yes but for example on number 11 how is the y intercept (0,-24) how do we get -24?


just substitute x=0 in the equation given to you


whenever you want to find y-intercept, just sub x=0


ok


so no doubts here?


not when it comes to the y intercept


I get that part now


yeah, moving on to multiplicity


so multiplicity of a zero is the power of its factor in a polynomial


so say I have a zero x=1


the factor of that 0 would be (x-1)


so the multiplicity is the power of this factor in the expression of the polynomial


so i could have a polynomial which is (x-2)(x-1)^3


here the multiplicity of the zero 1 would be 3


and the multiplicity of the zero 2, would be 1


So if I gave you a polynomial (x-4)^2(x-6)^4(x+1)^7, what is the multiplicity of the zeros x=-1 and x=6?


i think i get it


try out the example i gave you


the multiplicity of -1 is 7 and the multiplicity of 6 is 4?


perfect


now that you've got this, you'll nail the cross and touch part, it's super easy


i think i get it now


it just says that if a multiplicity of a zero is even, then it wont cross the x-axis, it'll just touch and bounce off it


if it's odd, it will cross the x-axis


I read the little summary on the first page but i didnt understand before


now i do


excellent


in my example, can you tell me which zeros will cross and which zeros will touch?


in your example, 2 = t 4 = t 7 = c


what are the roots corresponding to those multiplicities?


Remember i asked the zeros not the multiplicitiesd


4 = t 6 = t -1 = c?


gr8 job


now an extra, what is the end behaviour here?


Im not sure


remember the cases we did, just find the leading coefficient and the degree


what's the degree of the polynomial


no, the factors are multiplied remember


yeah!


so to find the degree in such cases, take the degree of the factor, then multiply it with its power. Do this for all the factors and then add this up, that will give you the degree


now in this case, what's the leading coefficient?


if you're confused about the degree, leave it for now, we'll come back to it while discussing the example problems


ok


what would be the leading coefficient in this case?


the leading example.comt the factor, remember, the leading coefficient is the coefficient of the term with the highest power


alright let me give you a method to think, that way i think you'll understand both the degree and the leading coefficient


so say i were to multiply this entire polynomial out...obviously a tedious process and i'm not going to even try, but i can find the term with the highest power


in the factor (x+1)^7, if i were to expand this, we are sure that the highest power of x that i would get would be x^7 right?


and i know it's coefficient must be 1 (if you arent aware of it, don't worry, take it as a fact)


i was overcomplicating it


do you understand till here, just hear me out for a second, it might seem a bit confusing at first but it'll make sense at the end


do you understand the answer?


or should I keep explaining


I understand


alright so what's the degree and leading coefficient in my problem


the leading coefficient is 1 and the degree is 13?


perfect


so should we go over the example problems?


no, I think i understand.


Thank you so much for your help!!


you're welcome


i'll end the session now, bye


Hello! I'm new to the platform, so I wanna see how this works.


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


I just wan't to see how the site works for when I wan't to use it later


Cool! I can go over a problem with you if that's okay! What topics are you studying now in your math class?


Ok, I'll need a second to get it though.


Sure! Take your time! :)


sorry, I'm in class and I have to go.


But thanks for offering the help


Okay! You can come back anytime you need help! Have a great day, Leo! :)


Thank you, you too!


I will be ending the session shortly.


Hi


how can I help


Can you help me solve some equations


sure


do understand how to do them


No i dont


Can you talk


no i can't talk but this paper is very difficult to see


itss blurry


Ill try to do it by my own


hi


How are you doing?


good


Good, how can I help you today?


I need help with my math homework


Great! Can you put the question in the chat?


Ok what is the question asking?


Solve for x?


yes


But you didn’t put it equal to anything


Is that the whole question


Feel free to come back anytime, here to help you out


Hey Jamie


What can I help you with?


translating and stretch and compressing parent functions


Okay perfect, is there any assignment you have to do or do you just want to learn the concept?


i have a test on it tomorrow and idk how to do it lol


Ohh okay, give me a minute to try to explain this in the best way


alright


Okay, so these are the rules for transformations


Let's begin with the first two


Do you know and understand how they work?


yes. i just need help memorizing them


Okay so I don't really have any tricks to memorize, but the ones on the board are the ones that you should memorize


great


Do you want to try some practice questions?


sure


Okay, so for the question I wrote, what would happen to the function f(x)?


where the question u wrote


Do you see it?


Its below the table


oh yes


it would move up 4 units


Exactly!


What about for this one?


it would move down 8


Perfect!


It looks like you already know the up and down translations


Let's continue


What would happen here?


right 9


What about for this?


left 2


And you know the reflections, right?


i think


Ok we'll come back to it


vertical stretch


Yes


How about here?


vertical compression


Yup!


Here?


okay can you take away the chart though so i cant cheat anymore lol


Ohh okay lol


horizontal stretch


Yes!


no idea


lol


umm


right 2


Not quite. Remember that when somehting is being multiplied to the x inside the partenthis, something will be going on horizontally


so horizontal compression


reflect across x axis


Perfect


how do i tell the difference between vertical compression and stretch


For vertical stretch, it has to be greater than 1


ohh


And for vertical compression, it has to be between 0 and 1


And I'm talking about the absolute value of it


Does that make sense?


i think


What happens here?


reflect across x, left 9


Not left 9


Left 9 would look like f (x-9)


okay so then down nine?


No, the 9 is being multiplied to the f(x)


so then stretched horizontally


Not quite


compressed horizontally


What would happen here?


horizontal compression


No, if it were 2x) then it would be a horizontal compression


when something is being multiplied to only the x then it is horizontal


but the 3 is being multiples to the f(x)) and not just the x


so it is vertical


vertical stretch


Yes


So then back to this question


vertical compression


How?


no idea


Don't take a guess when you answer, make sure you know why


What happens here?


Okay now?


Not quite.


how


im so lost


what is it then


No worries at all. Let's look back at the table


See how it says |a|


That means absolute value


bruh


Which means if we take the -3 and put it as "a", we get |-3|


So what is |-3|


Perfect!


so its a vertical stretch


Exactly!


AND since there is the negative, it is a reflection over the x-axis


Does that make sense?


ya


Okay


What happens here?


vertical stretch


And?


reflect across x


Exactly


What about here?


horizontal compression


Perfect, and?


reflect across y


It looks like you know the transformations pretty well now, do you want to do more practice or do you think you're ready for your test


ill be fine


Okay then


Bye Jamie!


bye thanks


Hi!


hello Alex!


How can I help you today?


i need help with my homework


Absolutely you can post it on the board


im screen sharing if thats fine


Yep i think this works too


perfect!


ill restart so you can get a better understanding of what i know so far


Alright sounds good


Oh wait don't submit it yet


Can you see my chat while you're on the page?


yea sorry


alright


im not sure how find the equation for this


You can solve it in a lot of different ways but I would say the easiest approach here would be finding slope and y-intercept


Did you learn the slope formula?


yea


its like y2 - y1 / x2 - x1 right


yep exactly


which means you need to find two separate points to use that equation


so first pick two points


and give me their coordinates


like the 2 points marked?


doesn't really matter


nice one more?


Cool


Can you derive a slope from those two?


so


yeap


so -2/2


which is -1


that's the slope


i see


and you need one more info to determine the equation for that line


which is y intercept


Can you find it based on the graph?


Exactly


so you combine those two


and the equation is: y = -x + 4


it's always y = (slope)x + (y intercept)


I see


yep so now that you have the equation you can just plug in the given coordinates and see if any of them works


would it be -x+4 = 0


instead of just -x+4


y = -x + 4


you plug in the coordinates


so for example if you wanna try option 1 which is (5, 0)


oh i get it


0 = -5 + 4? I don't think so. So you rule out option 1


And so on


alright


Yep let me know if you have any other questions on the way


so for 0,4


how would i do that


plug in y = 4 and x = 0


so it woild look like 4=0+4


yes so that makes sense right


yea


that's the answer


alright so thats one of them


mhm and you can try the same thing with the other options


so 2,2 would be there too right


2 does = -2+4


yes correct


does -4 become positive 4


since its -x


yes it does


im confused


I though i did all of these right


nevermind i accidentally did 1+5 at the end


i apologize


no problem


i think ill do one more practice problem


just to make sure i have it down


yup go for it


can i use 1,1 for the first point here


yes definitely


it doesn't matter which point when you're coming up with the equation


oh


so it doesnt have to be on the line at all?


nono it still has to be on the line


but im saying as long as it's on the line you can pick whichever


can i use 2,2 aswell then


No because it's not on the line


But you can use 0, 2


Because it's on the line


so is it y=-x+2


sorry that took a minute i was distracted


yes you got it


no it's okay!


ok i get that part now thank you


with this one


do i just olug the x and y values into the equation


yep no problem


Mhm and you'll get the rest


For example you can plug in the y value and it'll give you the x value


and vice versa


x is 3 here right


and what do i do if i get a decimal for one


are you referring to x = 0?


then you either put fraction or decimal


It's pretty much up to you but it also depends on the system so try both


yea decimal doesnt work


then you can just put fraction


i have -4.5


yep so that's -9/2


im at 12-4y=18


do i just add 4 to all sides to isolate y


you subtract 12 from both sides


so -4y = 4


then divide by -4


yup


Hey Ben, I unfortunately might have to leave the session now. Would that be okay?


You can always ask other tutors for help


thats all good! I appreciate you helping me learn the concepts


Yep no problem. Have a good one


you aswell!


Thankss


Hey, need some math help?


yep


alright, wanna get it up on screen?


will do


ok there its on properties of exponets


okay, so this is testing exponent rules. do u wanna try it first or do you want me to explain how they work


can you explain


yeah


so first ill ask this


what does "4^2" mean


so not what does it equal, but what does it mean


thats what it equals


oh sry


im asking what does it mean


ur good


it means to multiply the number the the exponet number


well that would mean 4x2


but this is not that, because that would get us 8


no


its times by 2 times


4 x 4


4 times 4


yes


notice how i started with 4^2 * 4^3


and im shoring why the exponents add


does it make sense why?


ohh ok


because when u write it out


thats how many 4s there are


does this one make sense so far?


ok cause there is 3 4s and 2 4s


yupp good


now lets see why this one works


it would be


so the idea is


when u have an exponent with an exponent


they multiply


and thats why


i under stand that


so based on that, see if u can try that original one u drew, it would not be 4^3 tho


one sec


np


ok done


good!


we dwait


sorry


its close


but remember


first we had the exponents


0 and 3


we add them and get 3


then we have a 6


what do we do with the 3 and 6


ok so


x4to 18


wdym by 4^18?


so in the examples i drew for example


theres no x


and times 4 means times four maybe, but we dont normally just write "times 4"


ok


why


because that would mean we are multiplying something by 4^18


but what are multiplying by that?


theres nothing here to do that


for example, why isnt it plus? or minus? where did that x come from


it came from the problem


okay lets say i asked u


ah I understand'


2 times 3


u would say its 6


not x 6


say here


the times is just showing u whats happening between the values


u "used up" the plus as ur solving it


2+3 isnt = plus 5


its just 5


4^0 * 4^4 is 4^4 and not x^4


oh  okay that makes alot more sene


okay nice


and ur correct it becomes 18


so u mighve accidentally done 3+1


then done times 4


because u wrote 4^0 is 1


which is true, but doesnt help us here


okay


want another example?


no its okay i understand thanks


Og


hi Lena, what' up?


