + 12 is 15.


If the question, question 4 doesn't give a unit, um, so


Great work!!!


and if it's area, then I would put unit squared, but I don't know what the unit is


to me if I'm wrong, I don't see any unit.


that usually depends on the teacher, my teachers always wanted me to just put units squared in that case


OK, thank you


Number 5


This one looks pretty difficult.


in my opinion


Oh, and there's two parts.


So in this case, would the scale be diameter or radius?


yes, I think that part a will actually help us with part b


this is separate from radius and diameter though


Oh


So what it means scale, it's kind of confusing to me because I don't know what formula to use, so, and that's where we start with, and that's what's confusing to me like what formula do I use because I don't really have


like the information that I would use, like find the radius or find the diameter or the circumference.


this one doesnt really start with a formula, it is a way of using a ratio to find distance


so its saying that one inch on the map is 45 miles in real life


Isn't a ratio just like a fraction.


yes!!!! that is the best way to solve them is to write it as a fraction


So underlined and red would be 145th of a mile.


45/1ths or 1/45ths


oh, I see what you are asking


the ratio itself would be written as 1/45


And the 5.5 would not be a ratio, right?


But that can also be the confusing part for me, like there's one that's not a ratio and one that is a ratio slash.


um fraction.


nope, 5.5 is used for part b have you used ratio tables yet?


I don't think I'm familiar about ratio tables. Can you show me to refamiliarize myself if I or we have seen it before.


yes, it is just like using fractions, and its really the only way I know how to teach this unfortunately


Im happy to walk you through this one!


Thank you


Okay, I did this upside down, but it doesn't really matter in the end. Using the ratio table, it is all multiplication of fractions left to right, but it is really useful to to be able to cross out the labels to make sure that we are doing it correctly


What numbers did you multiply cause I'm pretty sure 45 times 5.5 is.


you are correct, it is multiplying 45 and 5.5, but I think you made a mistake in the multiplication. Sorry, I just used my calculator


Oh, I actually did aition instead of multiplication.


ahh no worries, just remember that ratio tables always use multiplication


it is 247.5 iam so sorry


no worries :)


So does the end answer of Part A equal


miles


yes!! we can tell because the inches crossed out (because they were divided by themselves) and miles was the label that was left


knowing how this works, do you know the answer to part a


I'm sorry, but I don't really understand what


you just said. Can you rephrase it in a different way? I'm sorry.


Oh, and so they total answer would not be 24, 7.5 miles.


no worries! thanks for letting me know


the answer is 247.5 so in this case it is like dividing inches/inches so like any other number, when you divide by itself you get 1


I am so sorry. I just accidentally deleted the picture, reloaded it, so nothing on there was


well, I think before that was on there is now on there, but I have it on my paper. So


yeah, but we're on part of the problem.


okay thats good!


Sorry, I meant, can we work on part B now.


oh sorry, the ratio table and the 247.5 answer was for part b


So then what would the


answer for part AB because I don't think I caught that.


part a is a written response, just analyzing what 1inch:45miles means


So I would just say it means


um


do you understand? It is hard for me to say more without giving the answer


1 45th.


kind of!! that is another way or writing it.


I think of it as meaning that one inch on the map means 45 miles in real life


Oh, I see. Well, that's all for my first page, um, I really appreciate all your help


to, yeah, all your help with me and


you really pushed me to


learn more things and understand what I didn't understand before. Thank you so much.


No problem, good luck on the final!! you got this!!


Hellooo


hiiiii


What do you need help with today?


I need help with my math homework


Okayyy, do you have any examples ?


would you like me to put it up on the bored?


yeah of course


can you see it?


yup


alright what do you think your first step would be for number 7?


or a guess anything is fine


[ don't the steps may we start from scratch


yeah of course no problem


okay ty


so for 7 , you would 430/500


think about 500 being 100% and the part inside that percentage


430/500 will be the answer


does that make sense?


a little yeah


if you want i can go more into depth


yes pls


alright so ima make a drawing of this


okay


alright so the whole circle 500 voters


imagine we take a big slice of it


that slice being 430 voters


and we want to figure out how what is the percentage we took out


a percentage is a same thing as fraction. we can relate this chart to a simpler chart like this one:


so notice that we have 3 slices colored out of the 4 slices


which represents the fraction 3/4


its the same thing for our other chart


i dont see your drawing


scroll down


sorry


now you see it?


