The area between curves is generally given as


um


like area


equal 1/2


the integral of 1/2.


R2D theta.


I'm sorry, I


need to write that better


fix that


So


in general, the area


of determined


with polar coordinates


is dealt with, with this formula in general, 1/2 R2d theta.


and R


um R is the F theta and G of theta shown.


So, and the problem, there's a F theta and a and a uh I'm sorry, epitheta and then


G of theta


So that is going to be


the function that we're interested in plugging in


right here for our squared, OK?


And we're looking at the difference between curves. So that's why we're going to be subtracting


to get that area


So what we're doing is we're taking


um


I gotta figure out which one comes first here.


Looks like they're all taking G minus


F.


wait this is polar coordinates? i ahvent done that yet


which kind of makes sense


Yeah, so


wait so i dont need to study this


let me look at this for a minute. It looks like


you don't need to study this


is this like chatper 9


of calc bc


OK, um, I don't know, I, I'm not a teacher, but it is, looks like it is calculus BC to me. It's


more advanced calculus.


So, uh, if we don't need to do this, that would be great.


i think ik how to do this


OK


so you isolate and put the n on the outside


and if its less than it converges?


Um


so we're looking for something


where each term gets smaller.


in absolute value


um,


less than 1?


So, one thing is, um, alternating series is always converge


Yes.


So, so one thing, you have an alternating series here.


meaning that every other term is positive and negative, OK?


errr okay


So when you have an alternating series, as long as what you're alternating with


gets smaller and smaller than that should converge.


So they're all alternating because


every time you


change in, it'll become either negative or positive. It'll start out negative, then go positive, negative, positive. So that's what we call alternating.


Which one of these, however,


is getting smaller and smaller as N gets larger and larger.


Well,


let's look at this. The first one that's not happening.


uh, I shouldn't say that


um,


let me, let me look at this for a minute and see which ones make sense.


So, let's, let's look at this one for a second, the last one.


If you look at that


for each N


it does


it, it um


I


I take that back


Give me a minute to look at this so I can see which one makes sense to me.


wait can you do the math


Yes, I will


how do you know the first one istn?


How do I know the first one is what?


isnt


I don't yet


I don't


ohhhh


So, I, I need a minute. Let me give me a minute to look at these and make sense out of it, please.


So.


okok


OK


So if I look at the first one


let's write out the first few terms of the first one.


This one right here


Um.


this one right here


If I start plugging in


what I'm gonna get for N equals 1 is


When I put N equals 1


I get negative, 0. When I put N equals 2,


I get plus


and then when I


put in N equals 3.


I get minus


uh, put any equal, I'm sorry, this should have been positive 1/2


Let me, let me fix this


All right. I'm just putting in the first few terms to, to see what happens with the series. N equals 0


I get 0.


N equals


I'm sorry, N equals 1, I get 0.


N equals 2


and then 2 will give me


-1 over over 2. So, -1


-1 over 2.


When I put in N equals 3, I get minus.


and it'll be negative


over 3


Now, look what's happening to this one.


why are you plugging in stuff?


It's the, the numbers are getting bigger


sorry i dont get aynthihg


All right.


OK


Um, I might not be the best one to help you with this because if you have to


I, I'm trying to explain it my way, but you may be learning something different in class.


So I'm, I


I'm trying to


present how I would solve it.


Um.


but I find that putting in a few terms of the series helps me understand it.


wait i have to go thank you for all the help


All right, bye


ty!


Hello!


hi


Today I have an algerba 2 exam


and I don't have a study guide yet I am supposed to to finish it tommrow


I finished half of it


But


Now I need help with


Preparing to finish it


I did catch the topics


So, the first one is


First, I want to work on Average rate of change in Algerba 2


I don't have any materil, I did but I had to turn it in


So do you have any problems that we can use to practice this?


rate of change ?


Average rate of change


let me check


Another tip is that they're all mostly word problems


is this graph problems


Both but mostly word problems


All right, so how do we start solving this?


Fuel at \(100\) km (\(F_{1}\)): \(375\) LFuel at \(400\) km (\(F_{2}\)): \(125\) L


Hi


Hi I need help with #6,9,13,14,20


one sec


do one at a time


yup


so no 13?


yup we can do 13


okay, did you try to do it yourself?


yes I did but im still lost


okay, let's do it together


yes please'


sorry my ipad does not have charge, so it's taking time


no your fine


oh I think I did not have to simplify all that


give me couple minute to find a better way to do this


What is #14, 6, and 9


So 13 would be A


ok


let me finish it to move on to 14, 6 and 9?


so first we solved for a from the given expression, then we compare with the options


should we do 14?


the angle z is 1/2 of the sum of the intercepted arcs, so 1/2 (70+120)


that is 95 degree


are you still here?


Central High School 10th grade


hi Chloe


hi


yes. covers the whole semester


just the first semester


right


there are probably areas the you understand well, and areas where you could use some help


*areas that you


yes i have my final in about 20 mins


let's focus on areas where you need help


ok i need help with linear equations


the most


OK


graphing them?


yes


want to put a problem on the board?


sure


one sec


i dont have any can you put one up for me?


it would help to have an example of what you need help with


just graphing an equation in slope intercept form?


yea...


there's a problem and a grid


i have to go the bell is ringing


thanks for your time


graph the intercept


then use slope to graph one more point


then draw line between those points


i have to go the bell is ringing

thanks for your time


yw


I need help with the problem about recursive functions. I need to know the formula and how to write them and that's the thing I don't know so I need a tutor that can help me figure that out.


The problem says for the following pattern write a cursive function for the following:


hello


hi


how can i help


which question is troublesome for you?


right now, I'm having trouble with question D where it says for the following pattern right over a cursive function for the following


my issue is that I don't know how to write a recursive therefore it's a lot harder for me to figure it out


and I have finals tomorrow, so the sooner I can figure it out the better


ok


so first can u write down counts of each


figure 1 has 5


fig 2 has 10


fig 3 has 17


fig 4 has 26


so its +5 then +7 then + 9


so that makes it quadratic so then we go to the second difference


which is +2


i dont know what to do after that


yup


so what would the first equation be?


f(1)) = 5


because figure one has 5, right?


then after the first one


but u have to come up with an equation


not that


these are just points (x,y)


we need to find an equation that works for all values of n


f(n-1) +2n+1


oh wait what


it cannot be 5


y


f(1)=5(n-1)+2 does not work for any values


if i plug in 2 or 3 or 4 in f(1)=5(2-1)+2 that does not make any sense


so it has to be y = f(n-1) +2n+1


ur not rlly explaining it in a way i undstand


but how does that work?


how can i remember


the base case is f(1)) = 5


then we build a second equation on the base equation


ok


second equation is F(n) = F(n-1) +2n+1


if i plug in 1


it would be just 5


since thats the base condition


if i plug in 2


F(2) = F(2-1) +2n+1


F(2) = F(1)) +2n+1


so just change n to the figure number?


F(2) = 5 +2(2)+1


F(2) = 10


which is the number of squares in figure 2


n is the figure number


does that make sense?


cuz f(1)) = 5
1 is figure number and 5 is number of squares


okay what is the formul like f(n)=n+___+__


i understand what to put where n is but its the blanks im confused abt


theres no such formula because it depends on the numbers youre given


u would have to come up with a unique equation that fits the numbers


okay so for this the answer would be f(1)=5n-1+1??


no


the answer is f(n-1) +2n+1


and


f(1) =5


because i dont know how u got that answer


so the first figure has 5 squares so base condition is f(1)) =5


okay


it has to fit the numbers we gave initially


figure 2 has 10 squares and so on


which is f(2)=10??


like the second one is that?


yup


okaay


thats not the answer tho


how that's what ur not explaining


u need to come up with a new equation that fits the numbers


fig 2 has 10, fig 3 has 17 etc etc


there needs to be 2 since thats the increasing factor


does that make sense?


okay i get why theres a two now


yup!


so say, the differences were increasing by three it would be +3n instead right


not necessarily it depends on the numbers


yeah u had me then lost me after that one\


so we are using 2n since it fits the numbers better in this example


it might not necessarily fit all sets of numbers u will be given


u could make a table if that makes more sense


yes


do u wanna try the next one?


sure


yup


sorry which question are you on?


what did u mean by move onto the next one


question 2 part a?


the one right below D


yea


ok


so what about f(4)


im assuming each difference is going up by two


there is a better image if needed


so what would be the explicit equation


im writing it on my paper on moment


okay im a lil lost


its the same exact question we did


ik


the numbers are exactly the same


im aware


so the answer would be the same


its an explicit problem tho not recursive


theyre different


u would just replace the recursive bit in second equation with 5 and thats it


ion like ur attitude


sorry what?


why u mad im confused 💔


for part b?


yes


oki bye


hello


How may I help you?


can you hel;p me with this


what is local mini


a local miinimum is like the bottom of a valley.


where the arrows are pointing.


Make sense?