Algebra 2


Oh


Hi


ok, do you have a problem to work on?


Dividing polynomials


Yes


How do I send pictur


oh whar fun ;)


No not fun


I'm stupid


And have an F


dont see the picture yet


we'd better get you up to speed so you can improve your grade :)


I see it now


Ok yay


my teacher is too busy to help me


And I'm too slow


I'm not!


I only know the old way, so you might need to bear with me, should we work on 3)?


I only got one done but


I'm like 9th Grade math level


np. let me show you how to do 3)


I'll work below your post


Ok thank you


can you see what I wrote....I start by setting it up like any division problem....


Yes I can see


ok, so the 1st term we need to get rid of is the 7x^2, to get the 7x^2m we need to multiply by 7x....I'll show you


Does that cancel


like that, do you see what I did?


(x+4) * 7x = 7x^2 +28


Yes


ok, now we subtract   and you are right, we will get some cancellation


Okays


do you get what I did?


What is the purple by the 28 is that like a square root


no, I don't like to subtract so I changed 28x to -28x and added


Ohh


it helps me not make a mistake


Okay understandable


ok, now we need to get rid of the x term do that, we need to multiply x by -9


How


Oh


and look at this comes out nice and easy we are left with the answer is 7x-9


Okay is this corrct


should we try 4)?


Oops it's glitching


internet glitching?


ok yes


There's another ones above 4 but I had to crop it


do you want to write it out for me, or should we work on 4)?


Ok sure


not seeing it yet


Sorry it glitched bad


Yea it won't load


Hi Ben


Hi Chloe


How may I help you?


So the problem I need help understanding is finding the limits but using the conjugate or something lol i'm just confused right now


its a fraction but with a square root


Can you upload the problem on the board?


hold up let me try


like i think ik what to do but not at the same time


First off, if we plug in x=1, we get 0/0, correct?


yeah


We call the 0/0 form an "indeterminate form". Can you give me 3 minutes to solve, and then I'll explain?


okay


We can start. Did you learn what is the "conjugate" ?


If not, I'll explain.


the reciprocal of the square root, so it would be sqaure root x+8+3??


The numerator has the form: √a-b. The conjugate is √a+b. You flip the sign in front of one of the terms.


To solve the problem, we multiply top and bottom by the conjugate of the numerator.


I can show you the first step if you wish.


yes please


OK so far?


okay so i was like close i see i see, yeah i got that


Now we multiply top and bottom of the fraction by the conjugate. Can you do it?


umm wouldn't the top be 1 and then the bottom is (x-1)(sqrtx+8-3)?


Not exactly. I can show you the next step if you like.


I'll write to the right of the uploaded problem 4.


For the numerator, we have two parentheses to multiply. Did you learn the "FOIL" method?


i think so, but my teacher never called it the foil method


I can expand the numerator and write the first term.


Can you continue?


isn't the numerator x+8-9?


the sqrt cancelled out each other?


Correct. The numerator simplifies to x+8-9 = x-1.


What's the next step?


Good. You canceled out (x-1) top and bottom.


Notice that we no longer have 0/0. You can just plug in x=1.


thats rightttt


What limit do you get?


You're close. I'll show you.


i forgot the numerator


omg


i was there and not there at the same time


Anyway, I think you get the idea. When you multiply by the conjugate, the 0/0 (indeterminate) form disappears, and you just plug in x=1.


For problem 8, you can use the same method.


okok i think i got it


for problem 10 i have to factor the numerator right? and then for problem 6 what do i do??


Yes. For problem 10, you factor the numerator, and one of the factors will cancel out top and bottom. Then you plug in x=3.


For problem 6, can you give me 3 minutes to solve? I'll need to see what method to use.


okay


For problem 6, the first step is to add the two fractions in the numerator. Can you do it?


For example, if you have 1/a-1/b, the common denominator is a*b. And you get (b-a)/ab, etc.


You're on the right track. And don't forget the "x" in the original denominator.


Now you can simplify and plug in x=0.


Not quite. You plugged in x=0 too soon, before simplifying. I'll show you on the board.


Can you continue?


no i can't, I got confused why did you multiply the x from the denominator?


Look at the original expression for problem 6 in your upload. I circled the "x" in pink color.


i see


limit = -1/4 is correct. You got it.


i guess, but i'm still confused on why did the x get to the (2x+4)


from the original expression


I'll show more details on the board to explain.


ok


since the x was originally the denominator it just stayed there even after the fraction was being multiplied?


That's right. We can't forget the "x" in the denominator (pink color).


And the -x/x simplifies to -1.


I see, thats what i got confused on, cause it didn't make sense it was still part of the denominator for some reason but now i got it


Awesome!


okay thank you! this was very helpful


You're welcome. We can end the session. Have a good evening.


you too!


hello!


Hi Marcus


I need some help with this problem


OK. I'm reading the problem...


Which part of the problem do you need help with?


i have a set up already


i think my math is just wrong


let me write it out


The integral is correctly set up.


is this correct?


I'll show you on the board.


ok


The coefficient in front of cos(2x) should be 1/2 and not 2.


why?


If you differentiate (1/2)cos(2x), do you get -sin(2x) ?


yea


I'll write on the board to explain.


In other words, ∫-sin(2x)dx = (1/2)cos(2x) and not 2cos(2x).


ok i see


got it


i got 1/4 for the first integral


OK. I'll check your answer...


1/4 is correct for the first integral.


ok great!


Did you want to do the second integral?


yes


im doing it right now


i got -5/4


Not exactly.


The area has to be positive.


is this correct?


Correct so far.


is it this?


Now it's correct. The second integral is 1/4.


All that's left is to add the two integrals to find the total area.


so 1/8


1/4+1/4 = ?


Correct.


thanks :))


I have one more


i don't really know how to approach it


I'm reading...


First, which graph(s) shows the correct line for y = 8x ?


We can proceed by elimination.


3rd one


Good. Any other?


4th one too


OK. So we can eliminate options (a) and (b).


Now let's look for y=x/8.


Do options (c) and (d) have the correct line for y=x/8 ?


c does


Yes, and (d) does too. Now look for y=2/x.


Between (c) and (d), which one has y=2/x ?


it's d


Correct.


The next step is to locate the two points of intersection, circled in red and green. Can you find them?


sure


like the x-values?


1/2 and 4


Correct. We only need the x-values. Can you set up the integral(s) for the area?


ok


It's better to use parentheses, as I'm showing, to avoid confusion later in your calculations.


The two integrals are correctly set up.


is this correct?


No. I


I'll explain on the board.


so 1/16 x^2


Yes. Now it's correct.


Looks good. Can you simplify?


It's correct, but it can be simplified further.


2 (ln(4-1/2))


Using the property of logarithms: ln(a) - ln(b) = ln(a/b).


Correct. You can also write it as 2(ln(8)) = 2*ln(2^3) = 2*(3*ln(2)) = 6*ln(2).


i see


thanks so much for the help!


You're welcome. Enjoy the rest of your day.


have a nice day :))


Hello!


Hey!


How has your day been?


My day has been good what about yours?


Im glad to hear that! mines was good aswell


should I put the problem on the board?


Yes!


alright, it will be sloppy because I'm on a cromebook


That's alright!


this is the first question


I just wanted to make sure my answer was correct but I don't know if it is


Did you write your answer down/


I just did this:


Sarah all I did


Does the rule have to be a sentence or numbers?


numbers


Yes, its right!


oh ok!


give me a second to write the other one


its related to this one


Take your time!


thank yiou


ok I done


Do you have any idea what this answer could be?


no :(


oh wait


maybe \


letme see


I can't believe I didn't see that XD


Yes, I thought you'd get it!


I'm looking at my paper and I'm trying gto see if I can do it without help


Yes, good job. I'm always here to support!


ok thank you :D


No problem!


I will write it


Alright!


okay I wrote it


Do you wanna try to solve it or for me to?


u too please


I already did the math in my head


oh


is it 30?


Yes, its 30!


ok! yay


I wrote it


Yes, I'm solving it


ok


I Math 205!


how would you solve it


I don't get it :/


Well, I created a formal for it once I recognized the pattern!


can u show me how


olease


please


I used this formula!


oh ok


It's just recognizing patterns


I'm not that good at formulas :'D


It's okay and it definitely takes practice!


yes


You'll get the hang of ittt


yeaa


one second I'll be right back


Sounds good!


Me too also!


alright I'm back


Me too!


so I was thinking and this is my best guess


get ready for disappointment!


lol


There is not a drawing for figure N right?


no it just says that


I'm thinking there might not be any squares in figure N


how come?


Because they're using the original equation and when asking to check if the rule works for n=1 and up, I'm guessing that the number has to start at 0


oh iok


Then by checking the rule, we can see that the number is still coherent


what does that mean


coherent


That it's the same


And that the rule still applies


oh okk


I am slightly confused on wording for that question to be honest but I can't think of another answer


Same


0 makes the most sense if we're checking the rule starting at 1 so it's most likely not after 1 if that makes sense


that makes more sense


well thank you for your help that is all I have for today!


I hope your day tomorrow is great! have a good night!]


You're welcome! Have a good rest of your night! :)


byeeeeeeeee


Byee


Hello


my thing connect out


Yes thats okay


ok


So as I was saying,

Anything to the power of zero is actually 1


It is a given rule


So 2^0 is 1


Then 6^1? Do you know what it is?


ok 2x2=4


I dont see 2x2 anywhere


Do you know what 6^1 is?


No


That is 6^2


yes 6^1 is 6


Okay   do you see the drawing I made


yea


Oh ok you wrote it in


Alright what is a^2 times 1


Anything times one is itself


Hey are you there?