no


okay im going to try just explaining in text then


ok


okay how about this do you see my image?


alright then, well what im trying to describe is the reason we 430/500 voters is because a fraction is the same as percentage


you know how 50/100 is 50%


yes


or 30/100 is 30%


same applies 430/500, you plug it into a calculator it is 86%


does that make more sense?


alright ready for the next one?


this time ima try to focus more on how they did it on the paper


what number would be the "part"?


close that would be the percentage


since it has a percent sign next to it


so 40


yup yup


because 40 is "part" of the whole


so now you have 40=5% times "whole


okay can you explain that part


like how i got that or how to solve it


oh nvm i get it


okok


so what do i need to do to get the whole? we have 40=5%*whole and want whole by itself, so how can i get rid of that 5% next to "whole"?


can you explain?


of course🙏, so when we have number multplied by a variable in this case "whole" we do the opposite of multiplication which is?


division


yuppp, and in an equation we do it on both sides of it so our left side is part, and our right side is 5%*"whole". The reason we are dividing is because we dont want 5% next to "whole"


so now that we know to divide


what do i divide the equation by?hint is the number next to whole


yupp, this is the cool part, the 5% next to "whole" will just cancel out because 5%/5% equals 1


so now we have 5%*part=whole


oh wait sorry


r equals whole by the way i just noted that from the homework problem


oh okay you reedy to do the next one


yupp


okay can you see it


yup


problem number 9 is pretty similar to number 7, you want to try to do that one?


yeah but can you help me


of course just shoot me a question if you get stuck


ok


Hello?


sorry ive got the rest of it thank you for the help have a good night


Oh its okay of course, good night!


Hi Alex, I'm Ben how can I help?


Hello, I am currently doing some SAT review questions and was wondering if you would be able to check/let me know whether I am doing correctly or not.


Sounds good, I see you've solved 14


Correct.


Yep, looks good


and now you're working on 17?


Yes,


Yep, nice job sticking with it!


Not quite


DE and GH gives us SSA


which does not prove congruence


or similarity


similarity needs SAS, or AA


Ben, so for similarity, we need either: AA, SSS, or SAS


oh yeah SSS too


OK, let me redo this


it might help to make the triangles a little bigger to see the angles


Yep!


I didn't check the calculator portion but the algebra is right


and if a is 12.25 that part is right


Correct!!


Yep 12.25 is right!


Do you have any other problems or is that all?


Just to confirm:
For proving similarity, it could be through~ AA(A), SAS, or SSS.
For proving congruence, it could be through~ SAS, SSS, AAS, or ASA. Correct?


OK


wait what are you doing now?


you found it


What do you mean?


it's asking for the height


what are you calculating now?


Okay, oops, I had calculated the area


Yeah lol all good


doing a little extra


this is a fun problem


Yep!


Nice


That one was a little simpler


Yes


how did you find B was 20 degrees?


oh wait


isosceles


super good


because the two sides are congruent, the opposite angles must be the same


Yeah did you do that in your head?


Yep


Want a tip for this one?


Nevermind lol


you got it


OK, let me skip number 5


yeah this one is just pythagorean


I didn't do the calculator stuff but I trust that's right


Yep!


Not quite


what if x was 1


oh wait are you crossing out or underlining d


I am canceling out D


nvm


keep going mb


I think you're overthinking this one a little bit


Yeah that's how i would do it


I'm sorry I have to go after this one


Good luck on the SAT :)


Sure,


Perfect!


See you, feel free to make another session with a different tutor


Bye!


hi


Hi Ben! How are you today?


Oh I'm great


And you


I'm doing good! :)


Shall we get started?


Can I write some problems on the board


Yes! Of course


oki


OK This is what I'm working on in class right now


Okay :)!


Is there anything in this problem that you can do on your own? It's okay if you don't!


I think so


I can try and solve it and you correct me in my errors


Mhm! Of course :D


done


i will brb


Okay! So far you did very well! Specifically on the exponents and the addition! One thing that got you that led to the wrong answer would be the division in the parentheses; would you like me to help you on that?


Okay!


Yeah


Looking at your work I'm happy to see that you know PEMDAS :D


But on the second step, labeled G, the first step to solving this problem is P for parentheses.


i do'


Hehe I'm happy :D


My teacher calls it gems because parentheses is basically groupings


Oh okay! I like that term for parentheses :o


Okay! so working on the grouping, inside it says 3 divided by 7


right


When dividing number where the second number can't fit into the other number in a whole number it's best to write it as a fraction!