Have you seen that before?


ohhhhh


is there another type?


to find there local minima and maxima occurs you need to find the critical numbers of the function.


ohhhh


okay


Do you know how to find critical numbers?


no... i forgot


can you help me


trhe process


how do yk its a mini or max


The critical numbers are where f'(x) =0 or where it is undefined


okY


LET ME TRY IT


sorry caps


yes, go ahead


that factoring is not quite right


oh\


still not right


oops


When you factor it is best to first factor out any common numbers


okk


I factored out a 3


So what ate the critical numbers?


Hello?


hello, are you there?


yes


give me 5 mins sorry


it is getting late.


hello?


It is getting late, and I am afraid that I need to hear from you a minute or two to continue the session.  It has been 10 minutes since I have heard from you.


okay sorry


i was taking medicine


ok, let's finish up please


is that right?


what do we edo now?


pick a test point in each of the three parts and determine whether f' is + or - in that part


which equatin do i plug it into


f', the derivative


what happens if its the same sign


okay so there is a max


at -1


and min at 3


that's right


but what if its the same signs


if you have the same sign on both sides of the critical number, then it is neither a max or a min


Incidentally, it is often easier to use the factored form to figure out whether f' is + or -


but either way works'


it seems like you have some understanding of that now.


Have a good evening


thank you!


you are very welcome


do you ahve more tips?


that's it for this problem.


have a good evening.


bye


hi


Hi can you please help me with this problem st/r + x/a+b=z/y


is that the full problem


its not clear


Yes would you like me to use the whiteboard


yes


Ok one second


Ok it’s on the white board


Find a


ok


there are so many variables in this equation


we can't exactly find the value of a


a value will be in the form of other variables


Right


I dont think its possible


lets try


paste again plz


Ok


which one ./


lets try 13


subtract st/r on both sides


invert on both sides now


So E) none of the above


thats the ans


Ok thank you


if you take off - on both numerator and demonimator , it will be A


Yeah


hi


Hi!


How are you doing today?


good


Great


what abut you


I’m good too thanks for asking


What can I help you with today


math


Oh okay alright


So you need help with dividing is that right


yes


Okay lets get started then


ok


So the wrote it out so that it is easier to divide


Is that right?


Can you see my writing?


Okay


So we are going to go by each number


So first we’re going to look at the 7


So how many times does 6 go into 7


That is partially true


Yes you can’t multiply to get 7


But what number do you get that is close to 7


Yes and what number do you multiply by to get 6


Not quite


Okay so 6 times a number is equal to 6


So I’ll help you out with this one


It’s 1


Right


yeah


Okay so above the 7 you would put a 1


ok


Okay so what was 6x1


i now how to muplily


Yes I can tell!!


Okay and I’m confident you know what 7-6 is


So now we have to move on to the 8


But we have a 1 left over from 7-6


So we would bring the 8 down


so how many times can 6 go in to 78


Almost


How many times can it go into 18


times


YES


Perfect


So you would put the 3 above the 8


And we said 6x3 is 18 so


yes


And 18-18 is just ?


Right


Okay so now for the last number it is 0


So how would we get 0


Any number multiplied by what is 0


i no


That’s awesome


What is it


sorry i have to go


Oh okay that’s okay


thank


you


Yes ofc


Bye


Have a great day!!


You did amazing!!!


thank you


I need help with a statistics project final


Hello


hey Alex post your problems that you need help with


well its not really a problem, its a final


I can send the rubric


I don't know how to start


ok post it please


one second


ok


Maya how are youcoming with the posting?


I'm trying to find the file


it wont let me download


can you paste it in this chat area?


how you coming with the pasting?


wont paste it


can you write problem on board?


Uh


Maya?


Wow.


the


I'll write the rubric


and


insurance


rescue. You're super is the only asthma rescue inhaler FDA approved to treat symptoms and help prevent that.


I cant hear yiu


A sewer should not be used as a main instrument for asthma. Get medical help right away if your breathing doesn't improve or worse, but for serious allergic reactions like rash on


your tongue swelling, trouble breathing or swallowing, chest pain? You can your super more than prescribed could be lighter serious side effects increased risk of thru or infection.


faster heart rate, and higher blood pressure. Maya, can you hear me?


yes


Maya, can you hear me.


What is the rubic


Hello thank you for taking the time to teach me


hii of course!


what do you need help with


I'm learning about quadrilaterals and I'm so confused


I have a test pretty soon too


okay so is it proofs with qudrilaterals or just rules in general


Both of them


oh thats fine


okay thank you


no problem!


ill just draw the rules out okay


okay!


are you learning about trpaezoids?


yeah we are


alright


but they didn't teach us the rectangle yet


oh okay, you can learn it early!


do you know what these symbols mean


if they're congruent or not


yup!


do you have any qyestions


ill write the rules for the shapes in the chat


no I don't thank you


i'm watching you do so


great!


Parallelogram: Opposite sides and angles are equal, consecutive angles are supplementary, and diagonals bisect each other.
Rectangle: Opposite sides are equal and parallel, all angles are 90°, and diagonals are equal and bisect each other.
Rhombus: All four sides are equal, opposite angles are equal, and diagonals bisect each other at right angles and bisect the angles.
Square: All sides are equal, opposite sides are parallel, all angles are 90°, and diagonals are equal, bisect each other at right angles, and bisect the angles.
Trapezoid: Has only one pair of parallel sides (bases), and adjacent angles along non-parallel sides are supplementary. Diagonals bisect each other in the same ratio.


i know its a lot of info


but it is thorough


okay i'll be righting these down


do you have any practice questions you would like to do


yes please


okay ill write a proof up


do you know the different thorems


like SSS, SAS etc?


no not yet


oh then a proof would be slightly difficult if you havent leant it


because you need to have a theorem in the end


then i highly doubt your test would have it if you havent learn it


do you have any other topics you want to learn more about?


my teacher said, i'll have the trapeziods, diagrams of the shapes, finding the angles, graphing diong conclusions and calculations and trigonometry


ohh alright so you also have trig


thats fine


ill write problems and the board


on


okay!


alright do this one


alright


done


yes!


you got it
!


yay!


im going to share my screen


just solve the problems on the worksheet


okay


do you see it?


questions 5, 6 7 and 8


yes I do


great!


Which one should I do first?


which ever order you prefer


Okay then


have you written the questions down


can i pause the sharing?


Okay yes


thanks


And I did two I think


oh great


can you tell me your answers


yes for the first I got 4/5 and for the second one I didn't get to make it to the right amount but i got 39.3


I think I did the first one correctly


its is 39.3


so it is basically right


okay


ill cut you some slack for the 0.3


just 2 more!


Can I also get help on one of the questions in my review sheet? after this please


sure!


thank you


I haven't gotten the question you have for me yet


what do you mean?


im sorry my mac is acting up


i might have to leave the call


im so sorry


Hi, how can I help?


Hi


Solving  inequalities


Do you have any specific problem you working on?


I’ll put it one


On*


ok


It’s substitution


yes, you can do substitution


That’s the answer


But how do I graph it


so to graph it, we can find other informations from the equations, like x and y intercepts


Ok


Do you want to give it a try?


What should I do


okay, lets find y intercepts first for 2x-y=3


to find that you substitute x=0 in the equation


that would give us y=-3, so y intercept is (0,-3)


thats one point


now x-intercept, substitute y=0, find the x value


it should be x=3/2, and intercept (3/2,0)


that's two points


do the same for 8x+y=-18, find x and y intercepts


hello


Hi Michael!


What do you need help in?


iready


Did you put the material on the board?


no not yet


okay take your time!


here are the clues for a mystery number  the number is a decimal between 4 and 5 the number is closer to 4 than to 5


Is this the question?


The answer needs to be between 4- 4.5 since the answer is closer to 4 than five. So a possible answer would be 4.3.


yes


Does that explanation makes sense?


so what's the, answer


The answer could be 4.3


But any answer between 4.1-4.5 would be correct


Does that make sense?


Do you need help with anything else?


no bye


Ok thank you


Hello!


What questions do you have?


hello its loading on screen sorry


No worries!


Looks like it failed on my end


Can you see an image?


yah sorry hang on i will type it


Oh, there it is!


yay


I'm not sure I've seen this sort of problem tbh


Not off to a great start


its fine i promise


Do you have an idea how to get started without me?


I have an idea of something to try, but I'm not sure if it would work or if it's what you're supposed to do


not really this was work given to me when i wasnt there and i wasnt told how to do it


Let me get some background


What are you learning about in class?


Matrix multiplication?


yes


and add and subtracting matrixs


Do you know how to find the inverse of a matrix?


Ah, now we're getting somewhere!


Let me do a much easier problem to get the idea across


okay


I replaced the matrices by numbers!


Now it's easieer


Let me solve it super pedantically


I'm multiplying both equations on the LEFT by the MULTIPLICATIVE INVERSE of 3


Does that make sense?


Multiplying by the inverse cancels out the left hand side, leaving only B


Then I can do the multiplication on the right hand side to get the answer of 2


oh ok


Now, back to the real problem!