Okay


Do you know what a^2 times 1 is?


idk


right


A^2 times 1 is equal to itself


As I said previously


So it is equal to a^2


? No


It is a^2


oh yea a^2/6


2*1 = 2
3*1 = 3

Multiplying by 1 equals the same number


Yes that is it simplified


a^2 / 6


Is the correct answer


a^2/6 is the correct answer right


yes


Well done


ok thanks


Yeah


Is that it for today?


thanks


yea


Alright


I hope I was able to help you


Have a good night!


yea you were


you too


Hi How can I help you


Let me know what your question is


I have a test tomorrow and there are some concepts I am confused on


sure! Let me know what concepts


and then we can go over them


how to find the circumcenter from 3 coordinates?


ok


so first you have to find the midpoints


let me give you example


Do you know how to solve


I understand up to making the equations of the lines


ok so why dont you do that first for this


do what?


the equations for the lines


using the three points I gave


try to solve for the circumcenter using those three points?


yes


can you upload a picture of a graph for me to work on?


Oh on the whiteboard I gave you the points


so using midpoint formula


do you know what mid point formula us


is*


Okay so Using that formula, try to do that first


done


good


now find the slopes of those two lines


but for the slopes, you need to find the perpendicular slopes


so -1 = 1


and 1 = 1


understanding so far?


then use point slope form


and plug in the new slopes, and the points from the mid point formula


so you can solve that where I wrote it


on the white board


use point slope formula


wouldn't 1 go to -1 though?


oh yes that was my typo mistake


your correct


so now use the point slope formula


and find those equations


for bc and AB


let me know if you need help with that


I need help with thay


ok


so the point slope formula is:


y - y1 = m(x - x1)


where y-coordinate and x-coordinate are the points you found from the mid point


and m is the new slope


so Ill do BC for you


then you do AB okay?


And you should probably memorize this poin slope formula


point*


It is very important for your exam


very good so far!!


shouldn't you have done -1 for the slope?


nevermind


good


now to find the circumcenter


you have to use those two equations to find y and x


by combining them


do you know how to do that, any idea on how to maybe solve


I need help


Ok let me show you the set up


so lets find y first


to find y, we need to make all of the variables and numbers on the opposite side for BC


so y = 5/2 + 1(x-3/2)


understanding so far?


yes


ok then, you have to plug that y equation into AB


so it would look like:
 y = 5/2 + 1(x-3/2) - 3/2 = -1(x-3/2)


wait sorry


let me just write it for you


ok. let me know when you are done


yep I am done


so now you have to find x


do you think you can solve it


let me know


I can try


sure go ahead


is that the correct first step?


umm there might be an easier way to do it


can you go through what you would do?


ok


so I brought all like terms to one side


now do you think you can sole


solve*


remember 2/2  = 1


would x=1


yes very good


sorry I just wanted to make sure


but yes x = 1


now plug in x and find y


you can plug in x to any two equations AB or BC


let me know if you need help


does y=2?


yes


so the circumcenter is


undertsanding the steps?


How about you list out the steps to me


so I know you understand


should I try to solve a problem on my own


sure okay


will you make one or should I do one from my review


oh you should do one from your review


draw out the points on the whiteboard


so I can see


can you upload a picture of a graph to the board for me to work on


sure


ok. let me know once you have


here you go


ok


sorry just to confirm what are the points, its hard to see from the graph


so i can make sure your on the right track


(-2, 5), (5, 1), (-4, -5)


okay, thanks


you can continue solving


so -2 + 5 give 3 not - 7....


and 5 + -4 give 1 not 9...


oops


because midpoint formula is x + x and y + y


no worries!


good, you just need to find 2 midpoints


very good


now you can find the slopes


the perpendicular slopes


are those correct


now find the perpendicular of those slopes


yep, just need to find the perpendicular slopes!


I thought those are the perpendicular


perpendicular slopes are the opposite reciprocal


so 7/4 = -4/7


I thought I already did the negative reciprocals


hmmm


so


let me see..


ohhh okay I see what you mean


sorry I did it a little differenlty


your correct


you can continue with the point slope form


oh wait


check -9/4 again


im getting -9/6


I redid it and got that


ok good


you can continue


very good!!!


now solve for y by combining two euqations


can you remind me how to do that


so y = all of the variables on one side


do that for the first equation


yes


now plug in that y into the second equation


yes very good!!!


now solve for x


you may have to distrubute first


then solve


like 7/4x


and all


thats an easy way to solve


I would recomment keeping them fractions


to make it easer for the future


good!


if its easier for you to solve on a piece of paper do you want to do that


and then let me know the answer


I'm fine on whiteboard?


ok


whatever works for you


very good


how did you get 19/8


oh never mind


i got it


you can continue


very good!!!


that is correct


x = -1/2


now you can plug that into the previous equation(whichever one) and find y


let me know if you understand


(-1/2, -2)?


y is not -2


try again


(-0.5, 3.5)


y is not 3.5


try one more time


(-1/2, -1/2)


yes


good job!!


I hope you remember all of the steps


and practice more!


do you understand everything now


let me know!


ok


one sec


sure!


everything makes sense. thanks for all of the help today


thats great!


good luck on your exam!


Bye!


thank you


bye


Hello How are you?


good just a little stressed


Well I will try to help


determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.


OK I see it. WHat is the question


II seee


I must look in the chat


Sorry'


my test will be on wednsday since school is cancelled monday


OK pls wait while I copy text form chat


so I might be here for a while asking for help


Ok well I have almsot 2 hours.


At  8 PM Eastern I must stop


is that for every tutor?


My wife says no math or physics from 8 PM to ( PM lol


9 PM


OH no each tutor si diferent


oh okay well lets start !


I have gone fo my than three hours, but not lately


its currently 5:14 for me


OK


OK 6:14 for me


what do you think about thsi question?


confusing


well what would u do to 5/4 to get 5 ?


not sure


OK well there are several things but suppose you multiply it by 4 what do u get?


I dont know how to start


i know we have to use change of y over change of x


OK that try that


then*


how


maybe start a 0


to aviad fraction


from x = 0 to x -1 what is the change in x ?


I mean from x = 0 to x = 1


im sorry I just dont know


OK


Pls wait while I getr my iPad then I can easily wreite


That will take about 2 minures OK?


okay


I am back


must enable iPad and stylus pls wait


okay no problem


I will start after a questin


Do u have a defintion for the slope of a line?


yes f(x+1)/f(x)


that is a good start


suppose we have to points ((x1, y1)) and (x2,y2) how would you get ther slope?


two*


not sure what youre talking about


OK I will write on baord Pls watch


see the red and blu marks I put on the figure?


yes


isnt slope y2-y1/x2-x1


Yes that is it


so do i do that


Now using the secion I makred what are x1 and y1?


Yes pls


useing the section I marked


is x 0


good


ok let me do that


and what is y?


good OK pls calc slope


is it 15


ok


Now I will put mare marks


Now use the "pink" and green pari OK?


pair*


do i do the same thing


Yes thie time x1 is 1 and x2 is 2 OK?


ok yes


is it 60


yes


and that does not equl 15 so we do not have a linear realtion


Do you see why?


because it not constant?


Yes the slope is not constant and that sio required for a line OK


Now the x's are equally spaced  do u agree?


yeah it shouldve been 30 if it was constant right


noyt exactly the slope shoul dhave been 15 again


oh okay


ok so how i check for exponential


OK now let us look at the jsut they's (but remember that the x's are equally spced)


do you see the blue mark?


ok what is 20/5


Good


good


sotty


haha


now at the next point, what is 80/20?


I disagree


yes good


I will add mark


whoops


see the orange amrk?


yes


what number/80?


how do you know what numbers to divide


i am jsut using pairs from the h(x) column


oh ok


so for the orange what number/80?


and the top what do you think (5/4)/5 is ?


oop


I mean 5/(5/4)


Yes do u see a pattern?


OK Now IF the x's are equally spaced (as they are here) we can sue this method and sicne the ratios are constant we then we have an exponential relation


use*


ok


now if the x's are not equally spaced, I think there is a formula that you might hvae but I do not remeber it


Also do u know how u have done this in ur class?


there are ways to use a calcultor


we used this formula f(x+1)/f(x)


OK


well that is exactly what we did!


excpet we used the symbol H instead of f becuase the question says H(x) see?


yes


that's the only formula i see in my notes i copied from class


Good


now the question asks us to find an exponential formula


to go with this


DO u have any notes about how to do that?


i think we have to do the rate of change


because we need to make it f(x)=Ca^x


yes that look good


Now I think we now know that C = 4


beased on our work so far


Do you see why?


what does c represent


sorry Not C


I mean a


OK I will write on board (I hope stylujs battery holds up)


Pls watch


do u see the "pink" it is I think the formual you gve?


m I correct?


yes


ok


now a is the ratio


and we found the ratio to be 4


so I will write in blue (I hope)


Now we must find C OK?


OK let me thinkl


OK I think easiest way is to make x = 0


do you know what 4^0 is?


4 or 1 idk


it is 1


any number (expcet 0) to the 0 power is one OK?


ok Now I will write


so H(0)) = c


and from the table what is H(0))?


good so now we ahve c !!!


omg yay


OK now we msut check it


suppose x = 1, what does our new eaution gives us for H(1)?


good


and for H(2)?


ands H(3)?


Yes


and finaly


how about H(-1)?


yes so it work!!!


wait i was just looking at the table


OK


how was I supposed to plug that in


well


not sure what you mean do you mean for -1 or in general?


in general


ok


like all the values of x


I m gping to try to write in yelloq on the black


we'll see if that works


see that?


that is to check x = 1 ?


kinda confused so i have to put as c the value of y that was above the x


let me review


do u remember how we found the ratio 4 ?


yes


OK Now IF the x's are all separated by 1, which they are here


That gives us the "a" value OK?


i dont understnad


so I would use those numbers to get us 20


OK I will write more in yellow watch


I wrote the general formula in yellow


I sued H instead of f OK?


used*


OK I see soem orange


di you add that?


OK whagt do u want to aks about that?


the 5 and 1 I plug in to make the desired number which was 20 in this situation


ok yes


but the 5 is "c" and it is used every time


I will explain how we get  5


OK?


ok


I will write more in yellow


After we found the ration (a) to be 4, we had the equation I jsut wrote


we still need to find C OK?


ratio*


OK


now we do that by choosing on x and then finding out what c we need


I chose x = 1


I could have chose another


but I thoguht that we eiasiest


0 is touch becuase we have to think about 4^0


but any x will work


I will write igain


ok I get it


Then we can solve for c and get c = 5


OK one more comment


That all works


but then we checked each vlaue


for a short lsit that is possible


and confirmed that the eq worked


for along list, we msut either have faith of use other checks


OK?


ok


OK did this help?


yes


I have another question


OK then we continue


OK yes quesiton?


i meant a new problem I wanted to start on whoops you first


yes first let me ask two questions


In your course do you use scientific calculators and/or grpahing calculaotrs?