I didn't know that


I will write it on the side for you!


Hehe, It's okay! I'm glad to be teaching you it now since division is difficult!


It really is


Let me write it on the bottom actually!


OK


Yes :(


Like that!


First number is the numerator, second number is the denominator!


OK I got that doesn't seem too complicated


Yay!! :DD


Okay! now that you know that, should we try the problem again?


hm, How about a different one if that is OK with you


Yes! Okay!


How is this


Similar to last time you made a tiny mistake on the grouping part, 3 divided by 6 should be 3/6! However, after that all of your work besides the mistake, you followed the PEMDAS method perfectly :D!!


Do you want to help you on the parentheses part?


Yippee!!!


Yay yay!!b:DD


OK to you I don't understand how to like add The Fraction entered a problem because I don't know how to add it in with the other stuff


You know what I'm saying


As in write the fraction in the equation?


No I understand how to do that I mean like how do I add it with the other stuff like add it to the problem


mix it in with the other equations


Oh yes! I can help you with that!


OK


If you have a calculator with you, we can simply turn the fraction into a decimal form!


I have one in my dresser I'll look at it see if it's not dead


Okay!


It's it's solar powered so it's kind of dead


If you calculator can't do it, I will teach you a different way then!


Awe! It's okay!


Let me see I have one on my phone


OK so how do I turn it into decimal on the calculator


Okay so in the problem we just did, input 3 divided by 6!


It's one half


or 0.5


Okay! Great!


By the way how long has this session been


So instead of writing it as a fraction make it 0.5!


Sorry I know it's off topic


It's okay don't worry!


We started around 7:19!


You Geometry 201


So it's almost been an hour


Oh yes!


oki lets continue this lesson'


Okay! So, whenever you see fraction thing try and see if you can put it into decimal format!


Yes!


However sometimes the decimal format might be very long, so would you like me to teach you what to do if that happens?


It's okay if you don't want too! :D


Yeah I'm up for anything as long as I get my math grades up


Okay!


Let me select a part from one of your problems!


okay


I wrote it on the bottom and added a 2 if that's okay!


Yeah that's OK


Firstly, we will start with the grouping!


Okay! to add the 2 with the 3/7 we want to make 2 to be in similar terms of 3/7. What I mean by this is to get 2 to have a denominator of 2!


ok


I will write it on the top since there isn't space!


okii


Okay! If you look up, I wrote the 2!


In math, below the 2 there is always an invisible /1 below it!


I will write this in pink!


oh yay


Okay, now that we have that we need to get to 7, we know that 1 times 7 will get us 7 :D!


oh yay :D


That makes a lot more sense


Yes! I will write what I do in teal!


Yes, okay! :DDD!!


OK look I'm really sorry I have to go though


for dinner


It's okay don't worry!


Please enjoy dinner!


I appreciate and thank you for helping me today


Have a good night


You're so very welcome!


Thank you hehe!


Great work :DD


OK bye bye


Bye bye!!


To finish off, with the 14/7 use that and add that with 3/7.


14/7 plus 3/7 is equal to 17/7


Keep denominators, add numerators!


Hello, what can I help you with today?


Good afternoon Elara


I need help understanding the interval notation


Okay sure, do you have a problem you are working on or would you like me just to explain it?


I have 2 problems


Okay sounds good


Okay so first should we look at the domain>


ok


So for interval notation do you know the differences between ( ) and [ ]


yes


() means that it isn't included and [] means it is included


Yes so for domain where does it start?


and is that number included or not


So the domain starts at -8 or -9 (can't tell from the numbers being squished) and its not included


Yes thats correct, i think its -8


Actually its -8 from looking at the lines


Yes, so would that be a ( or [


It would be a (


Exactly thats right so lets look at where it ends


So based on the function


it ends at 9


Yup, and what is the bracket for the endpoint


The bracket for the end point would be ] as its included


Yes great job, so now for domain we have (-8, 9]


Do you want to try the range?


Yea


so the range is the opposite as the domain correct?


Yes its y's


okay


so the range is (-3, 4) because they are the lowest and highest points on the Y axis


I think the lowest might be -4 but your highest is correct


But since 4 is included it should be ]


points on the line are included


oh


Does that make sense?


yea


Wait


so if the line crosses over the point its included?