Let's do the same thing


Can you find the inverse of the pink matrix?


yes


Awesome! Go for it and let me know what you get :)


is that right?


One moment, math is hard


wait i did the wrong one


This looks a bit off though


What did you get as the determinant?


Or did you do the reduced row echelon form method?


my teacher taut use to swich a and d then swich the signs of b and c or is that wrong


Close! But that helps a lot


Let me put up the formula for my own sake


Otherwise I'll get confused :)


ok


Does this formula look familiar?


kinda


The determinant is new?\


yes sorry..?


For the 2x2 matrix, the "determinant" is ad-bc


that is the way she showed use


Nice! You might see things called the "determinant" in formulas. It shows up in various places


But for 2x2 matrices, you can just memorize the formula


In any case, let's try the inverse again!


okay


What does the 1/(ad-bc) equal?


Check the sign!


-9*1=-9  10*-1=-10   -9-(-10)=1


Swap the order in that last step!


we want ad - bc and not bc - ad


so it would be 1/-1


That looks good!


Written without the fraction, it would just be -1, right?


yes


So we can do the rest of the formula and get an inverse. Does that make sense?


Awesome! What do we do now?


find out how we get [-17 -7 -1 0]?


Let's go back to the easy problem and see what we did there!


What'd we do with the inverse there?


make it a fraction then multiply it on both sides?


The multiplicative inverse of 3 is the fraction 1/3


So 1/3 is already the inverse


then just the multiply part


But you're right! We multiplied on the LEFT by inverse for both sides


Can you do that with the matrices?


I'll right it out


Alex


Sorry, just realized I made a mistake writing the inverse


Should be a -10


math is hard :(


those cancel out and the other two equal to [-17 63 -1 0]?


Can you show your work on this part: [-17 63 -1 0]


Or, check your multiplication on the right hand side!


Ah, I see! That's not quite how matrix multiplication works


Let's do a refresher!


I'm going to scroll all the way to the bottom


k


Let's get the first entry!


Matrix multiplication is pretty weird, but do you see what I'm doing there?


yah


So basically, if we want the position in row i column j


For blue, that's row 1 column 2


ok


We multiply the ith row in the left matrix by the jth column in the second matrix


So for blue again, that's the first row in the left matrix times the second column in the right matrix


I didn't draw the arrows for those because that's too many arrows


But hopefully you get the idea


We can also check we found the right inverse before!


If it's the true inverse, we should get the identity matrix like we expect!


Let's do thje multiplication to see!~


Checks out!


Does that make sense?


yes


Awesome! Can you retry the matrix multiplication in the original problem?


[-8 -7 -7 -7]??


That's what I got! Although I do occasionally make mistaks


Any questions about anything we did here?


no


Perfect! You should be able to do the next problem without me then :)


Want to give it a shot?


Let me know what you get for the inverse and the final answer. And feel free to ask questions if you get stuck


okay


inverse i got 1/-10?


The full inverse should be a 2x2 matrix. Are you talking about the determinant term (1/ad-bc)?


Gotcha! Check your work. Be careful about the sign!


(0*2=0)-(-10*1)   0-(-10)=-10? then we put the one over it 1/-10?


Check the last step there


What's 0-(-10)?


what keep change flip so it would be 1/10


Yep! I can show you a really dumb trick


okay!


There's a lot of lines between the 0 and the 10


But if you squint, it becomes a big "+"!


lol kinda


Oh well, that's what I do in my head :)


Keeping track of sign is hard


But subtracting a negative turns it into addition!


one of my old teachers taught me keep change flip


That also works! Whatever's easier


Anyway, we found 1/(ad-bc) = 1/10


What's the full inverse of the [0 -10 1 2] matrix?


is it [1/5 1 -1/10 0]??


Perfect!


Now what do you do?


multiply that on both sides


Right! Then on the left, you get A


And what do you get on the right?


[-10 -40 7/2 11]???


Hmm, that's not what I got


I think I see what happend


Did you do this multiplication?


yes...


Ah, this is an important thing to keep in mind.


Matrices are weird]


With numbers, order in multiplication doesn't matter.


2*3 = 3*2


With matrices it DOES matter


oh ok


So if you multiply both sides of an equation by an inverse matrix, you have to make sure it's the SAME SIDE of both sides of the equation


ok


FWIW, you did do the multiplication correctly!


It's just the wrong multiplication :(


FWIW??


For what it's worth


I'm too old


nah i just dont get out much


relatable


so the answer would be [3 -9 4 -2]??


That looks right!


yay


Nice work on that one! You picked up matrix multiplication real quick


It's pretty weird and hard to get right in my experience


Any questions now?


well i had great help and no


Thanks! To recap:


These sorts of problems are just like the ones you'


ve done bnefore with numbers


like 3B = 6


It's just that everything is harder with matrices


You just kind of know the inverse of 3 is 1/3


yah def


But for matrices you have to do this whole thing


And the other critical bit


Is that the order of multiplication matters


so if you want to cancel the 3 in "3B", then you have to multiply on the left


for both sides of the equation


understood


Awesome!


Have a good rest of your night!


you too!


bye


Hi, how can I help?


I need help working on my review assignment


okay


9 review assignment: exponential functions


can you upload ?


yes


ok


State if each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, identify the common difference, d If the sequence is geometric, identify the common ratio, r. 32,38,44,50


can u unmute


my speaker is not working


I will type here if that is okay


An arithmetic sequence has a constant difference between consecutive terms, since the difference is the same each time, the sequence is arithmetic.


common difference d=6


yes that's ok


38-32=6, 44-38=6, 50-44=6


thanks


so this arithmetic


it is not arithmetic, check if it is geometric, find the common ratio


yes, he ratio is -5, so the sequence is geometric.


but how u know that


so first check if it is arithmetic, find the difference between each the terms like we did for the 1st problem


if they are not same, then it is not arithmetic


then check for geometric, find the common ratio


if the ratio the same, then it is geometric


here's how you do it


check the whiteboard


ok


questions?


did you get it?


so for arithmetic it has to be the same


yes, differences between two consecutive terms has to be the same


are you trying to clear the whiteboard?


no not the whole whiteboard just what I did


oh okay


So what does geometric mean?


A geometric sequence is a sequence where you multiply by the same number each time to get the next term.


oh ok


For example, in the sequence
2,−10,50,−250, each term is found by multiplying the previous term by
−5. That number is called the common ratio.


are you still here?


yes


okay


do you have other problems you want to work on?


no


thank u for the help


have a great rest of your day


you welcome


and you too


bye


hi Emma


hey


I need help with math review


exponentials


It says to write an exponential function for the graph that passes through 16 ,.


r u able to turn ur mic on


you can use mic. I'm not alone, and can't use my mic or speakers


(1,6) and (2,12)


was


How are you able to do this


(1, 6) or (1, 16)?


It's 16.


It's 1.6.


and an E parenthesis 212.


you said 16 , before


you meant (1, 6) and (2, 12)?


Yeah, that's what I meant. But when you say into the mic, it doesn't say it like that.


mic translation is not perfect


Yeah, you're right.


What's the formula for this?


this seems linear to me


oh, maybe we can fit an exponential to it


wait


give me a minute to think


plug in 1 for x and 2 for y. see what you get for a


ok


ah, that works


the y values of 6 and 12 made me think that 2 was the base


after that, you just have to try a few things to see what works


I think y=6 times 2^(x-1) also works


you still here?


I'm leaving in 2 minutes, again


yes


wait why


I was going to leave because you weren't responding


oh ok


sorry was doing something else


but I'm back


are you staying here with me, now?


got another math problem?


like the same but different points (1,2) and (3,50)


does any base come to mind?


this time going from x=1 to x=3


what is the base


the base is the number that you raise to power x


no, not 3


no


if x goes up by 2, that means the exponent of the base goes up by 2


b^1 becomes b^3


multiplying twice times base b, takes 2 up to 50


divide 50 by 2 and take the square root


so 5


yeah


2 times 5 once gets you to 10. times 5 again gets you to 50.


just need to find a


how to do that


plug in some known values for (x, y)


they gave you 2 (x, y) pairs


if you work on the board, I can help you.


ok


I can't stay much longer


and I can't help you if you don't put anything on the board


do you understand what I'm asking you to do?


is that the answer


yes


do u have to go


I can get you started on 1 more


might not have time to finish it


So the next question says rentals in a high-rise apartment building get more expensive, higher up since the you get better, the ground floor and 40 rent is


260, the rent increases 2% for waive the rent on the 6th floor.


I don't think that translated well


Rentals in a high-rise apartment building get more expensive higher up since the views get better, the ground floor rent is


1,260.00. The rent increases 2% per for waive the rent on the 6th floor.


waive?


No, it's what?


I'll read it one more time.


The rent increases 2% per for waive the rent on the 6th floor.


Rentals in a high-rise apartment building get more expensive, higher up since the views get better, the ground floor floor 0, rent is, so rent increases 2% per floor. What is the rent on the 6th floor?


The number is 1.260.00.