Yes, we use scientific calculators but on the test we gonna have just calculators


not allowed to use graphing ones


OK I  see


well most grpahing calcs can fit data and tell you the answer


I can see why you can;t sue them


But in the "real world" we do LOL


can i show you the next problem


Yes


may we clear the board first?


yes please


OK


I see the figure


OK so we need to choose one from A thru H?


no we just need to match one funtion to that graph


Yes I think that is what I mean


I mean we msut the function (from A to H) that matches this grpah. Am I correct?


yes


OK Any idea how to start?


i know this decaying


OK good


does that help you eeliminate soem choices?


i think a can be eliminates


OK first I have  a ques


Are you sure that the A to H are all the choices?


are there more below H?


ok


no just those options


becuase I think this func is not in A thru H


Ohh hsorry OK


only these I a wrong my badd


I need to try to read chat while I type


Ok


so which ones are not decaying?


A


I will cross that ouy


any others?


I struggle with anything related to graphs or maybe I think its just math


I miss taking algebra classes


OK


I am here to help


How does E differ from A?


I think it moves just down 1


Yes


good


and it is still not decaying OK?


not decaying


so E i snot decaying


Can we eliminate E too?


yes


Now what do u thin about C ?


not sure


OK I will write here: y = -(3^x) I think that is what C means


it is A with a miuns in front


what does the minus do?


reflect


across the x axis


in other words


ye


so all y will be negative


does out graph have that?


our*


no so we can cross that out


good


now let u slook at H


what do youthink about H?


not sure how that looks like


OK remember from earlier what is 3^0 ?


growing


I disagree


what is the exactl vlaue of 3^0  ?


so plug x = 0 into H what do you get?


into h?


yes plug x = 0 into the eqaution at H


1 i assume


not sure what you mean by h


but what abouyt the other   one in frnt?


I will write on baord


in bl;ack


see the black writing?


yes


so when x = 0 what does H give us for y ?


sorry im confused


OK


where are you getting h


I will add some color


do you see the pink arrow?


OK I htink that point to the formual form H  in the lsit


Do you agree?


from*


list*


what


My eyes are not good so may be worng


the pink arrow is I think the same equation as choice H


we are talking about b


ohh


OK I was tlaking baout sorry


OK what do u think about B ?


wait Im seriously lost , I assume we were talking about b


OK was trying to elimnate H


ohh okay


but we should talk about B, whic I htink might actually be the correct anser


How about we fin sh H then do B?


yes


ok the pink arrow I added points to the equation for H am I correct?


in my black writing


OK


Now I am goign to sue that equation with x = 0


what y vlaue do I get when x = 0?


I disagree


pls follow what I wrote in bllack


I mean the final u value


Yes


Now on the gprah what is the vlaue of y when x = 0?


i dont know


OK I will corcle in red


sort of circle


I tried to circle


trhe question is what is the vlaue where it hits the y-axis?


I think it +1


oh yeah


ok


so when x = 0, y = +1


but for choice H when x = 0 y = 0


so grpah cannot go with H


yeah its b then


we still have others but I htink it is b


yeah because y=3^x is the growing exponential one


and if we want the decaying one the we can just reflect it by putting a negative infront of the x


yes


I agree


and we can check some vlaues


what does b give whne x = 0


good I cricled that and it is correct


how about when x = -1?


not sure


how would i plug that in


OK well it is 3^-(-1) = 3^1


what is that?


Yes good I will cirlce that on grpaj


well I was a litte low


but I htink you see what I mean


now how about when is very large


what happnes to b?


when x *


not sure what you mean


OK I will write


in yell


dos that make sense


x is going to inifinty?


yes


and where does 3^-x head in that case?


i dont know infinity?


I disagree


try this what 3^-100


you might need calcultor


I did gave me a bunch of decimals


ok


it is very very small


you see as x gets big 3^-x gets small


and it *approaches* zero just as in the grpah!


i dont understand


See the dotted orange lien at y = 0?


I mean the one built inot the grpah


ok the blue curve gets clsoer and closer to that as x gets bigger and bigger to the right


ok...


so I htink b is correct


ok I have two problems I wanted to work on


OK I have 20 minuites


questions 49 and 51


I will make it a little bigger fo rmy old eyes


OK good


OK


where shall we start?


what do u think is general idea of 49?


the same as the question


ok


wait


nevermind I dont understand


OK have you heard ofr parent functions?


yes


parent*


OK for 49 what do u think that parent function is?


exponential


Yes


I think it is 3^x BUT maybe your course considers that too specific


but let us start with 3^x anyway is that OK?


OK now in gneral


if we have f(x)  and then f(x - 1)


what does the  -1  do?


make it go to the side 1


dont remeber


I think it shifts the grpah to the *right* by one


ok


so if we know the shape of y = 3^x, the y = 3^(x-1) is same grpah *except* shifted rigth by one


OK


so do you think now u can grpah 49 ?


on the test we wont


because we dont have calculators


we need to do it by hnad


OK that is what I menat can u do that?


i dont know that will look


how about y = 3^x do you know what that looks like?


yes


ok wekk you draw that and then shift it all to the right


so what *was* at x = 0 will be at x =1


what *was* at x =1 will be at x = 2 and so on


what so my new graph will have x=1


well you new grpah will look just liek y = 3^x excapt all ofit will shifted to the right by one unit


I know you will not be alloed to use tech


on test


but pls try tha on Desmos and/or grpahign cal jsut to see


calc*


i did but Desmos had put it down 1


OK I will try to send you  a link


pls wait


but i think i have an idea what it looks like


Maybe it *looks* liek ti is down 1 becuase of th right shift


OK


I have time for one more


of these


should we try another?


i need the domain


ge


Ok sorry


I forgot


what does domain mwean?


like the x values


yes


i think all reall numbers


for 49 are there any x's that are *not* allowed?


but I dont know why


i dont think so how would i know that


I think you are correct becuase all real x;s are allowed


you see there are no divide by zeros or other things that could be illegal for some x


does that help?


no


OK wellI write domain as x-values input


to remind em that is the vlaues that we cna put IN for x


some equations like f(x) = 1/x have vlaues that we cannot put in


like x = 0 for 1/x


but the eqwuation in 49 has non of those


so would questions like 51 have a restricting number


i do not hitn so because the x is in the exponent and *any* real exponent is ok


Okay


here is an example f(x) = sqroot(x)


lets continue


domain is ix x >= 0


ohh


beucase we cannot hae sq root of neg number OK?


OK


range for 49?


i kinda understand


how about range for 49?


- infinity to 1


I disagree


is that function every negative?


ever*


ueah


I think that function in 49 can never have a negative vlaue for f(x)


does the grpah ever go below the y-axis?


I see it


I meant x-axis


the grpah never gloes belwo the x-axis


its comung from the negative


those are the *x* values


but the range talsk about *y* vlaues


talks*


ohhhh


I think the range is (0, infinity)


why 0


the ( means it apporaches y = 0


it never gets there


if it got there I would write [0,intinity)


not understanding


OK look at the left side of the current grpah


The grpha is very *close* to y = 0 (which is x-axis)


but in ever really gets there


I will try to circle


or point


but the line goes through 1


Yes the it the y-intercetp


but see the "pink" arrow?


yes


ok the curve is getting closer and clsoer to y = 0


that is why I wrote (0 Does that help?


no


OK well  am out of time


pls look on the Web oseek another session


I will mark on other thing thou


thoguh


oh no


The  grren arrow points to the -intercept


y-intercept


which is 1


yeah


and horiz asy i y = 0


is*


I will add red arrow


as the grpah goes to the left it *approaches* y = 0 so that is the asymptote.


OK?


ok


OK imsut og


MIGHT be back aournd 9 PM Eastern


cannot promise


I hope this helped


okkkk thank youu


BYE BYE


byee


Jordan, The original graph on which I put the green arrow is for f(x) = 3^x. The function  f(x) = 3^(x-1) is shfited to the right by one and it has y-intercept of 1/3  (not one, as shown). If you plug x = 0 into the shifted function, you will get 3^-1, whcih equals 1/3.


Hello, how are you?


I've got my mic on if you want to turn yours on.


I cant as of right now


That's OK


Do you mind checking a couple questions for me


Sure


I see it. Uh, give me a minute to look it over.


So what about B?


What do you think about B as well? I do see N


um,


what do you think about B


I'm wondering about the words without replacement.


B isn't Binomial


OK, can you tell me why?


the trials aren't independant


OK


Uh


2 balls were randomly selected.


What, what's the difference


Why do you say um they aren't independent.


on the first draw of red the probability is 3/5


so on the second draw it would be


So


um, what about D? Doesn't that have the same problem?


OK, well, I'm not sure I can say, uh, with my knowledge, if you feel D is good, uh, that's fine with me.


okay


All right. Let me look at this one.


OK. I, that looks like you're right to me. He does look good.


You're saying 4 or greater?


and each has a probability of


Sounds good to me


OK, let me read this one.


OK, I agree with you, Alice


Mm


I agree E is the answer.


Can you bring that down a little bit. Um, it's cut off.


There you go. Thank you


Yes, D is the answer


Yes, E is the answer


Yes, B is the answer.


okay thanks for all the help


have a great day


All right. Have a good day.


hi!


hi


i wana know about sector and segment


and isncirbed and centralangles


okay!


ill try to find it


plz wait


okay np!


a bit laggy so be a bit more patient like 10 mins


oki


still trying to find


its very laggy


cant you help me find  findind circumfernce and arc lenght too


we can start a bit later im a bit lagy


sorry though i'm not free anymore i have to go now


heloo


what do you need help with?


we can be doing


central angles and inscred angle


and power of the point theorem ( secant secant tanget etc etc.)


ok! Should I give you some questions?


yea


A central angle measures x + 20° and intercepts an arc measuring 3x − 10°.


Can you try finding X?


x is 5


ok! your steps are very good. There is just a minor mistake


good job! that's correct.


Next question:

An inscribed angle intercepts a semicircle. What is the measure of the angle?


oh um 90


that's correct!!


lets  do this more on legnth


ok let's try the question you attached


but we have some asn keys


i just hid it ra


that's good


Let's first try using the pythagorean theory to find the measures


For MP?


so it 8


yes! it is 8


its b


2 is a


its 2


bc if total is 8 since all are da same


we minus 8 adn 6


that's right! good jobb


so then what would MB be?


its c


bc 8-3 is 5


Leo! that's very good


can you try getting CD?


yea


can you help me for a bit for this


idk this part


ok


we know that segment AB is 5


but dnt tellthe asnwer


ok!


yea 5?


if we draw a line here, what would CM be?


oh i get it not


ok!! try the rest.


square of 39


yess!


mp


MP  is


b


yes! that's good


the ak here is wrong


you are doing really well


actually i used the wrong


when asnwering this by accident


ak is e


ok. let's still try getting it again to double check


yes!! that's right!


oki theres more


More questions?


is one 40


and the other 84


that's right!!!