Yes its more like since were in the middle of the line and theres no open/closed circle and no endpoint its included


Because its on that point


Did that help explain it?


yes


Ok great


Lets do increasing and decreasing now


ok


So for increasing we want to find the x values for when it increases up to a point


So where does it start to increase and is it included?


well it starts to increase at -5 which isn't included


Close i think it starts to increase at -8, where the line starts


Like from that point up to the peak it is going up right?


Based on how my teacher explains it


the interval of increase would be the next point on the x axis it increases


Yes that is right, but the main idea of increase and decrease is to look at the lines/points going left to right


so you start at the leftmost part of the line


ah


And so if we start at -8 we increase until what point?


positive 1


Yes and so what would our interval for increase look like?


(-8, 1) I think


Yes


So now were at 1 which is the peak


So we start from there to find the decreasing interval


Well I know this one


(1, 9)


Yes but 9 has a closed circle so it should be (1,9]


Great job though!


Just realized


Its okay


Now we have avg rate of change


So how do we find the rate of change?


So the formula for rate of change for the whole domain is: change y/ change in x


so the changes in x and y is (largest x - smallest x)


oh


Does that kinda make sense


so would we have to use the idea of finding the slope?


or is it different


Its kind of similar it depends on the graph


So for this one lets start with change of y values


ok


We can take the largest y - smallest y


What would these 2 values be?


4 - (-4)


Yes


so its realistically 8


Yup


Now for x's?


9 - (-8)


which is 17


So now we write it as change in y / change in x


So our form is = 8/17


so this is our avg rate of change?


Alright


that seems easy


Yes you got it


so


what if its a graph?


For avg rate of change?


Or are we looking at the table now


Well I put a new equation


its the table


Ok lets see


Sorry one second I was looking at my work and i think we messed up one part for the avg rate of change


which was?


For the y values we take the y values at each of the endpoints not the peak and min value


oh


So for the max y it would be the y at the closed dot


and the min y would be at the open dot


Sorry for this


wait so you mean that its supposed to be


-1 - (-4)


Yes it think its -2 -(-4) though


Ah


So then its 2/17


our x's were right


Does this make sense?


yes


Okay then lets look at the table question


So its the same idea for domain and range, except we do a set of values


Have you learn how to write that with { }


Actually no


but I assume its the same as regular brackets


Yes pretty much, but for this problem does it say to use interval notation?


Well it doesn't say


but I think it wants you to do so


Alright then, i think we can just write it as a list because it doesn't make sense to do interval notation


Because we don't know if the endpoints are included or not if that makes sense


well doesn't matter then


So for listing the domain and ranges of tables you can just do { all x values } and same for range and y


guess we could say they are all included since they are all listed


Yes


well using the same knowledge


the domain is {-2, 7}


With the sets you usually have to write all the numbers in between, so it will be kind of long


oh


Yes but its pretty straight forward so x is like {-2,-1,0,1,2,3,4,5,6,7}


and we can just do the same for the range


You don't have to type it on here though since its a lot of numbers


Just let me know if you have any questions with those t


alright so on paper you would have to write all of them out or no?


Yes write them all out


If your teachers instructions are different though then i would follow what that is


ok


But for this problem it doesn't specify anything different


So let me know when we should move on to increase and decrease


we can move on now


Okay


So same thing lets look at the x values to find the increase and decrease


well


that means


actually wait a sec


the y axis and the x axis are confusing me


Yes so lets look at it point by point, because since all the x's are increasing the y's change


So for -2 -> -1 it goes from 10 to 7 and it keeps decreasing for a couple more points


what x value does the y stop decreasing


at x value 2


Yes


and it becomes a constant


So we can say it decrease from x= -2 to x=2 or just -2 to 2


alright


Now after that where does it start to increase


at x value 5


then 6


Yes up to 7 right?


yes


and i think we should include (4,2) in this because at this point it increase to (5,12)


so how can we write it with just the x's


Well lets include up to the max x because its still increasing


well from what I see


it actually slightly decreases


Yes at what point


Yeah so right now we have it dec from -2 to 2 then inc from 4 to what


after that point it dec again


well wouldn't there be 3 intervals of increase


Wait let me see again


it dec from -2 to 1 then again at 6 to 7, and it inc from 4 to 6


ok


but then at 1 to 2 i think it increases again right?