Is that clear?


if rent on second 1st floor is 2% higher than on ground floor, what number would you multiply times 1260?


no


twice as much is an increase of%


what is 2% as a decimal?


or 0.02


yes


so if we multiply some number times 1.02, the 1 gives you the original price and the .02 adds an extra 2%


1260 * (1.02) would be the price on 1st floor


if you go up to 2nd floor, price goes  up another 2%, so we would multiply times 1.02 again, right?


Emma?


sorry eating dinner


well, I'm going now to cook my dinner


Bye


bye have a great night


Hello


u there?


Hello!


hi


mics?


yes sure!


Hello?


Hi


How are you


I'm good. How are you? Can you hear me properly?


Yeah


Yeah. OK, great.


OK


So


what do you need help in?


Um


math


So, would, like, do you have homework of it?


No, not really. As I'm just trying to like


understand it more, I guess.


Mhm, OK, sure. So, um, what's the topic?


Um.


uh,


algebra


Algebra, OK. So is it like?


do you have a graphing? Do you have factoring


or is it just


Uh gra


graphing


Mhm.


So


let me


give you this


OK.


I will send you


OK


this. OK, I'm just gonna write it down and see if you can graph it for me.


OK OK


So Y equals


X


I think you can graph it for me


Uh


Have you learned quadratics


Like quadratic equations.


No


No, OK, I'm sorry. So,


let me give you


have you learned how to graph lines.


No.


No? OK, so what, so what


question would you get for graphing? Would you like


would they give you a graph and then ask you questions like the domain range.


Uh,


well, basically, I'm just trying to like, I don't really know because I'm homeschooled.


OK


Can you hang on a second?


Yeah, sure


Hey, sorry about that. I'm actually gonna have to go.


OK, no problem


Bye.


Bye


hello


Welcome to Charlie. How may I help you this afternoon?


Need help with a packet of work in a few minutes.


In a few minutes"


Yes.


I am not sure what you mean.


I need help with a packet of math work in a few minutes? What’s confusing


I don’t understand


Do you have a problem that you want to work on now?


I will during my lunch which is in 4 minutes.


Do you have time to wait of no?


Or


Sorry.  You should make your request when you are ready.


I don't hold my sessions open waiting.


hi!


Hewoo


Sarah :)


good - what can i help with?


Solving proportions :)


ok


we start by "cross multiplying"


oki


now multiply 12*12 and what do u get


now divide both sides by 11


so what is p?


or approximately 13


yep


next question? :)


well thanks for helping me


i just learned something new today :)


thank you!


I hope you have a great rest of your day Mr. Thompson :)


you too


Hi!


hi can you help me


of course!


okay


one sec


stay here in case you need more help


what about 455xx666


thank you


watch that real quick


ok


woah


that's innapropriate


69 x 4


oh ok


Hello, how is it going?


What can I help you with today?


I would like for a deep understanding for algebra 2


Like an overview?


Yes for solving quadratic equations by factoring


Oh, you would like to go over that specifically?


Or just an overview of what it looks like?


Just an overview


Alright, cool.


Well, I'm assuming you have some foundation with factoring quadratic equations, yes?


Like x^2+6x+9 - those types of equations.


Yes


Yeah.


Alright.


Well Algebra 2 expands on that (a little bit).


You might be asked to solve for the roots given a quadratic equation set equal to 0. I'll give an example:


(3n-2)(4n+1) = 0; solve for n.


You might be asked to solve for the following:


2x^2+8x+9 = 0; solve for x.


If it can't be factored, use the quadratic formula!


You might be also asked to factor a quadratic expression when a is not equal to 1.


Meaning the leading term is not x^2.


It would be like 2x^2 or even 5x^2. Anything than x^2.


You also might be asked to interpret different quadratic equations via word problems.


That's probably the core of what you're being tested on though.


I would assume there is nothing else, but if there is, you have the skills!


Alright thank you very much


Of course.


Is that all?


Yes that’s all thank you for helping me, I was having difficulty remembering but now I remember


Hi Jamie, I'm Chris, how can I help?


Could you help me with exponent rules?


For sure!


Just to clarify you mean things like x^0=1


yeah


or y^6 times y^6=y^12


Awesome, do you have any problems you want to work on or should I write them?


It would be fine if you wrote them


Cool, let's start with what an exponent literally means


6 to the third power is the same as?


Perfect!


how about y to the third power


(y)x(y)x(y)


Great, so how about y to 6th power times to y to the 11th power


in terms of powers


you don't have to write y x y x y x y etc.


y to what power


can you look at the board


this one is a little hard to write in this format


or actually let me change it a little


what is y to the 6th power to the third power


y to the 18th power


Exactly, because its the same as y to the 6th times y to the 6th times y to the 6th right


yeah


how about y to the -1


y to the -6?


not quite


well let's think


can you see the board?


if we have y to the third


it's y times y times y


if we take it down one to y squared


it's as if we divided y to the third by y


if we divide y squared by y


we get y to the first


if we divide y to the first by y


we get y to 0


and what is y to the -1?


which is 1 divided by y


what's 1/y divided by y


Perfect!


so y to the -2 is?


yep!


and y to the -3 is?


and y to the -8?


Amazing!


Does it make sense how we got there?


yeah


Great!


do you have to know how to raise a number to a fraction


like y to the 1/2?


no


alright, how about y to the 6th divided by y to the third?


Yep!


do you have to know how to do (w+x)^2?


and it is?


It's alright if you're not sure


im not sure


Well let's start with it in it's most basic form


(w+x)^2 =(w+x)(w+x) right?


so, how do we multiply (w+x)(w+x)


are you familiar with distributive property?


well if we have (w+x)(w+x)


we can do what's called the rainbow method


basically you multiply w(w+x)


and x(w+x)


ok


and add the result


so what's w x w


w times x?


wx


so that's w(w+x)


now what's x times w


xw


and x times x


Perfect!


and what two things can we combine


wx and xw


And they turn into?


wx + wx = w^2x^2?


not quite


Perfect


so we end up with?


Yep!


Want to try a similar one on your own?


sure


and 2(6x) is?


I think that's all


Anything else you'd like help with?


Exponents were what I was having trouble with


So no


Great, and exponents are now making sense?


yeah


or more you want to review there


Awesome!


If that's all see you!


Thank you


Have a good night


Of course, you too!


Hello Alice, my name is Ben! How can I help you today?


Hello


Im just looking for a topic we can talk about


Okay, what can I help you with?


multi step equations


Okay! Do you have a specific problem in mind?


alr like y=15x+23-21x+2


So first lets combine like terms! Do you see any?


15x and 21x


Yes!


ok next you do 15x-21x correct?


So what is 15x-21x?


it is


And what is 23+2?


Perfect!


That is our answer!


so -6x+25


The -6x+25 is as simplified as it can get!


ohhh


so y=-6x+25


ok thank you


Of course! Is there anything else I can help with?


slopes


like the graph


Okay, I only have around 5 minutes left, do you have a picture of the graph?


oh then nevermind then lets do 1 more multi step equation


Okay!


Okay try this one on your own and I can check it!


ok


done


Yes!!!!!!! That is right!!


Great job!


thank you


Yes! Have a great rest of your day!


alright bye


hi, how can I help you?


hi could you give me any 2 step algebra 1 regents question for practie


practice*


what are regents problems?


clarify for me a little more and I would be happy to give you some practice problems


maybe


sorry?


Expressions


okay


ill give you an example problem, let me know if that is not what you are expecting because I have not heard of regents problems.


try that!


what is 31-11?


double check that


oh sorry


correct! make sure to always plug x back in to the origional equation to double check you work. I will put another one up on the board


how would do a problem like this with fractions?


Is this different than what you usually see?


yeah


wouldn't 1/2= 0.5 ?


yes!


is x 32?


great Job!


do you want me to give you a harder question?


or stay at the same pace?


can we try Inequalities


of course!


I'm somewhat confused on these questions


thats okay! with inequalities, remember that when subtracting and adding numbers you can essentially treat the inequality sign as an equals sign. try to focus on isolating the -7x first! let me know if you need help


am I heading the right direction?


lets move one step at a time. the first step you made to subtract 2 is correct. rewrite the expression now that you have subtracted 2 from both sides and we can move on from there


so we keep the 9?


Subtracting 2 from both sides means that the right side is 9 - 2 so you can simplify that!


remember to keep the inequality sign


would it be -7x-2 < 9 or -7x-2 > 9-2?


since we subtracted from both sides we initially have -7x+2-2 <= 9-2. we can reduce the right side by subtracting 2 from 9, and 2 and -2 cancel each other out since -2+2=0. try rewriting the equation now. let me know if I am confusing you!


yeah I'm confused could you write it please


yes, of course!


now we can do the subtraction and we get


do you see what I did?


yeah 9-2


great! now what do we do?