Do you need to go through it step by step, or is it ok?


the 9 is 68\


10is 73


11 is 98


12 is 100


yes! 4/4!! that's all correct


yay


Leo


wait trying to upload new


18is 182?


close, try again!


17 idk pa still doing it


oh


remember that all angles in a triangle should add up to 180 degrees


yeaaa


what about 17?


the 17 is 55?


yeesss!! good job :)))


not sure pa


oh it is


oh...


remember that inscribed angles intercepting the same arc are equal


Got it!


yess good jobbb


yes! can you also tell me why?


Its because they share the same


itersecting thingy ill draw it onred


okk


yes!! that's good!! but for 19, you can also say that x=35 because


not just for these questions, but if you see two lines forming X like that, the angles that are looking at each other is always equal.


oki


ill upload more


Leo did you also get number 20?


yea! good job!!!


theres one more


ok!


is that your answer?


yea but tis wrong


it's okk


let's first try finding angle p


the pink one


you can write your answer in the chat


howd we could find the pink


remember that


can you see the pink thing??


yup


can you tell me why it's 2.2?


4pi/11  x 2 is 2.2


ok, so here, radian is actually how you show angle measure in a different way


2pi = 360


even though, in the calculator, 2pi is about 6, that only applies when it's in the "degree mode"


oki?


what do we do now


in the "radian mode", 2pi = 360 degree


so it's actually simpler


oki


think of pi like x


and try multiplying 2


2 pi is 6 in my desmos


morespecifically 6.3


that's correct, but only if it is in a degree mode.


In this question, it is in the radian mode


no


no, 260


yea so pi = 260


whatdo we do with this info


but first, let's think of pi as a variable "x"


like that


2pi divided by 2


when divided


pi= 130


or x-130


i mean x=130


pi would be 180


huh 360/2?


oh


nvm


but in this question, we can make it less complicated by ignoring the pi first.


oki


for example, 2pi*2=4pi

6pi/3=2pi


like this


so can you try the same thing with 4pi/11 * 2?


ill try


ok


4pi = 22?


ay


wait


just think like this

4x/11 * 2 =?


huh


think of pi as a variable


wait what


wait I will show you on the board


if there is something like this,


Yesss that's perfect!


now let's get the other angle


what would that red angle be?


can you tell me why?


minus 360


you are on the right track


can i leave ok ra


i have some errands to do pa


but remember, pi is like a variable here


oki


wait


i have to go na


bye


okok! I hope it helped


byee have a nice day :))


hi


how are you?


im good


great


need some math help?


yeah


can you put the first question on the board?


i'll upload a pic of my page


ok


sorry if its blurry


that's ok


I can see it


so you've been drawing the lines for the equations


i wanna check if im correct


ok sure


so 1 looks good, slope -2, intercept +1


for 2


we need a slope of 40/1 right?


so it should go UP 40 and across 1 square


does your line do that?


oh sorry I see it does


oh ok


I thought each square was 1


but you've marked it right


each square is 0.5 on x axis


good work


ok 3


I'll be more careful


ok


slope is -1/3


so it will go down 1 for every 3 across


yeah


so if it starts at +3 on the y axis


what should it get to when x = 3 ?


right!


it should go down from 3 to 2


with a change of 3 on the x axis


so your line is a bit too steep


oh


do you want to re do it?


you can do it on the screen


sure


wait but


i did go down from 3 to 2


and i did 3 to the right from the y axis


this point is 0,3 right?


and when x=3 what value should y be?


which is this point right?


yeah


do you want to draw the line between these 2 points?


ok


then it would be


3 to 2 which is 1


and then if it goes to 2


isn't it like making the slope like -1/2?


no the slope is -1/3 when y decreases by 1


when x increases by 3


oh


ohh ok


do you see it now?


yep


great!


ready for #4 ?


ok so the units are a bit hard to read


it goes 120 on u


y*


and 1-5 on x


so each square 120?


yeah


hhm


is 120?


yes


ok then each square above it must also be worth 120


ok


so this next line will 240


ok?


oh seperatd them


like one line in between them if that makes sense


what will the next line be ? 240+120


yes!


keep going, what's the next one>


and the next?


right! 600 will be here


and this is where the line crosses the y axis


so the line will go down from here 120 for every 1 on the x axis


want to draw the line now?


you got it!


excellent!


does it make more sense now?


yeah


great


you're doing really good work


ok i have another homework page


ok sure


want to upload that one? I'll clear the board


ok


ok I see it thanks


so first one looks good, up 10 and across 3


second I can't see too well but I think it's right


starts at 2


then down 3 when x does across 4


7 looks good


I see you have 2 for each square on the x axis


and 8 looks good too


down 5 when x goes across 4


excellent work!


you're doing great!\


what about 7


yes 7 is good


4 and across 2


thats all


thank you


ok great!, you're welcome


keep up the good work


hello


Hi, I'm gonna put a picture of like a problem I just did about rationalizing and simplifying. Can you like check that if I did it right?


ok


looks good!,...yoiu know though you could easilty check it your self by putting both in the calculator and see if they come up with the decimal number


How


just divide the sqrt 5 by sqrt 2 in calc


then put sqrt 10 diviided by 2 in calc....1.58


ya done good though


just gotta get the radical out of the denominator all the time


I got 2.5


ha,https://www.example.comy again,https://www.anothermathsite.orgybe slipped a digit like I do all the time


I did it’s not working. I don’t know what we’re supposed to calculate. Can you tell me?


I mean, we are done with answering the problem


I’m asking, how do you put it into a calculator to simplify?


its just that ya could check your answers by putting the unsimplified problem in the calculator and get that answer


then put in you simplified fraction in the calc and see that you get the same answer


for the unsimplified one


in calculator,...punch in 5 then square root it


Hi Sarah


hi


How are you doing


im doing good you?


doing good!


how may i help today


i want to learn something new in algebra can you do that?


sure, what topic?


uh any will do just want to freshen my brain before STAAR testing


Alright one second


ok


Okay, i'm not sure if you might know this problem, tell me if it is too difficult


I just searched up STARR practice problems


i understand


ill try to understand


Okay, do you know how to approach this question


no not really


just one question, do you get a calculator on the STARR?


uh i think its built into the test


oh okay perfect


so first thing i would do is check what square root of 50 is on a calculator


as the last two choices are decimal answers


mhm


alright so square root of 50 is 7.02


so not the last two


Now, do you know your perfect squares?


like 4 is 2*2 and 9 is 3*3


uh yes and no cause i dont know why but we just started on this lesson


oh ok no worries


il write down them on the board


does everything make sense so far


yep


alright so since they are perfect squares


the square root of 4 is two


does this kinda make sense?


yeah its making sense


alright, just fill in square root of 16 just so I know


yes perfect!~


alright, now we are able to actually simplify a square root


il kinda explain this in detail


or actually il give an easier example


so we have the square root of 25


do you see it on the board?


yes


alright


we can change the square root of 25 to square root four times 5


WAit


I meant to say square root of 20, my bad


but do you understand this so far


these are both equivalent


its alr everyone makes mistakes even you did


yes!


alright anyways


square root (4*5) can also be written as


NOW


Do you see the vision


can you write the new equation


Very close!!


so square root of 4 is 2


so it would be 2 square root 5


ah cause you circled the square root 4


Ye!


even though one of the choices shows 2sqrt5


lets still just try and find out the simplified equation


I like to do this trick


We can find two numbers by


dividing by the perfect square root


so like 50/4 and 50/9


so on


mhm


and just finding a number with no decimals


do you have a calculator near you


uh no i dont sadly


oh ok no worries


il write it on whiteboard


but i can use the browser?


sure


can you find the perfect number that gives a number


that isnt a fraction


yes!


could you tell me the perfect nmbers that go with 50 please?


yeah sure Sarah explain it deeper


so first number will be four


its the first perfect square root


that equals 12.5, so thats not it


lets try the next


YES!


so 50 divided by 25


is two


which means


our new equation is


does the new equation make sense?


Sarah


alrigh


im back


alright


so do you understand how we got 25 and 2


yes


alright perfect


so what is the new equation?


heres a hint


very obvious dont ya think?


hmmmmmm


Uhh not quite


Remember our perfect squares


Whats the square root of 25?


no?


No, its five :D


five times five is 25


ah im sorry my heads hurting BAD rn so its messin with me


No problem


if you ever forget you can look back at the chart i made


cool


anyways


square root of 25 is 5


then, we cant simplify square root of 2 any further


So that would be our final answer


Nice job!


did you do the confetti?


Yes :D


hmm


do you fully understand


yes this really hellped Mark thank you


alright, no problem!


Unfortunately I have to go now


If you need any more help, you can request a new tutor!


hey can you tutor me tomorrow at like idk 12:20 or so if you are free?


Have a great rest of your day Sarah, and good luck on your STAAR test


Uh, i'm not sure, maybe


I'll have to see


o


ok


But have a good one Sarah


you too


Good LUCK!!


hey!


good evening


hello


uhm I'm sorry but are you there?


sorry my PC acted up


but I'm here


so what problems do you have?


Ok the first problem is, "the equation p=3s respre


wait my bad


its a 8th grade math problem


it says "the equation p=3s repr


is that the full probelm?


no


represents the perimeter p of an equilateral triangle with side lenght s.