Sorry I keep confusing myself


its fine


At point (1,-3) it goes to (2,2) so it increases there aswell


So inc you can write it as the points or just the x values, what do you prefer?


Ok wait


there is only 2 intervals of increase actually


Yes i think so


-2,2 and 4,6


Thats for decrease actually


wait a sec


since technically it finishes decreasing there


Yes


Sorry lets just write each one, one at a time


So decreasing


-2 to 1 and 6 to 7


does that seem right?


yes


Okay so increasing


1 to 2 and 4 to 6


That one too?


Alright, did this all make sense i know its kind of confusing


constant is 2,4


Yup


so now its just the average rate of change


Yes and it says only from 0<x<6


So its the same formula we use, change in y / change in x


alr


so this would be


13 - (-3)


it is <6 so we should use 12 i think


because that would be at 7


So 12 - (-3) right?


Now for the x's


I just realized that I said 13 instead of 14


anywho


Its fine


5 - (-2) I think


since its less than 6


they said for the x values between 0 and 6, 0<x<6


So everthing in between


oh


5 - 1


Good


So what do we have now?


calculating


Alright


or 3.76


Yes looks good to me


I think its fine to keep it as whatever


Did everything make sense for this?


yes


thank you for your time Elara


it really helped me better understand


Yea no problem, have a wonderful rest of your day!


Great job today!


Thanks!


Hi Leo


hello how are you


I'm well, thanks. How are you doing?


I am doing well


i have more related rates problems


OK. I have about 30 minutes this morning.


ok i will be quick


i am posting a problem


I'm reading...


Are you able to upload the figure mentioned in the problem?


I see it. Are we starting with question (a) asking for the volume V ?


yes


The first step is to find the relationship between "r" and "h". Can you do it?


is this fora


a


bc don't i just have to plg in 5


You'll need to plug in 5, but we don't know the value of "r" yet. That's why we need the relationship. Hint: use similar triangles.


Do you see the similar triangles?


They are similar because all the angles are the same in both triangles. Therefore, the ratios of their side lengths are all the same.


OK so far?


Now that we have the relationship: r = (5/10)*h = h/2, we can take the formula for the volume V and replace r with h/2.


is that right


Correct. That's the answer for (a).


For (b), replace "r" with "h/2" in the formula for "V", then differentiate with respect to "t". Can you do it?


i think so


Not quite correct. I'll show you on the board.


ok


Can you differentiate the expression I wrote in blue with respect to "t" ?


As a rule, it's good to simplify an expression *before* you differentiate, as I did.


Now it's correct.


Plug in the values of h and dh/dt, and that will answer question (b).


Your answer is correct, but they may want an "exact" answer, -15π/8 after simplification.


We can move on to (c). Can you write the expression for the surface area of water, as a function of "h" ?


Hint: the water surface is a circle of radius "r".


is there a formula for that


surface area of water


I'll write it on the board.


I have only 5 minutes. I'll show you the last step.


OK so far?


yes


I'm showing the constant of propoertionality in pink color.


is that the answer


Yes. dV/dt = constant * A, so it's directly propoertional. And the constant is dh/dt = -3/10.


yes it makes sense thanks for your help


You're welcome. Enjoy your day.


hello what do you need help in


hi i need help with exploring similar triangles and slope


ok, do have a example problem


oh and also dilation sorry


ok so should i explain the topic or a problem


the topic then a problem


ok


two triangles similar if they have the same shape, through proporitnate sides or 2 same angles


does the diagram help?


there are 3 ways to check similarty


AA, if two angles are the same


SSS, if all sides are proporntate


SAS, if two sides are proprtiante and include an angle


Slope


right


Slope is rise over run, which is y sub 2- y sub 1 over x sub 2 - y sub 1


it tells how steep a line is


if the slope is - then it will go down


if not it will go up


slope of 0 is a horiziaontal line


undifined is vertical line


so it will go down not up ?