I'm not sure


divide?


yes! remember that when we divide or multiply with negative numbers with inequalities we have to flip the sign of the inequality


1> x?


this question will be more clear if you keep the x on the left side! if we divide by -7 on both sides, what do we get?


yes! we get x <= -1, but remember that we have to flip the sign so what do we get?


correct! remember that it is -1 is less than or equal to x, as shown by the problem. do you want to try another one of these?


yeah


try that one, and let me know if you want ones that have fractions as answers or in the problem


correct!


oh ok


another one?


could I try a harder one


of course!


do I add 3? or subtract


you want to cancel out 3, so in this case you chose correctly, add, because -3+3 = 0


ok


Sorry about the space


all good


two things here. the first thing is that you need to double check 18/-6, and the second thing is to remember that we are multiplying or dividing by a negative, so we have to flip the inequality sign every time. try that again and let me know if you need help!


ooh I see


x< -3?


correct! want me to give you a different topic of your chossing?


yeah can we try Solving Multi-Step Equations


look at the top of the grid


try that one


can I combine the terms and subtract 3 from 20?


yes! this is because the both dont have x in front of them, so they are similar


could x be 5.6?


we have 3x+17 = 0, so remeber that we need to subtract 17 which gets us 3x=-17


*remember


so now what is the answer?


correct!


could we try a problem like this with fractions


fractions are confusing to me


yes! do you want them in the equation or in the answer or both?


the equation


try that


you can keep the numbers in fractions if that is okay with you and is like what you need practice for


could do demonstrate the first step please


yes!


what happened here?\


in order to subtract fractions we needed to have the same denominator, so i turned 2 into 10/5 which is the same thing but with the same denominator as 3/5 so now we can do the subtraction here


this is not necessary but makes the problem easier to do without mistakes, so if you find this method uncomfortable you can always do 2x - 3/5x in your head


oh ok


how would I subtract the fractions


is it 7/1?


the top is correct, but remember that when adding or subtracting fractions we keep the denominator the same!


hello?


so what would be the next step


well first what is 10/5x-3/5x?


correct! now what is the equation?


yes! now all that is left is to isolate x in one step


how


we divide both sides by 7/2, just like we do with any other time we have a variable times a number, say 5x = 1, we would divide both sides by 5


could you please do it on the board


what is the final answer?


I'm not sure


when we multiply a number by a fraction all we do is we multiply the numerator by the number and leave the denominator as is. try that now!


so 6x5=30 and now divide by 7?


correct!


so x=4.28?


yes


oh thank you for the help


have a good night


you too!


Hello


Hello! I am Riverside What how i help you with today?


can*


Understanding Numerical Expressions


I’m having trouble


alright


I can help you with it can you please tell me what you already know about it


Not much but all I know is that when it’s asking to multiply you got to put a multiplication sign in the expression


No problem! i will write an equation on whiteboard or do you have a specific question you want to work with...


So on my homework it says Add 6 and 9,and then multiply by 3


It’s kinda difficult for me


I got you no problem!


I put (6+9)  * 3


Yes..


first you add the 6 with the 9


Okay :)


And then it asks stuff like what’s 2 times the sum of 5 and 6


I don’t get that…


could please provide me the full question...


Okay


Thankyou


It says Write a Numerical Expression and one of the questions asks what’s 2 times the sum of 5 and 6 on the homework


And I don’t really know what it means by that


so first lets break it down it saying two time which we can tell the word "times" means multiplication and then we go to the second part of the question which says the sum of five and six which would be adding the both numbers up...


Okay so basically all i am supposed to do is add both of the numbers ?


yes let me show it to you on the whiteboard....


so basically your are multiplying 5+6 two times


which gives you an equation 2(5+6)


Do you think you got an idea of it?


Yes thank you @MathProAlex!


Your welcome!


Have a great great of your evening!


thankyou


hello


example.com this is real?


Welcome to Tutor Provider!


how may I help you?


I'm trying to make sure this is not an automated system, and that you're a real person


How can you make sure of that?


By asking


I am indeed a real person.


Lol ok


do you have a trigonometry questioh?


Im really just trying to find a reliable trigonometry tutor for my Tutor Provider.orge's failing 9th year and needs help.


Well, at this site, she will get a variety of tutors.


Great! Thank you for your Tutor Provider.netl have her download the app.Hopefully she can find the guidance she needs here. 🙏🏽 have a great day Liam


you too!


bye


Hi Lily!


hi


i need help learning natural base “e” because i wasn’t taught it yet


OK, do you know anything or are you starting from scratch?


starting from scratch


i think i’m gonna be applying this to exponential functions btw


OK, no problem. Give me a minute though?


ok


OK, so e is defined as the "natural base" becuase the the log of e to the base e is one. ln(e) = 1


I'll write it on the board.


but how does it relate to exponential functions?


like growth and decay?


So an exponential function is like e^x, so we're doing a power of e.


so if i had e^.25x would it be growth or decay?


So as x increases, what will happen to  y = e^0.25x ?


it will increase?


yes, because the exponent is positive, the result will grow.


and if i had e^-4x it would decrease right?


yes because the exponent is negative for positive x.


ok that’s all i really need to know is the basics


OK, can I answer anything else?


no i think im confident with it now thank you so much!


OK, then have a great day!


hello


what do you need help with


i need help with my hw


okay lets go through this


Maya


can you tell me what is triangle congruence


yes


its when in a traignle both traingle have same easure side and angles so two same triangles


do you know the different types of triangle congruence


HL, asa, aas, sss,sas


yess


okay so can you tell me what is shown to be congruent for both traingles


ok


do you know what the dash is on the side of the traingles


oh sorry iw as afk


/um


/yes


/those sides are same


congruent sides


good


quick question: do you watch taarak metha ka Ooltah Chashmah or cid


um i know about cid


nice


i believe you are right for this question


um


because vu is not congruent to pq


yh


this one


okay give me a sec to analyze


i know Tyche. its a greek goddess that refers to wealth/money


yes thats true


oh nice


do you know your reasoning for this?


/yes so


ima mark it on paper rq on this screen


k


i believe you are right


bc both are correct


do you need help with anything else?


last question


alright


i said none


for this


done


i know hindi cuz i am from Delhi


yea


to muje mera kam ches Arjun for ur time


sir


of course koi bath nahi


ok


Hi, how can I help you today?


i just wanna learn and take notes if thats okay


okay


thank you so much


im gonna grab my notebook


im back


we can get started


so what do you want to learn today? What do you want to work on?


we can work on anything


i just dont wanna feel dumb anymore


well, you are not dumb


so tell me what you are learning at school


we can start from there


im a dropout at the age of 17 trying to afford online, i barely have any credits when i left school


well that doesn’t make you dumb at all. You’re trying now, and that’s what matters. You haven’t missed your chance.


we can start at whatever you want


okay, do you want to work on "Completing the square"


or Factoring?


we can do factoring for right now


okay


okay whenever you wanna start


okay, let me grab some material first, few problems for us to do, give me couple minutes, will that be okay?


yes of course take your time


okay let's start with factoring out the Greatest Common Factor


Do you know how to do this one on the white board?


i could try


is the 2nd number 9x right?


yes


would the answer be 36x+9x?


no


So, Factoring is like unpacking something that’s been multiplied together


so here we have two terms 6x^2 and 9x, What do both terms have in common?


they both have x


what else


their both low numbers i think


or like they’ve always been multiplied


not always,  their both multiplied


okay we also have 6=3 times 2 and 9= 3 times 3, so do they also have 3 in common?


yes but where’d the 3 come from


3 comes from 9 and 6, if we write 9 as 3×3 and 6 as 3×2, they would both have 3 in common


okay i understand


look at the white board, to get 6x^2, we multiply 3 , 2 , x ,x.. so to do factoring we unpack


same goes for 9x


now looking at it what do you think both terms have in common?


they both have 3 in them and also have x


yes, good


but one has 1 x n the other has 2


yes, that they do not have in common


yes correct


we factor out what is common in both terms


so, lets factor 3x out


so then we’d be left with 2x times x


and 3


yes and we write that as 3x(2x+3)


does that make sense?


a little bit


okay, tell me where you getting confused


why did we only factor out 3x but we were still left with 3x and 3


so from 6x^2 we took 3x, so we are left with 2x, and from 9x we took 3x and we have 3 left


ohh


okay now i understand


okay good. now can you do 5x^2+15x


yes is it the same number for 3?


we have 5 and 15, what do they have in common?


they both the x and also have the number 5 in them numbers


good


so if we factor that out, what do we get?