Go on ...


is there a proportional relationship between the perimeter and the side length of an equilateral triangle? explain thats the problem


sorry I took so long to respond


Yes


See a proportional relationship is expressed at the equation y=kx, where y is the dependent variable, k is a constant, and x is the independent variable


in this case, p corresponds to y, the value of k is 3, and s correspond to x


ohh ok


what's next


sorry I cant really understand that much the way you explain it and I have to go now


did I at least help you?


yes somewhat


hi what do you need help with today :)


hello!


hi :)


i see that you need help with your homework


yes


the picture doesn’t want to load


let me try again


ok great take your time


ok the first question


i tried to do it but im not to sure what im doing


yes you are on the right track!


before you do the distributive property however, you have to list allofthe givens


including that AB=3(5x+1) and AC=13x+5


so


like that


yup but dont forget to write "AB=" and "AC="


ok


yes amazing!


now we are trying to find what x is equal to


and in order to do that we have to have AB=AC


but first we need to prove that AB is equal to AC


so the next line would be AB=AC, and the reasoning would be "definition of a midpoint"


does that part make sense?


a lil


what part doesn't make sense? i'll try to explain it in a different way


actually wait it does because


right?


sorry all is see is your message that says "actually wait it does because right?"


is that what you meant to send?


you dont see the work


no i'm sorry i dont where on the whiteboard is it


i scrolled up some


i just drew a line then said AB+BC=AC


i don't see the work but yes you are right!


okay


AB+AC=BC


wait


y BC and not AC


aren't we on question 1?


yes


then it says that A is the midpoint of BC so AB and AC come together to make BC


oooh ok


and that is allowed because of the "Segment Addition Postulate" which is defined as "if A is between BC then AB+AC=BC"


does that make sense?


a little more than last time


ok great :)


and now we are trying to solve for x correct?


so looking at what is given to us, how would you try to solve for x


ignore everything about line segments and what AB and AC are equal to


ok


if you were just given 3(5x+1) and 13x+5, how would you solve for x


13x+5=0 then i would subtract 5 and do the same on the other side


ok you're on the right track


but we can't assume that 13x+5 is equal to zero


oh


for this problem we will set 3(5x+1) to be equal to 13x+5


since A is the midpoint of BC that would mean that AB and AC are the same length


is that makeing sense or should i explain it in a different way?


soo


i would be


it*


yes!


and then for the proof


on the statement side (after we state what is given) we would start with AB=AC, and the reasoning would be "definition of a midpoint"


because since point A is in the middle of line segment BC that would cut it directly in half


the reason would be multiplication


almost! after stating that AB=AC the reasoning would be the distributive property like you said before (great job with that one by the way) because to get to 15x+3 we have to distribute the 3


is something not making sense?


no it makes sense


ok amazing!


and then once you get to 13x+5=15x+3, you can solve it normally


with the reasoning being addition, subtraction, multiplication, or division depending on what you use


yes correct!!!!!


so x would be equal to????


yes great job you did great on this problem!


is the reason for that one subtraction


yupppppp it is subtraction


then division for x=1


correct!!!!


okok


yay


you're doing amazing Springfield!!


can we do one more


yes Ava!


do you want to do #2 or a different one


great!


if you don't mind could you enlarge the picture a bit please?


great thank you!


np


ok so first we will start with writing out all of our givens


ok one second


take your time :)


ok im ready


great :)


so with proofs you always start with writing out all of your givens


and then i see your work at the bottom


it is correct and is a very good model to help visualize the question!


thank you


and after we write down all of our givens we needs to find x to eventually prove that KG=9


so it'll be a little bit different than question one but not too different


so after we write down all of the givens


we need to next prove that JG+KG=JK


and we do that with the "Segment addition postulate"


because since G is between J and K, JG and KG together become JK just like you drew at the bottom


is this making sense?


ehhh


kinda


one second lemme reread it


cool cool :) and if it still doesn't make sense i'll explain it in a different way


nope i dont understand it


that's perfectly fine i'll explain it in a different way


do you get why we start with writing the givens?


ok done


ok so now we are trying to prove that KG is equal to 9


and your sketch on the bottom shows that g is in the middle of j and k


so the segments JG and GK make up JK


do we get that?


yes


great!


so because of that we can agree that JG+KG=JK


does that make sense?


great so the next statement after writing the givens will be "JG+KG=JK"


and the reasoning will be the segment addition postulate


are we doing good so far?


amazing!


and then now we replace JG, KG, JK with their equations


and the reasoning would be "substitution


is that making sense?


y do we replace


we replace it so then we can solve for x


oh ok


so how do we replace it


how would that look


instead of JG+KG=JK it would be 3(x-4/3)-2(x-19/2)=-x+25


and that is substitution


yes it is substitution


ok


and then from there we can solve it normally using distribution, addition, subtraction, multiplication, or division


so do i slove that


last statement


yup


ok one sec


almost its +19 instead of +9


but other than that you are correct great job!!!!


that distribution


yes that is distribution


and then you just continue to solve for x afterwards


addition?


almost! it is 3x-2x=x instead of the -6x


yes addition and subtraction since we add 19 to the -4 and subtract 2x from the 3x


it can be 2


no it would be a different line for the addition and subtraction


i dont understand that part


what did you mean when you said "it can be 2"?


like addition and subtraction together in the reason


to play it safe lets not put both of them in the same reason


put one statement with just adding and then put the reason


and then another statement with just subtraction and then the reason


ok so just addition


and then afterwards subtraction for the 3x-2x=0


ok


and then after solving it x is????


so the equation would be
x+15=-x+25


so if you add x on both sides you would get


can you solve it from there?


yes!!!


and then x would be???


that’s division


yes amazing job!!!


we're almost done with this problem now


because remember we're asled to pro ve that KG is 9


so what do we do with the fact that x=5?


yea


we have to substitute the x in KG=-2(x-19/2) with x=5


and the reasoning would be substitution


does that make sense?


yes


and then from there we keep solving until we get KG=9


😅 this a lot


yeah this problem was a long one


but you powered through!


good thing you make it easy


good for you!!


aww thank you Olympia


np!!!😉


ok let’s finish


yup you got this!


so what do we do now


you use substitution for
KG=-2(x-19/2)


you substitute the x for x=5


ok


one second


yup all good take your time


i got a decimal


can you walk me through what you did?


i see, so according to the order of operations (PEMDAS) you have to start with the equation inside the parenthases


then subtract-19/2


oh ok


so you have to start with the
(5-19/2) in the equation
KG=-2(x-19/2)


so


wait no im confused


i add those


ok thats fine we can take it step by step


so we have KG=-2(5-19/2)


so first we do 5-(19/2)


which gives us -9/2


do we get that?


yes


so now our equation is KG=-2(-9/2)


and then we multiply -2 and -9/2 to get 9


so then we get KG=9


ooh ok


is that all making sense?


great!


you did good with this problem too!!!


i'm proud of you!!


thank you


really


of course :)


bye


bye bye good luck with the rest of geometry :)


hello!


hello


can you check if this is correct?


It's marked incorrect, isn't it?


no that was my last submission


i changed the number


and i think this is correct


is that a 26?


If so, then that looks correct


Is this BC, by the way?


yea


you are doing integration already, so early in the year.


yea my school is weird


are you all set now?


yup :)


thanks for checking


OK, have a good weekend


bye


hello


hello, are you there?


I'm sorry but if I don't hear from you in a minute or two, I will have to close the session.  You can always repost your request when you have more time.


i need help with this


What rule do you think you would use for this?


Are you in a class?  Perhaps you should do this later when you have more time.


yes


im availabel


OK, but you haven't been responding to my texts


Are you really in the session now?


sorry


can you help me


OK, what rule of differentiation do you need to do this derivative, do you think?


not sure


It seems like you are not in the session, so I am going to close the session. Please ask your question later when you have more time


Hi Marcus! How are you today?


Hello im just exploring options for tutoring, I am really struggling with recent assignments.


No worries! Let me see if I could help you。


Would you like an example of the math?


Sure! Please give me an example.


Okay give me one moment


OK


this is an example of the problems I have to solve


Nice! Have you already tried these problems?


Yes and I always find myself not knowing what I am doing


No worries! Can you please show me your calculation on the white board? Then I can see how it is going.


I don't even know where to start


for example question a


can you identify what operations are involved in this expression?


subtraction multiplacation and exponents


That is correct!


I can rewrite the expression in this way, right?


Yeah that makes sense


can you tell me where should I start？


start with multiplication because of pemdas


true! can you write it out ?


is that correct?


YEAH! That is right!


continue please


That is great!


Thank you


You are welcome!


Do you want to continue with question b?


or any other one that interests you?


yes please


what do you know about this?


I have a difficult time multiplying negative exponents


No worries!


do you agree this step?


Yes I do


how many negatives multiplied?


2 negatives?


Yes! That is right!


2 is an even number, right?


yes


does that mean that it is a positive?


so they can cancel out.


yes! it is a positive


So any even number multiplied by anther negative numebr equals a positive?


any even number of negatives multiplied is positive


oh okay I was just a little confused


so you can simple an expression in this way


Oh, that makes sense


any other question?


we can do f and then I will work independently


Sure thing!


do you do 1/4 divided by -2 first?


Yes! You can.


because the expression involves times and divides only


so you can do either or first?


by associative law, you can do 1/4 divided by -2 first if you want


or you can do 24 * 1/4 first


so 1/4 divided y -2 would be -0.125?


yes!


okay just making sure that I had that correct.


please write this out on white board


that is right!


Thats great


then carry on


do I multiply 24 by the top and bottom?


top


numerator


is there a - in front of the fraction?


yes


is this clear?


That is awesome!


thank you so much for helping me today.


No worries! You made a great progress today! Congratulations!


I will be back for more help, I dont know if I will get you but you are great.


Thanks for your knid words! Welcome back to get more help!


See you!


see ya


Hi Ben! How are you?


Hi, good, you? My questions are also on the board


I'm good as well. Let me take a look


Okayy


I have two more after those


Okay! I'm ready


Do you have any idea where to start with number 1?


Not really


We know a polynomial of degree n has at most n-1 turning points


So 8


At least 8, yes!


And for the local extrema, can you draw out the two possibilities of what the a function with 7 turning points could look like generally


So 7?


Yes there would be 7 local extrema.


First, I would highlight the interval we are looking at, (-1, 3)


Or draw a box around it or underline it, just so it's easier to see what portion we are looking at :)


What's the highest value the orange line takes on in between the dots?


Almost but not quite! Can you circle the highest point on the interval?


I'm not sure


Can you trace over the orange line from x=-1 to x=3 with your finger? Try to find the spot where your finger goes up highest on the y axis


Can you circle the point you think has the highest y value?


yes!


very good :)


Yay


Do you have any ideas how to start this problem?


Not really


How many roots total does a fifth degree polynomial have?


5 actually! It's the same as the degree. Like how quadratics have 2 zeros and degree 2


Ohh


So if we have 5 zeroes total and we are given that -4 and 1/2 are 2 of them, how many zeroes do we not know?


And we know at least one of those zeros has to be non-real complex because the problem told us the polynomial has at least one non-real complex zero


Yes


Then, we remember that non-real complex zeros always come in conjugate pairs


So how many of the remaining zeros have to be non-real complex?


Yes!


And what about the remaining zero we don't know? Is it complex or real?


Real


yes! Good work


Is that all?


I think so


Okay perfec


t


Given the function f(x)=x^4+6x^3−x^2−30x+4, use the Intermediate Value Theorem to decide which of the following intervals contains at least one zero.


Is the answer [1,2]


That was what I thought it was.


So f(1)) is -20


And f(2)) is ...


f takes on every values in between -20 and 4 between x=1 and x=2 according to the Intermediate Value Theorem


0 is between -20 and 4, so there is a zero in this interval


so you are correct! :)


Yay


Okay last question


Okay


Looks good!