I am sorry if it is unclear, if the slope is - it will go downwards, if it is postitive it will go up


ok i understand


good


Dialation is resizing a shape either bigger or smaller with chagning the shape of the shap if you get me


Scale factors tells you how big or small it gets


scale factor of 2 doubles the sides


scale factor of 0.5 cuts the sides in half


it is related to similar triangles


do you understand


yes sorry im just taking notes


ok cool


so basically, to sum it all up dilation is a transformation that changes the size of a figure but not its shape and slope is a measure of how steep a line is right


i am not sure if AA SSS SAS will be covered in 9th grade


yes


i have not heard my techers say that so i don't know


ok you can ask your teacher later to confrim


i can give you problems now if you want


only two though because i have to join my other session


Triangle ABC has sides 3, 4, 5 and Triangle DEF has sides 6,8,10 are they similar i will draw the diagram if you want to more speficy the sides


i will do it quickly


Slope question


Find the slope of the line that passes through the points (2,5) and (6,13) the x values are 6 and 2 and the y values are 13 and 5


ok


i make a dialtion question that you can work on later


A triangle has sides 4, 6, and 8 which are dialted by a scale factor of 1.5. what are the new side lentghs of the triangle?


tell me the answers after your done


for the first question i said yes because i used the sss method and all the corresponding sides have the same ratio which is 1/2


so it isn't because in the diagram more spefecily, 3 coressponds to 6 which is 1/2 so u are right for that, but 5 coressponds to 8 not 10, and 5/8 is not 1/2 and 4 corresspodsn with 10 making it 2/5 which is alos not 1/2. This is because the angle helps determine the corresspsoded angles.


oh ok


but you can use SSS to prove that aren't similar, so you were on the right track


ok im working on the second question


cool


the second one is 2 i think


nice you got it right!


yes!


ok and the new side lengths for the last one is 6,9 and 12 i know this because the scale factor is 1.5 so i multiplied 4 by 1.5 and got 6 i did 6 by 1.5 and got 9 i did 8 by 1.5 and got 12 so thats the new lengths


correct!


Is it time for the other session?


yes


ok goodbye and have a good weekend.


ok see ya! and you have a good weekend, i had a very good time and you did a great job teaching me


nice


thank you


the math festival!!


bye!


I am getting notifications from a student, are you the person?


I can help if its you.


no its not me


ok sorry


its ok i might need help later


ok


hi Ben


are you here?


yes!


how are you? ill post my question on the board now


I'm fine. Thanks for asking. How are you?


not too bad myself!


hmmm, this requires some thought


did u want me to seek another tutor?


I'm having a hard time seeing that shape as a single quadratic function


oh, wait


it's not quadratic


there are exponents to be found


yeahhhh


and a polynomial can have n-2 inflection points, where n is the degree of the polynomial


so the degree is 3


how many inflection points do you see?


I think that makes the degree 4


hmmm


it has to be in this format


4th degree, and 4-2 inflection points


yeah it looks like 2 or 3 hills its hard to tell


and the function has the same value for x=110 and x=200


yeah thats the baseline


also since at (110,80) the line crosses the mutliplicity is odd


which we could just say one


r u there


function is convex opening down until (170, 100), then convex opening up until (200, 80), then convex opening down again after that


2 inflection points


ok


so 2 extrema which makes a degree 3


can't be degree 3. end behavior is the same at both ends


ok so what degree would it be


plug 1 for x 2 for y to find a


wait


for (200,80) it bounces so it would be an exponent of 3


not 2


so exponents 1 and 3?


yeah


do u know the odd and even multiplicity rule


no


oh ok


can you solve for a im gonna put this in my notes rq


something's not right


i'm getting a to be a small, positive number


it has to be negative


hmm


lets leave it a fraction


i tihnk thats what my class would want


but a has to be negative for the function to open downward


where did you get,00 i got 81,000


still not negative


20/1620,000 is 1/81,000


oh, right, it's 20, not 2


haha


lets just put a negative symbol its fine


so now we can write this out


now we have to find the max height


how do we do that?


let me figure that out


kk


the "simple" answer involves taking a derivative. this is pre-calculus. have you covered derivatives?


hmm no i havent


let me see if there is another way


ok


the only other thing I'm finding is to use a graphing calculator


I don't coach calculus, but I know how to take a simple derivative.


should we try that?


yeah


lets graph it


also, I think our 80 is wrong, since we had to make a negative


no, still 80


Michael


the derivative of (x-b)^n is n(x-b)^n-1


derivative of a constant is 0


I keep wanting it to be 810,000, LOL


LOLL


ur good  🤣🤣


whats after this


sorry, that much is not right


oh


Ugly!!!!


we would have to expand that out and find the roots


oh boyyy!!


let me search one more time


kk!!!