2x + 1x


if were factoring out the number 5 thats what we’d get out of


it


but we do it with taking out the whole 15 itself it would be 2x+x


so x^2 means x-square, in case you are confused about that


now look at the white board


its the same problem as the last one


yes


so 5x^2 = 5.x.x and 15x=3.5.x , factor 5x( they both have that in common), so we get 5x(x+3)


okay, so 2x wouldn’t exist even if we took out the 5 because its a x square which also is part of the 5, so it would be x+3 instead of 2x+x


I thought you are getting confused about x^2, this is just x-square


thank you for letting me know i get confused sometimea


sometimes


that's okay


let me know if you get confused about any symbol that I am using


okay i will


okay do 15x^3+30x, x^3 means x cubed


okay


we would get 15x(x^2+2) i factored out 15


good


30 dived by 15 = 2 that’s where i got it from


yeah


you are doing very good


okay now we do something a little different


thank you, okay


okay, do you know how to do this one?


i think so


okay, give it a try


its a difference square because x^2 - 16= x^2 - 4^2 right


yes


one would have to be subtracted n added


yes, so what would be the factored form?


which would lead us to (x-4) (x+4)


im a quick learner when it comes to certain subjects


looks like it


just dropped out because my mental health got bad and wanna do online school but cant afford it so im trying to find a job to get the education i need


yeah, I understand


I dropped out too for my mental health


so I understand what you're talking about


i hope your doing better because its always a light at the end of the tunnel


i wish i could do tutoring so i could help and also provide for myself for my needs but i dont think im smart enough for that nor do i know how i could do it knowing im only 17 and nobody is looking for a <AGE> year old as a tutor


You should focus on getting better for now, you will be able to provide for yourself in few years when things get better


you are very young


so don't worry about that now


thank you, im proud of you for how far you’ve come if you havent heard that in a while


Thank you


Do you want to learn how to factor trinomials now?


im a little tired its late over here


okay


Get some rest, and good luck


thank you so much, it was nice meeting you!


hello


Hi can you help me with my trig hw?


ok


Can you put your problem on the board?


The value of a car t years from now is given by V(t) in how many years will the value of the car be about half what it is now?


Do you want to give that a try?


Would I just change it V(t)? Then start putting numbers in for t?


What is the value of the car now?


right. So whatwill V be would the car is half the value it is now?


right


Then that is the equation that you want to solve for t


First step is to divide both sides by 2


Are you able to do that on the board?


OK, do you know how to solve this kind of equation?


I think so can you see my board?


So far so good.


Now multiple 1/2 over?


I don't know what you mean.


take the logarithm of both sides.


How do you do that?


What course are you taking? this isn't trigonometry.


Thats the class I’m in is trigonometry. The paper says it’s Exponential Functions at the top but idk what she gave me it’s supposed to be trig though


Do you know anything about logarithms?


Some not a lot


I did it on the board.


Do you see it?


Yea I see it


Any questions about it?


How did you get t out of being a  power?


That's called the power property of logarithms. I will write it on the board.


that's why you take the take the log when you have a variable as an exponent.


Ok I understand that now. But yea she never taught us this stuff with logarithms yet


But I think I got it thank you


You are welcome


hello, are you still there?


It seems that you are no longer there.


Have a good rest of the weekend.


bye;


Hello! How can I help you today?


Hello , I need help with this problem


For the first part, they already gave us down payment and the total pay


Ok


So to find the percentage of down payment from the purchace price, we just do 45,000 divided 150,000 then multiply 100 for the percentage


Ok I’m doin it now


I wrote the equation out


Their down payment 45000, is (aka =), what percent (x percent) of (times) the purchace price (150,000)


Is the answer %30


30%, yes


Nice work!


Now it’s asking a 67,500 down payment would be?


Yes, which means we need to change the 45,000 to 67,500


The rest of the equation stays the exact same


It is just asking us what percent it would be if we switched the down payment to something else


So down payment price would be the only number that changes


Yes!


I got it correct


Awesome!


Usually the percentage symbol is written after the number :)


But the answer is perfect


Ok I uploaded a new problem


Okay, I see


The answer is d


Did the website say it was correct?


I'm not too sure about D, because I have some doubts on another answer at the moment


Not yet  I’m questioning my self


Honestly this question is also stumping me XD
I'm trying to figure it out too


C was incorrect


C or D? because you were thinking about D earlier


The correct answer was A


Now part b of the question is what’s the total cost of bill


It says the tip of 2.2 was 20% of the cost plus tax


So we can set x as the total cost plus tax


Ok


so 2.2 is 20% (aka 0.2) of tax (multiply by x)


So to isolate x, we divide


What is 2.2 divided by 0.2?


Yes!


So the total cost plus tax is 11


Now all we need to do is add in the tip


so 11 + 2.2 is?


Yep!


That should be the total bill, unless there was a computation error


Correct thank you


No prob!


Ohh, that would be why we didn't need to know the tax was 5%


for the original question


because we never used it to solve the total bill


Makes sense now


Yeah, it would have been a little better if the part a came last


Okay, for this one, the first part wants us to 285% into a decimal


Ok


to turn a percentage into a decimal, we just divide the percentage by 100


285 divided 100 is..


yep!


And what is the closest whole number that this decimal can be rounded to?


Yes!


so since we rounded 285% to 3, 285% of 40 is the same as 3 times 40


So 3 times 40 is..?


So a good estimate for that would be what we just calculated


Did I put 120 in the wrong spot?


No, that should be correct


I think 120 belongs in both spots


Because what we just calculated is a good estimate


The problem is right only 2 left and I’m done


Great job!


Alright, we have the bicycle 137, and helmet for 19


I think the first step would be to add it up, because we want to find the total cost


What 137 + 19?


So we found that the total cost is 156 dollars


And we also know that the total cost is (=) 130% of (times) the original price


Ok


130% is in percentage form, so what would it be  in decimal form?


So is 130 divided by 100


Not quite, because it is talking about the total cost


137 is just the helmet


I mean bicycle


So we added the bicycle and the helmet to get the total price


Now it says that the total cost is 130% of the original


Which means we can write an equation 156 = 1.3 time x


We set x as the original price


The 1.3 is the same as 130%


We just divided 130 to make it a decimal


(divide percentage by 100 to become decimal)


So we have to isolate x now to find the original price


What is 156 divided by 1.3?


156x1.3 divided by 1.3?


Aw I got it


What is your answer?


Yes! x is 120


So the original price is 120


So if the original price is 120, but Alex sold it for 156, how much did he make?


We just have to do subtraction for this part


Yep!


So we have 120 as what he originally spent, and 36 as his profit


Perfect I got it right


Awesome!


For this question, i think x is representing how much we spent this month


I’m thinking C


I would think the same


We can check it, or you can full send it


Next question says I spent blank this month


That means you just have to solve for x


So using your equation, isolate x to find how much you spent this month


140x30 divided by 100


Yes!


And that would be?


They bought it for 55, so that is the purchace price


And he sold it for 66, so that is the sale price


So what percent can be written as x/100


of the purchace price, so times 55


is (=) the sale price (66)


Now we just isolate x


66 divided by 55 is not 11, so I would check again :)


Yes, and then multiply by 100 to find the percentage


Yep!


Last one


This one, the purchace price changed from 55 to 45


And since sale price is 120% of the purchace price, we can find the new sale price


So we can set the sale price as x


Ok


and it is equal to 120% of 45, the purchace price


So 1.2 x 45 would be the new sale price which is?


So he sells each jacket for 54 dollars


Now we need to know how many he must sell, to make at least 260 dollars


We can set up another equation


This time, we put x as the number of jackets he sells


Because that's what we need to find


54 jackets was incorrect


We didn't finish solving


the 54 is his new sale price


in the other equation, we put x as the sale price


for this new section, we put x as the number of jackets


and since he needs to make at least 260 dollars, we use a greater than or equal to sign


So now isolate x and find out the amount of jackets he needs to sell to make at least 260


260 divided by 54


Yeah


What is your answer


It was a longer number


Got it, I need to recheck


Because we found out how many he has to sell


This answer should be fine


But we can't have a decimal


because you can't buy half a jacket


So we always need to round up


Which means he must buy 5 jackets, to sell them each for 54 and make at least 260


I didn’t know it was a pt 3 last question sorry


First box should be 5 I think


The top box is correct yeah


To fill this bottom part


We just look at the equations we used


Earlier we already found the percentage of the sale price


So we can use the exact same percentage


and we already calculated 120% of 45, so that answer is there already


Ok got that


The other box 54?


Mhm


120x54 6480


120 is the percent


before you multiply you have to turn it into a decimal


What are you solving for?


We never did x 54 in our solving


For the explanation part you basically just put in everything you solved beforehand


Last box is 5?


The very last box is 5, yes


But I don't think 120 x 54 is supposed to be in there


that would give us a giant number that we never even solved for


Oh strange


Scroll down the bar


None of those answers would be correct, because they don't match with what we solved for


I circuled it in red


To isolate x, it would be 260/54


Read the question carefully, because it wants a decimal answer for 260/54


You already have 5 as the very last rounded answer


so give the answer before it was rounded for the other box


Yep


All done thank you so much and good night


You're welcome


Night!


Hello


hello


How are you today?


i am fine, thanks.


That's good.


I am having trouble visualizing this. I think that I would end up with a triangle, but I am not sure which lengths belong to which sides.


I think that is what it looks like.


Okay.


I marked the angle of elevation


Okay... I am not sure how we could find that angle using trigonometric ratios. I think that is what I am supposed to do


what is x?