Thank you so much


You are welcome :)


Have a nice day! Good work today :)


You too, thank you


Hey, I'm Maria, how are you?


im great, how are you


I'm great, first off, do you know what vertical angles are?


yes they equal each other


Great, and what do they look like?


Exactly, so based off our diagram, what other angles do we know are 49 degrees


those 2?


Not exactly, vertical angles are opposite of each other right?


What angle is opposite of our 49 degrees


sorry im confused


i see it now though


Alright, do you know waht corresponding angles are?


yes


Label some corresponding angles here


What do they look like first?


Where would some corresponding angles be on the diagram I drew below


1 on the outside and 2 is on the inside


Could you label it with an angle mark


Like that


Great, and since they are corresponding what do we know about them


they are congruent


Exactly, so looking back at the diagram above, what angles are congruent there


Which of those angles are corresponding?


Great, what is that angle corresponding to?


Perfect, any more?


Which angle is that one congruent to?


Not exactly, notice the 11y-1 is cut up by another line


Look at this agnle


Is that angle corresponding?


yes?


It's directly below the 7x-23 right?


the 7x-23 is congruent to 49


if thats what you mean


Almost! The angle is actually amde up by two different angles


Not just the 49


Which two are they?


Sorry I was trying to erase our marks on the picture


is it made up of 11y -1 and 3x?


Check again, the 49 degrees is aprt of it


What angle is right next to it?


the 3x


And now, we have to add on the 49 right?


So what is the angle equal to entirely


If it is made up of 49 and 3x, it would be these two added together right?


yes it would


so the whole angle would be what 49 and 3x are added together


Exactly


Now, look below


I drew the same diagram, but I removed the line in the middle of everything


Do you see how these are related much easier now?


there related because their right next to eachother?


Exactly, are they are just like angles 1 and 2 above right?


What does this mean about them


they are equal?


Exactly!


Since, they are equal, we can write them out like that right?


yes


Now, we can solve for x can't we?


so my first step is to set the equations equal


we can


So how would we do that


We should cancel everything out until we only have x alone right?


Let's takes the +3x for example, how could we get rid of +3x


If we are adding 3x, what is the opposite of addition?


subtraction


Exactly, so adding 3x means subtracting...?


inverse?


Exactly, what is the inverse?


subtracting


So what do we subtract by here


Great, so we subtract 3x from both sides


then you add 23


Remember, what you do to one side, must be done to the other


What do we have on the right side of this equation now


Now what?


What will this give us now on the left side?


What can we do now to figure out what 1 x is equal to


x is 18


So, now we can solve for our unknown angles


What is one of our unknown angles ?


Looking back at the top now


What angles ahve x in them?


the 7x -23


Great, and what is x equal to?


So we can just plug x into these unknown angles now


Look below, what is that 3x angle equal to


or the 7x-23


The 3x


I drew it on lower on the board


i see


Exactly, so that hidden angle is 54 degrees right?


yes


What about the 7x - 23


Exactly, so it is degrees


Now, what angle is still unknown?


Looking back at the top again now


The 11y - 1 is missing right?


What angle is this angle congruent to?


49 and 7x-23


how do inkow which one is right tho


ones vertical and ones corresponding


i may be wrong


Picture it like this, whenever you want to know what angles are congruent to one another just picture them in our normal parallel line model


i see it a little bit


Always picture them, with just the two parallel lines and one line going through them


Look below, after I removed the line that wasn't parallel, is it much easier to see what's congruent?


All I did was remove that line, that wasn't parallel to the ones that made up 11y - 1


so thats what i should doo


Yes, it may help to imagine the lines as if it is just two parallel lines and the tranversal only


Now, what angles are congruent to 11y - 1?


You can use the diagram below to figure it out if you want too


sorry give me a minute pls'


Sure, that's alright! Take your time


im back


Great! What angle is congruent to 11y - 1?


Note exactly, try labeling which angles are congruent to each on the diagram gram


Or just type it out actually if you'd like


<2,<5. <4<7, <8 <4


1 5


What does it mean for angles to be congruent?


they equal each other


Exactly, which angles look like they equal each other here?


What angles is angle 1 equal to?


for 6 its 7 and 2


Anymore?


for 6 its 5 and 4


Double check 6 and 4, are those equal?


i oput the wrong number


meant to put for 8 its 5 and 4


for 3 its 7 and 2


Is 8 equal to any other angle?


No?


Right now, we know that

<8 = <5 = <4


What did you say <4 was equal to?


and 1


i missed that 1 i thin


Exactly, so <8 is also equal to <1 right?


So,
<1 = <4 = <5 = <8


What about angle 2, what is this angle equal to?


What else?


Anything else?


and 7?


Great! So
<2 = <3 = <6 = <7


If I tell you now, angle 1 is 40 degrees, what is angle 5 equal to?


degrees


What other angles are 40 degrees now


Remember, what angles is angle 1 equal to?


4 8


So how many degrees would 4 and 8 be


If tell you angle 2 is degrees, what other angles equal 125 degrees?


Remember, what angles are equal to angle 2?


6 3


So what would they all measure?


Now, going back to our original question


Do you see how the angles relate to each other?


That's our original diagram right?


yes


If I remove everything else and just make it two parallel lines and one straight line


What do you notice now?


there corresponding


Exactly, so waht does it mean?


congruent


And which angles are congruent exactly?


the top picture?


The bottom picture


Remember, the bottom picture is essentially if I removed one of the lines from the top picture


Look again at the bottom picture, I am going to restore it


They are the same now right?


The bottom picture and the top picture


But If I remove that line in the middle


Now, can you see what angles are corresponding to each other?


Exactly, what does that mean about them


they are equal


So 3x = 11y -1 right?


yes


And do you remember what 3x was equal to?


X was equal to 18 right? So what was 3x equal to?


49? or yhr 7x-23


No, if x = 18, 3x will be equal to 3 times 18 right?


yes]


Remember, we solved for the angles below


Below our diagrams, we solved for x


7x -23 was equal to
3x was equal to what?


What is 18 equal to?


hello


heyy


i hope you are well


what would you like me to help you with


algebra i think it is


I am rather confused on a formula or "strategy" my school has introduced


and is making us use


I can send screenshots of it right?


definitely


ok


One second please


take your time


that is the main screenshot


sorry if it is a bit messy


the one on the bottom right is a bit neater


would you prefer that?


wait sorry what am i looking at


lol


we are supposed to find both values of x


What i thought was the normal way to do this was using the quadratic equation or formula


but we are supposed to do the question like in the image


Ill explain


as best I can what i wrote


but our teachers go through everything so fast that I cant get it all


1.)  find factors of a and factors of c


then put a into (ax +- w)(x +- z)


so in this case it would be (3x +- w)(x +- z)


do you prefer typing or speech?


am fine with any one your comfortable with. i understand you pretty clearly. unless you're talking about me


Im just thinking speech would be faster tbh


ok lets do that then


alright


wait i dont think i have microphone on


do you have a microphone?


i can hear something


*mic


yh i do


I just turned it on


ok


Hello


u saying anything?


Hi


OK


Yeah


I don't get this. It's not at all.


wait i cant hear you very well


Uh better?


to fix the microphone quickly.


Better or like still, nah.


better


The transcript is like really bad.


OK, so, um,


I'm sorry, I don't understand what you


help me


What do you, what do you need me?


Um, I just like don't get exactly how to do these problems like the work is there, but


Hm


so I just don't get um some of the steps. Like I don't know like why some of them were done.


but also just like


like it's also just not organized enough like I don't get like where this goes and like what to do with that


OK


Um


Yeah


I'm also still trying to like make sense of it cause


Like, it's, it's like a weird thing, but my school in general just makes us do like a weird math.


Oh, I understand. It's just


um


over the place


Yeah.


Um, but you need to give me like


a minute to understand.


like


cause I can't explain if I don't understand.


if you want to see the bottom left.


Uh, I can see that too.


Mm


I can see it


very well well


OK


I think you should make it like a big uh.


Wait


It's not


better.


yeah


Yeah


But like half of the


thing is missing


OK, it's fine enough


Like, it's out of order maybe or like all over the place, but like this is just like exactly what was on like what they were doing.


It's like the way they teach is like they just write


whatever at the front and then we just have to follow along and stuff.


So this like you you just write to them.


Yeah, like this is just what they did and how they told us to do all this stuff.


OK. And you don't understand what you're saying.


Yeah, I don't really get, um, a lot of this


OK, that's fine. I just need a minute


to


just look at the


fish and see what's going on.


OK


OK, I think I understand now, like.


I think I understand now.


Mm.


so


and like quadratic equations.


Can you see


what I'm writing at the bottom.


Uh, yeah. Also, if I scroll, does that change the what it is on your screen or?


No, it doesn't


OK.


So, um, basically


a cosmetic equation.


which is this


right. The A


the factors of


A times C


should add up to give you the.


So


you have to find a factor of a times c.


That would add up to give you the.


and


and the question over here.


A times C is 3 times 12, which is


36. So we need to find factors of 36.


that would add up to give you 2.


So if you come to this side.


this side


Um


I see that your teacher is like


finding the factors of


and then over here, she's like


adding them up to see which one would give you 20.


Yeah


So then that one


yeah


2.2 x 18. So that was like.


the values of ANC that would give that would multiply.


Wait, what am I saying? The fact is the factors of 36 that will add up to give you 20. Switches 2 and 18, and


I'm guessing over here, there's some sort of like


format


like, um,


I


it's some sort of like format you're supposed to like write it in because


if you just scroll down a little bit.


Once you get


the factor of A


times C, the add-up to give you


B


It will look like this.


Hey, what is that? Is that a, wait.


like X-2.


times


What what did you say


OK, cause what did, what did you uh write for the second parentheses.


X


plus minus 18.


Wait, what


Share I write it again


I mean


for me it just says like X + or minus 2 times something


C+ or minus 18.


OK


Just narcos, I think it was like um


where you put 2 and 18.


It was like


M and N, I think, but I'm not sure.


Mm


Or would M&N be in like somewhere else?


Wait, what's M&N?


Um


What's that


it's like a


it's like an equation that we used to think it's like and I believe to the


first route or like the first except.


And we know I can't use that there then.


Yeah no that's 11


Mm, sir, I, I, I don't know what you're talking about.


No, no, never mind, like, it's uh unrelated to.


Oh, OK


OK. OK, so


like when you get the factors of


AC that add up to 18. This is the format that it takes, but then,


uh, your teacher wants it to be in this format, and


with


yeah.


and you


one thing, like the


but they want us to do is like they, they want us to do like the aerial model which is like that thing that you have that's there, so like it's either we don't make mistakes or something or.


uh, well, yeah.