WAIT


sorry, everything I'm seeing is either set the derivative = 0 or use graphing calculator.


what idea did you get?


my teacher informed us that for the maximum point we're actually using the graphing calculator for that and we're gonna round the decimal whatever we get for the y value


i just looked back at my teachers notes LOL


like I said, derivative = 0 or graphing calculator


yeah


sooo how would we put this in a graphing calculator


make sure you put in 81,000, 20,000, LOL


OKAY


Back in my day, we were still using slide rules, not calculators


I can use a scientific calculator, but never used a graphing calculator. can't help you there


put in the equation or the 3 points, I guess


its sad and unfortunate that i have to learn through calculators and not do the work myself


ok let me try


it is


even for exams they let us use a ti84 calculator which is literally like a smart phone you get the answers by just putting in the equation


i got.3 for the max height


sounds about right


ok


Michael, can you stay for one more question? if not I understand


I can only help you get started


Michael


I would start with graphing calculator


what will you look for to see if roller coaster goes below ground?


hmmm


i would look for where it crosses the x axis?


yeah


that will give you the decimal approximation


the exact value requires that you find the exact root


the only way I can think of for that is to guess at a root, and use synthetic division


im putting it in graph calculator now


look


can u see


we only look at 140 feet


are you sure you got the equation in correctly?


let me check


it doesnt go under it seems like


silly to ask you where it crosses x-axis when it never crosses


yeahhh


frrr


and wouldnt 140 be the relative maximum


you can estimate where it crosses at around 137 ft and 150 ft, and point out that neither of them is between 140 and 160


(140, 40) is the relative maximum


how about relative min?


are you still here?


ok


yes my bad


min?


yeah


the min would (170,0


I've got to go now


thanks for ALL your help!!!
take care


yw. bye


hi Jamie


Hello!


i needed help checking my answers!


looks good, but I think you should label 1, 2 and 3


okis!


do you think those labels are correct?


yes


did you draw those graphs, or somebody else did?


i used desmos


and i did


#1 has two roots. which curve crosses the x-axis twice?


so 3 should be labeled 1, right?


ohhh I'm sorry i did the backwards and yes it should be labeled 1


3 doesn't even touch the x-axis. which graph should that be?


yeah


that leaves 2, with one root. it touches the x-axis, but doesn't cross it


doesn't that make more sense?


yes it does


do you have time for 9 questions?


depends on how long it takes


we'll see how far we get


okay so im all good for this question right?


correct


yayy


6 correct


problem 6


I'm doing 7 now


ohhhh


7 is also correct


funny that they used the plural "What are the x-coordinates"


correct answer, though, (singular)


looking at the next one


lol yayy ok I think like 4 more are left


I don't remember what quadratic regression is. I'll have to look it up.


i used like the a+b+c thing


I don't know that, either. why don't you show me your work on the board?


umm it might take a long time but ill have to re write it


nvm


I found a quadratic regression calculator online


it gave me: y = 2x2 + 3x + 1.9993


that's 2x^2


so a=2


yay but lol I did all that work, I could've done it on a calculator


I think it is actually 2x^2+3x+2


oh


still a=2


oh okk


I found an equation for the parabola. (4, 4) is not on it


hmmm, I don't think any of the points is on that parabola I found


hmm


did you find an equation for the parabola?


no i jdid  2 + 2, 1 + 3


i just*


but graphing gave me (4, 4)


yeah, 2 to the left of vertex and 2 to the right have the same y


so  (4, 4)


yaa


yay*


Question 2 is correct


okayy


that one is also correct


yayy that was the last one


we got through all of them!


yayy thank you so much for your help thank you for helping me understand!


yw


bye


byee


Hi


Hello


Um


so I just need a


like help on


reviewing for a test tomorrow.


and you can't use a calculator.


So, uh, I just have like.


I think like 4 problems to go over.


Oh yeah, this is the first one. It says find X and Y.


Hello?


Yeah wait please


Wait please


I need a new board


Ok!


I dont know how to clear the board


Can you do this for me


Yeah thanks


Do you get it


hi


wdy need help with td?


can I put it up on the board?


yep


ok so first we see paranthesis and thats our first step to do distribtuibe property and multiply -6 by (-6c+8)


i think i accidently erased the photo...