I'm not sure... would I need to solve for it using 4108?


the horizontal red line splits the line segment CE into two parts, x plus DE, right


do you have a question about that?


Could you please explain how we know that section would equal AB?


ABCD is a rectangle, right?


Yes


so then AB must equal CD.


CE = CD + DE


But CE = 4108 they tell us.


I did it all out on the board. Any questions about that?


No, it makes sense.


Good. Now you can use trig functions to find the angle of elevation


The method I used of splitting up CE into two parts is used frequently in problems like this.


Oh okay


I'm getting about 6.14


Yes, that's right. very good.


Okay, thank you.


You are very welcome


Can we do one more?


ok


OK. You should go ahead and draw a diagram


Okay


where is the campground on your diagram?


At the top?


where is the man on your diagram?


Oh wait, no


The man would be at the top, and the campground would be at the bottom


where is ground level?


not sure?


Yes


Let's start by drawing the ground level.


How high above the ground is the campground?


2405 ft


OK, put that on your diagram


How far above ground level is the man?


5389 ft


OK. now put the man on your diagram.


OK. Now put in the line of sight.


OK. Now it's a lot like the last problem, isn't it\?


go ahead and give that a try then


Okay, could you please explain what an angle of depression is?


the angle of depression is the angle with the horizontal, i drew it in on my diagram


Ohh okay


Would the missing side be found by subtracting?


What do you mean by "missing side?


That section, so one of the sides in the triangle


show me what you mean


I am not sure what you are referring to. Label it on my diagram, if you could


no, that is not the missing side


do you remember about the rectangle?


Yes, we had to subtract the length of the opposite side from the total


OK, go ahead and do that.  What do you get when you do that?


I will get the missing side of the triangle


What do you get for that?


yes!


Now you can figure out the angle of depression


Yes


Angles `1 and 2 are equal because they are alternate interior angles of parallel lines


Oh okay


OK, have a good rest of the day.


Thank you, you as well. Thank you so much for your patience!


You are very welcome


Hi Sarah! How can I help you today?


Hello I am Sarah's Parent I see she has been struggling in math, and I wanted to test this program out to see if it would help her.


Alright then! If I may ask, is this your first time trying Tutor Provider?


Yes it is


Welcome to Tutor Provider! We’re so glad you’re here. Our platform has many nationally certified tutors, myself included, and your daughter is absolutely in good hands. She’ll receive patient and good support every step of the way.


What topic in Algebra 1 can I help your daughter master today?


Not today I just wanted her to make an account and see how user friendly it is for her. So far so good I'll have her sign back in Monday


Absolutely! If you’d like to continue working with me, you’re welcome to schedule a session through DM after we wrap up today. And of course, you can always explore our other fantastic tutors here on Tutor Provider as well.


If you need any further help, feel free to make a new help request on your interface.


This concludes today's session. I hope you have a great rest of your day!


If you would like to schedule a personalized session with me, feel free to chat over here!


hi again!


hey'


can you help me with this one


ok


I don't know this one sorry


ok want another one


yea


one moemby


moment


hello


Hi I need help with an optimization question for AP Calc AB Unit 5


ok'


What are you trying to optimize?


the volume of the cylinder


How would you write the volume?


do you mean the formula?


yes


That equation for V has 2 variables.


can you see a way of getting it interms of just one variable?


can we find the radius or the height


In these problems you often have a constraint equation to help you do that.


do you know what I mean?


is the constraint equation the SA one


almost


can you write the surface area equation for this problem?


no because we don't know the radius or height


Use r and h for radius and height


okay


what should I do?


is it okay if I use my mic


I can't use my mic right now, but you can use yours if you want. write the equation on the board ifyou can.


Hi, so what I'm confused about is that um I have two equations surface area and volume. Um, and I know that I have to use like a constraint equation, but I'm just unsure like how I would figure that out and


um I've done like similar questions before, but this one, it seems very complex, so I'm confused what


equation you're asking me to write on the board.


what is the formula for the surface area of a cylinder?


The surface area of a cylinder is 2R2 + 2 rh.


However, they say that this cylinder has an open top, right?


yes


Will that change your formula in any way?


Would it just be 22.


I'm a little unsure which part


we would have to remove out of the equation.


there are two parts to the formula


OK, so if that's the case, then


I think it would just be two pir quad.


as the


end equation.


Sorry, I mean two RH.


Oh, wait, never mind, it would be


there wouldn't be two pie R squared, it would just be


high r^2.


+ 2 pi RH.


and what is the surface area of this cylingeder?


do you mean the end result of the equation


they tell you that the SA 700 cm^2, right


yes


the point of all this is that you can use this equation to express h as a function of r


OK, so,


would I have to isolate for H then?


with this equation


OK


OK, that's what I got, but then can I also um


cancel out


NR and a pie.


Or wait, not a pie. Well, yeah, I could.


NO!!!!


Oh no, I cannot. OK.


do you see why?\


Um


I don't really see why is it because the there's a negative pi and then there's a positive pi, and the art is R squared, but underneath it in the denominator it's R


But in the first term of the numerator, you don't have a pi or an r


Oh, I see. That makes sense.


you can't cancel just one part of a numerator


Oh, OK


Oh, OK. That makes sense. I understand.


So now, do I plug in


h the volume equation.


yes


OK. Um, do you mind writing because it's taking me a while to write. So could you please write um


volume equals pi r^2 multiplied (SA minus pi r^2).


over 2 pi.


Thank you


some.


Now do you just multiply the R squared into the parentheses.


Oh wait, we can cancel out the R squared.


you can cancel a pi and one r


OK


So I think it's gonna be


of


the


to


OK, I know that we have to find our


Do we


take the height and divide that by 2.


Oh, I see. That makes sense. I was a little bit confused at first because


I didn't know what to do with the


um with the R, so that makes sense now.


You want to find the maximum of V, right?


Yeah.


How would you do that?


To find the maximum, we first take the derivative.


and then we find the critical numbers.


and we put it onto a number line to see if it's a maximum or a minimum.


yes, or you could use the 2nd derivative test, either way


ok


So when we take the derivative of negative r cubed. What do we do with the pie?


pi is just a constant, like any other number


OK, so would it just be 3 r, I mean 3R2.


go ahead and take the derivative.


Is that the correct derivative?


no


where is pi?


Oh, so would it just be, since native pie is a constant


Would it just be 0, so 7


to the derivative will just pi/2.


Oh, we still keep the pie. OK, so would it be?


yes


-3 piR2.


OK


Now we set this equal to 0.


OK, so if we multiply each side by 2. We're just going to be left with


11 minus


And when we subtract 711.


it's gonna be 3 pi.


R squared. Let me just do this real quick and I'll give you the answer.


OK, so when I square r, I get 15.394.


But would I keep the pie?


What do you, keep the pi.


what happened to r in your equation?


OK, what I did was


I set everything equal to 0 and so I had R squad and I square rooted.


I square rooted 20037


please write on the board. I can't tell what you are doing\


you have an equation on the board that doesn't have r in it


OK, I will, one second.


Okay that makes sense because I had to round to 3 decimal places


OK, I am going to have to go in a few minutes.  Now that you have r, you should be able to figure out the height and the volume.


And prove that it is indeed a maximum


yes I understand what to do next. Thanks for all your help!


You are very welcome!


have a good week.


Thanks you too!


bye


Hello, I’m working on practice problems to prepare for my final next week. I’m focusing on Obj. 1,2,4,5,6,9,10,11,12,13,14,19,20, 21, and 23. I’m currently on problem 1 of objective 21. I haven’t done these in a while, so I may need some help. Here's the link to the pdf: https://example.com/math_problems.pdf


hi Sarah how can i help


I wrote them out on the board


so i do -3-6?


yup


are you sure?


do you wanna recheck the coeff of i


mhm


Sarah just to let you know i can only stay for 15 minutes


kk


answer is -9+3i


yes


Hello!


How are you?


How can I help you?


Hi


I´m doing good


I just need help real quick with an intergration question for calc


Okay


I´ll write it down on the board


Ok there it is


Let u = sin(x))
Then du = cos(x)dx


Do you know the next step after?


hmmmm


So then sinx would be to the third power?


Using a trig identity

Use the identity: sin(x)cos(x) = ½sin(2x)
So the integral becomes: ∫½sin(2x)dx = -¼cos(2x) + C


Does that make sense?


Ok let me write it out


OK


so what happens to the third power when you change it to the trig identity


I'm so sorry i confused it with a 2.


Let u = sin(x))
Then du = cos(x)dx

The integral becomes:
∫u³ du = u⁴/4 + C = sin⁴(x)/4 + C


[sin⁴(x)/4] from π/6 to π/2


Here are the steps. Let me know if this doesnt make sense. = sin⁴(π/2)/4 - sin⁴(π/6)/4
= (1)⁴/4 - (1/2)⁴/4
= 1/4 - (1/16)/4
= 1/4 - 1/64
= 16/64 - 1/64
= 15/64
The answer is 15/64.


the last parts make sense


Ohh wait


I think I get it now


since the du is the cos x we dont have to integrate it anymore right


Yep.