So to write it in this format.


uh


You need to


mm


you need to


change this 18.


to 3 times 6. That's what your teacher did.


She changed the 18 to 3.


and


Yeah, OK


But they they got the 3 x 6 from um


like


you can see like


they go from like the factory from I think it is.


which is like the 3 x plus minus W times x plus minus Z equals 0, and then they do like the area model thing, so they actually multiply them together, and then they go back into the standard form, I guess, but like with W and X


and then


yeah, it's so weird, but then they go simplify it more.


and then they do


it's, it's weird but like they do 3.


extra


wait, I'm coming. I, is this


where is the answer?


The answer is like in the bottom right.


It's uh here


There's like two answers


Mm


Uh, OK. Um,


so I'm just going to be very honest with you. I, I don't understand this method of solving like


hm


forgetic


like I'm not


Like I know you can use like quadratic equation too, which is like


yeah, I'm not


I I forgot it was fun, it's like.


oh, I'm not used to this me. I've never used this method before. I don't understand either.


Neither do I know what your teacher is writing.


I don't know what I'm looking at.


And I also don't know what I'm seeing, so.


Sorry, I don't think I can help you.


OK


I mean, I might just go to mass tutoring on my school then because I just don't get it. They have it there, but like it's an afterschool thing, and it's like filled with kids who are like, like they don't get anything at all.


Like normally I get stuff like this.


but


it's like super like weird to me.


Um


uh, why can't you like?


um ask your teacher to like,


break it down after class or something.


No, cause they don't really have time after class. We like, mostly like our schedule then basically it's like


we get there, we have like a breakfast type of thing, and then we have


uh ELA and then math.


Oh wait, no, sorry, uh, ELA then physics, and then we go to math.


And then we have history, and then we have like a little period of time, I guess that might work for


that, but the teachers usually use that to either like eat.


great assignments or like do something because they're pretty busy most of the time.


And then they go to recess, like we have recess still, which is weird, but


OK


And then


yeah, and then uh we go to


electives, which is like art, uh, chess, theater, this, that.


Mm


And then we do problem solving, which is like regional math basically, or uh instead of that, we do physics Res prep


Oh


which is basically another physics class.


that, that, that's a wolf class.


but we don't really have like


any time where it's like you can just go ask the teacher unless it's after school.


or


you get lucky


Yeah, I have a.


Yeah, I was thinking that too, but like after school, the only time they're going to be there is for tutoring.


and


for in tutoring, it's like they're not going to be with just you so that you, you have to like


like if you


Yeah, but I'm sure like


yeah


you can ask questions.


Yeah, I can ask questions, but like if I don't get the whole thing, it's uh just a question. I won't do everything.


Mm, well,


me


Like it's not like a, like in physics at least there's formulas with this, it's like I don't.


I just don't got it


physics formulas are more complicated, honestly, but I think


um you should


are you from? Are you from the Los Angeles?


Yeah, where are you from


Mm


I'm French.


OK


but uh


I think maybe if you get matched with another tutor that is from where from.


They might understand all of this cause I don't know, I'm not familiar with this, and I don't understand what I'm looking at. Like, I actually can help you.


and I'm sorry.


I know it's fine. It's like no, like only a few people get it. Of course, like uh my Pakistani friend gets it. He spends like a bunch of time doing work, uh, but


Oh, wait, like, why don't you ask your friends to explain.


yeah, it's, but it's like he's not gonna teach me the whole thing though. He'll like he'll tell me the answer, but he won't like


Yeah


like he also like doesn't.


I want to break it down


Yeah, I might have to pay him, I think.


OK.


He's your friend


She, he, he gives me a friend discount.


since


You're not supposed to be at all.


Uh, I might ask him, but it's just also like a time thing because like he does uh hockey and then


yeah


No, I'll see


OK


Well, good luck.


Good luck. OK.


Bye-bye


Bye


Hello!


Hi! So I'm confused and struggling


So here's the link to the classwork I did in class but solving it on my own i'm confused: example.com


currently working on one that a past coach created for me since i want diff numbers and the exact problems from my worksheet


Oh like this is different numbers from what's on the worksheet?


yes


Like this is just a check in thing


got it


its just practice


i want practice to get better at it


is this right so far?


Wait walk me through what you just did I'm a little confused


this a method a past coach showed me


Have you learned factoring by grouping?


That's what I would suggest here instead


If not I can walk you through it


walk me through it


Here wait rewrite just the problem on the board


k


Is it just that?


mhm


Okay so first


When the number in front of the x^2 is different than 1 that's when you know you have to use factoring by grouping


So here that number is 2


ok


And then we look at the constant which is the -3 because there's not x attached to it


So the first step here is to multiply those two, you might've learned the rainbow method in other lessons


yep i did 3 times 2


Then you get -6


Which is the number we're looking to find 2 numbers that multiply to make


then we look at the -5


That is the number we need these two numbers that multiply to -6 to add to


If that makes sense


yep ik that part


Do you know of the two?


-3-2 i said that to the past coach and they said its wrong


You're really close actually


if we used -3 and -2, when you multiply them you get positive 6 not negative


Yes it fulfills the -5 part but multiplying them doesn't equal -6


oh true


-3 times -2 is positive 6 but we need the two numbers to multiply to -6


Any other ideas?


it cant be 3+2 bc thats positive 5..


the middle is -5


Right


I'll give you like the tiniest hint haha it's not 3 and 2 it's two different numbers


omgg see this is where i get confusd


Don't worry this trips me up all the time too


Perfect!! See you got it


-6 times 1 is -6


and -6 + 1 is -5


Great job there!!


So after we get those numbers


Remember how they add to -5?


We kind of just put them into the problem


I'll show you


so its (x-6)(x+1)?


Do you see what I did there? It's a little hard to explain but because they add to -5, we can replace them with it


Like the -6x + x = -5x


So replacing it is just the same thing


Look okay so far?


yes


okay perfect!


So now here comes the grouping part


ok can u give me another one


We basically just split this down the middle


oh its not done yet


Nope haha


Almost though


We split this down the middle so there's two terms on each side


Now it's a little easier to deal with because we only have to take out a GCF for the two pairs of terms


Make sense?


im confused


i thought it was -6 and 1


You're right it technically is -6 and 1


and those are still there


I just left out the 1 when I put x


i thought that was the answer tho


Because -6 and 1 add up to -5, we can replace them in the equation


Not exactly, for these questions where the number in front of the x^2 is different than 1, it's a little more work after you find those two numbers


if this problem was like the others on your worksheet like x^2-6x+6 then those two numbers would be the answer


this is very stressful


oh yeah thats how its doneon the paper


im trying to solve it the way it says to be solved on my workshet


Wait let me look at that


k


To be honest I got kind of confused reading that


The way I was taught is this grouping method because it's easier


Actually


nevermind I was looking at the wrong page


It does the same kind of thing I'm teaching you


The AC method


It's like the same thing


so is my answer right or no


For this one?


the -6 and 1 alone isn't right just yet we still just have to factor the two sides


omg idk anymore this is confusing


how do you know your supposed to do that


To do the grouping thing?


just give me a new problem


bc idek this is just confusing


Yeah I'm really sorry it's super confusing


This was hard for me to learn at first too


can u give me a problem and then after this im calling it a night


Yeah of course and stop me at any point if I'm not making sense


You can read that fine right


yes


so would i do 2 times 2


Yep!


ok


now what


So for the grouping thing basically you need numbers multiplying to 4 (because 2 times 2) and adding to 5


So here that would be 4 and 1


So like we did for the last one we can rewrite this


Does that make sense?


It's just a way of expanding it


to make it easier to factor


ok holdon


that quals 11


Oh I see why you think that


Basically here


nvm i get it


We can't add terms that don't have the same variable


so its (x+4)(x+1)?


Not exactly, after we do this we basically have to GCF each side


Remember how I said like split these 4 terms down the middle


yes


omg this looks confusing and foriegn to me


my teacher hasn't went over a problem like this one yet that has to be solved like that


Sorry btw that was supposed to be 2


I probably should've changed colors to make it look better


But essentially you're just splitting up the equation to make it easier


and once you do that


you're basically factoring 2 parts of the equation separately


Do you see how there's a (n+2) on both sides?


That's what we want basically


That means we did the factoring right


where the 2 come from tho


the n+2?


mhm


I took out a GCF on each side


Like for the left I took out a 2n


which leaves you with n and +2


you had it witten as 2n24n1n+4 at first


oh k


Yeah I wrote 4 instead of 2 at the end


It originially was 2


yeah idk still confusing


goodnight


Hi!


Hi Jordan, looks like you have a problem to work on...let's take a look


Alright!


The assignment is Extrema and End Behaviors by the way!


I see, so your teacher wants you to graph to find the answers?


I think so


Let me graph it real quick


ok, i'll do the same


I graphed it on the desmos graphing calculator


yep, what I got too


oops I made a mistake, now mine looks like yours.


What do you mean?


I made a mistake when I put in the numbers, but now I got it right and got the same graph as you


Alrighty


so, we need to find the min?


I think?


I see one local example.com you agree?


Yes, the point at the very bottom of the arch going down?


there...right?


yes!


does your calculator give you the numbers for that?


yes lemme look


(-0.51313, -4.12664)


that's what I got too!  now need to round to nearest hundreth


would that be the 1 or the 3 in the first number


two decimals, so the 1 in the 1st number


ooh alright


Ah, that was correct!


Now I have another one


very nice


let's see the next one


ok, what do you think...where are the minima?


well it seems like it wants just a single number and not a point so I'm not sure


would they be -4 and 2?


it is worded strangely, but I think it wants the y values for the minima in the first box, and the x values in the 2nd box


oooh


so then the first one would be -5, and the second one is -4 and 2?


yes, for the second I think you need -4,2


since it wants a comma to separate


It says it was correct!


nice!


Okay I have one more and then I think I get it


ok, let's start my idenifying the local minima


I see maths.comree?


I agree!


they occur at the two points (0,3) and (-2,-3)...right?


Right


so the minimum values (for the 1st box are)...what?


would they be the y values because it looks like they flipped them


oops, 1st point is (3,0) not (0,3) right...


oh yeah


so would the first one be 0 and -3? for the first box


yes


and then the second box is 3 and -2?


yep


Thank you so much for your help I really appreciate it! It was correct


You were very helpful, thank you


it was my pleasure, enjoy the rest of your day!


Thank you! You too!


Hi


How can I help you?


I have a question about areas


sure


can i paste it


ok one sec


take your time


thank u


computer slow


I understand. please take your time


thx


Is the question to find the area of the blue box ?


wow good question


I think


that is just blue are


and right triangle is there to he;[


yea confusing until u ask