Im mostly confused about where the signs go and what goes in the final expression. I understand the concept of keeping the sign with the number but I am making a mistake somewhere in the process


ok try working that out what i wrote out


ok ur close but remember its -6 times -6c


so -6 times -6 which is 36 since negatives cancel out so you have 36c


but can't you only combine like terms


when given distirbutive property and its multiplication like this, inorder to actually combine (add or substract) you have to get rid of the parenthesis and use multiplication


so now when we combine like terms we only combine the terms that have the same variable so -8c and 36c


and we also combine the whole numbers: 7-6-48


but If you have just a normal number, Can you multiply it by a number with a term


ohh


ok


so like 5 and 5c can be multiplied to get 25c


thats just an example


ya it makes more sense noe


now


oh ok good


so whats ur final asnwer


c


-8+36 would be 28


cuz remember like a number line


yep I did not see the negative sign


ok yeah and then dont forget to combine your whole numbers: 7-6-48 bc thats part of the final asnwer


why is it - 48 and not +48


-6(-6c+8) right and then -6 times positive 8


oh


would just be -48, negatives dont cancel since there is only one negative


ya


so final answer would be -47+28c


you dont combine those two numbers since those arent like terms


that makes a lot more sense


but wasnt the 8 8c


no bc in the equation in the pic we see 7 - 8c -6 so -8c not 8c


that is making sense


yep


ok I submitted it and it said it was wrong


what did you put


so now I have a new question


oh wait i realized my mistake im sorry nvm


i accidently put -6 in the final equation but that was already distributed sorry


sorry


its ok


can we try another


ok so i have to actually go study now im sorry but you can always find another tutor


that's ok


do you understand this better though even if i ot it wrong, sorrry again


yes


bye


Hi!


Hello! I got my test back, and I saw that the “R” means revise, so it’s partially correct. I’d like to know what my mistake was so I can fix it, and then I’d like to try a similar problem with different numbers for extra practice before I retake the test and redo those sections. I am currently on page 2 problem 4. Here’s the link to the PDF: https://example.com/document.pdf


okay iwill check it


kk!


could u plz wait me a moment? i need to change my classroom:(


Yes!


I hate school:(


Lol


so for the first one it's -3+5=2


No


I know that


I am on page 2 problm 4


oo sorry


its ok


is it bc i put 2 instead of 4


yes i think so


Hi do you know how to do proofs?


Hey


Yes go ahead


Especially parallel lines?


Hello, Leo. Can you hear me?


Yes


Um, OK, so.


uh, all right. Let's look at this question together. We give that line AB is parallel to CD and that angle one is concrete to angle too. What we need to do is prove that AD is parallel to BC.


So let's write with Leo, which is statement one


A, B, D, C, and let's write this first.


Wait what write what


of OK if you don't understand, we'll start from the first place, um, let's look at the question together. The question is we're given that line AB is parallel to CD, and that ankle one is concreent to angle II.


What we need to do is prove that AD is parallel to BC.


So luck you've written the statement one, and the reason is given. Now look at the diagram. since AB is parallel to CD, the angles that are


on opposite sides of a transversal are called alternate anterior ankles, that mean that 1 and 3 are alternate interior angles, so they must be they must be congruent.


So the statement too, let me write it for you.


Where did you write it?


And the reason for the first one is given for the 2nd statement, if finds the reason is if lines are parallel, alternate interior angles are congruent. OK, now we note that.


uh one equals 2 or 2 from that is given, and we've also found that the reason for the second statement, if angle I equals both of them, and then that's called the transversive property of concurrence, the soul statement 3.


Oh, would you like me to write a statement one for you?


Didn’t I already write statement 1


Um yeah, that's why what I'm saying, like you asked where do you write it?


Which one is angle 3


Uh, what, uh, which, what are you talking about? Where I was what?


Oh I see it now before I didn’t see it


But uh um I'm sorry if you uh if you have any questions, ask me or you haven't understood what I've I've been saying. If you want I can start over or I can just keep going from State 3.


Which angel is angel 3?


which angle is angle 3? OK, good question. So Ankle 3 is the one down here at the bottom right? It's a front line D and C meetss BC.


Let me point it out for you.


You see how line AB is parallel to a CD and Li B cuts across both of them that makes Ale I and angle 3 alternate interior angles. They're inside the two parallel lines, but on opposite sides of the transversal, so angle I as at the top right.


and Ankle 3 is directly below the um bottom right.


Think of it like this if you trace down from angle I along the line BC. The next angle you reach at the bottom is angle 3. That's how you remember which one it is.


Is angle 3 vertical angle of 2?