Ohhh ok


I think that was the part I was confused on


Sounds good.


Ok I´ll try working it out real quick and let you know how it goes


Okay Perfect!


Ok I got the same answer


Thank you for your help


Hello, I’m working on practice problems to prepare for my final next week. I’m focusing on Obj. 1,2,4,5,6,9,10,11,12,13,14,19,20, 21, and 23. I’m currently on problem 4 of objective 21. I haven’t done these in a while, so I may need some help. Here's the link to the pdf: https://example.com/math_workbook.pdf


Hi Maria. Do you have any specific questions that you need help with?


Yes, I don't know how to solve it I'm just confused


Problem of 4 of Objective 21, correct?


So for this specific question, we need to know what the conjugate is.


Yes


The conjugate is a number that has the same real part but the opposite sign on the imaginary part.


I tried to solve it by distributing the 2 but idk


Can you write it on the whiteboard


yes of course


for this question, we are going to find the conjugate of the denominator first.


Using the definition that I gave you above, can you tell me what the conjugate of the denominator is?


Wait no


That's not the right one


Its 8+6i/2i


I meant to say #5 lol


oh haha. no worries


Yes this one I am confused on


and stuck on I tried solving it 2 diff ways but idk


so this question is somewhat tricky, but it can be simplified if you know the key rule that 1/i = -i


let's first break up the fraction into two parts before we get on with using this rule


ok


do you understand so far, all i've done is seperate up the fraction and then simplify both


i thought it's (-i)


1/i is equal to -i


and that would be our next step


after that, we find out that our simplifed anser is -4i+3


do you understand?


I think so


that's awesome!


so the answer is -4i+3?


yes that's correct!


well 3-4i


oh ok it was that easy then lol i tried doing it a difficult way


alright now #6


so do you understand how to solve question 6?


-4x6 gets u -24


is the answer this?


so this is a problem that has to include an "i" somewhere


This is because we are taking the squareroot of a negative number (or -1) in this case)


yep


So instead of -2 root 6, it would be 2i root 6


because the i would then be the squareroot of negative 1


i thought its 6i


the i would not be under the squareroot, because i is the squareroot of negative 1.


Let's break -24 up like this (4) x (-1) x (6)


we could squareroot the (4) into a (2) and then we could squareroot the (-1) into an i. however we would just have to leave 6 as root 6 because we cannot square it


so it would be 2i root 6


Ok now


(3 + root 5) times (7 - root 5) correct?


yes


now i'm going to expand this


ok


so we would therefore get the answer of 26 + 4i root 5


do you understand fully how I got that answer?


David


let me solve on paper


Makes sense


Now obj. 23


which question specifically?


i got #8


yeah that's right


now #2


do you understand how to solve it or should i help you with it?


Hi! I was wondering if you could help me with a few problems. I put the first one on the board.


hello


I already tried this but got the wrong answer. I'll show you what I did


OK


I did 2 * pi * radius because that's the distance around the circle and then times 4800 gives you the number of revolutions per minute


I suggest that you use units.]


How many radians are in 1 revolution?


wait why did you set up the equation the way that you did


What is inside the parentheses is a conversion factor


Have you had chemistry?  This is similar to any conversion between units.


ok


the value of the quantituy in the parentheses is 1


why is it 1?


that is true of any conversion factor. It is 1 because the  numerator and denominator have the same value


but 2pi isn't equal to 1


that's not what I said


i had that the numerator and denominator have the same value


1 revolution = 2pi radians (and also equals 360 degrees)


oh ok


since I used the radius in my calculations, what question was I answering? because I wasn't finding angular speed.


We can get some insight into that by attaching units to those quantities


what does the 3.625 inches do to it though?


oh


so it gives the distance but not in radiand


It gives what is called the linear speed.


It is how fast the object is going in inches/minute


A basic point here is that every point along the radius of the saw


has the same angular speed.


But the further the particle is from the center, the faster is its linear speed


Okay, that makes sense.


Can we do another problem please?


ok


ok its on the board


amplitude of 1/2 means there should be a 1/2 in front of the cos


correct


in order to get period of pi/4 you have to divide the original period by something so I'll divide 2pi by pi/4 to get that


Almost, not quite right


What is wrong with it?


The phase shift is not corrrect


but if it were plus pi/8 that would be right because it would be going in the wrong direction


*wouldnt


That's not what I mean


There are two ways to write these, and I don't know which your teacher prefers. I will write it both ways.


but wouldn't that make it a phase shift right of pi, not pi/8?


I uploaded a standard form. Do you see it?


yes


why does th eperod multiply the phase shift?


*the period


Those are just exactly equivalent ways of writing a sinusoidal function


oh. ok


that was all for today. thank you for helping me.


When figuring out the phase shift, look very carefully to figure out which of those forms the person is using.


If it is the one I uploaded then the phase shift is just C


ok. but if its the one to ther right that you wrote on the board, it's not


But if they are just using one set of parentheses,


then its not


then the phase shift is C/B


That second A should be a B. Sorry.


I will write the other form below the upload


ok


Do you see the difference?


yes.


the bottom one is obtained from the top one by distributing the B into the parentheses essentially


yea, its more concise but you also have to do more work to figure out the phase shift


So be careful when figuring out the phase shift and check which form they are using


Exactly.


thanks for heling me today


You are very welcome


have a good weekend


you too


bye


Hi Leo! How can I help you today?


Do you want to work on this problem together?


yes that would be great


ik that BDE is right


so i selected that


that's right!


how do i find the value of y and x


Okay, so we see the in triangle BDE, one angle is a right angle and the two other ones are 4x and x right?


yes


Do you know the sum of all the angles in a triangle?


thats right!


using that, do you want to try set up an equation using the angles in triangle BDE?


could you explain for me step by step?


4x and x=180


I see! Because the sum of ALL angles in a triangle equal 180 degrees,


is this correct?


we have two angles of the triangle here


and we need to add the third angle into the equation


That's really close! But when we are looking at triangle BDE, the last angle is 90 degrees


Because its a right triangle


ohh


so replace 95 with 90


thats correct!


That's absolutely right!


how do i find y


so knowing that x is 18 degrees, can we replace the unknown angles on the diagram with actual numbers?


I can see where you are going! remember that y is not part of the triangle though


if y is not apart of the equation, how do i find y


Lets do this together!


So we know that 4x = 72 right?


yes


if angle DBE is 72, what should the angle vertically opposite, Angle ABC, be?


you got it!


So now we know two angles in one triangle, so can we find out what angle BAC is?


Remember that angle y is not the same as angle BAC


when we get angle BAC, we can then find out y!


ok


so BAC is 72?


your equation is almost there! 72 + 95 + BAC = 180- because they are all three angles of triangle ABC


is this making sense?


ya


great! Now we can solve for BAC!


using what equation


the equation you set up! just regard BAC as a variable and solve for it like you did for x!


can you show me


sure!


you've got 72+95


which equals 167


but the BAC is missing here


is this clear?


BAC is 13- thats correct


but do you see how angle y is not the same as BAC?


yes


angle y and angle BAC are on a straight line


do you know the angle of a straight line?


Hey Leo are you still with me?


yes sorry i have to go


thank you


That's okay!


Have a great rest of your day!


hello


Hi, how can I help?


would you be able to check my math homework its 5 pages first i am going to give you the transcript from the video that goes with it


Transcript: Narrator

(Scene Start: A person is standing among some broken stones in the background. Scene End.)

I’m Narrator. My friend Alice and I are working at an archeological dig. Sometimes the crew finds some pretty cool stuff.

(Scene Start: The person is standing near an inverted trapezoid. On-screen text reads, “Voussoir: [vu-swa] n. Trapezoidal shaped stone used to build an arch.” Scene End.)

Yesterday, we found this stone called a voussoir... vo-us-soir...vo-usso-ir..vou-ssoir...

It’s a stone shaped like a trapezoid.

(Scene Start: The person is standing with the background which has Romans arches. Scene End.)

What, you might ask, is a voussoir? The Romans created arches by stacking these trapezoidal stones together into a semi-circle.

(Scene Start: The person is standing beside another trapezoid which has the markings “84 degrees” on both vertical parallel sides and the label “Congruent legs” is present. Scene End.)

The problem is, we want to know how many stones were in the original arch, but, we only found this one stone.

Here’s what we know. The stone has a trapezoidal face with legs that are the same size, and each of the acute angles measure 84 degrees.

(Scene Start: A picture of another arch appears, where the trapezoid stones are highlighted. Scene End.)

Alice guessed that there were 9 stones in the original arch. She drew this great picture to prove it.

But I’m not convinced Alice drew the trapezoid with the correct angles. I think we need to recalculate the arch, based on the angles of our stone.

(Scene Start: The person is now standing beside the text “Were there 9 stones in the original arch?”. Scene End.)

Is Alice right? Were there 9 stones in the original arch?


tell me when your done reading and doing that this is the first page


okay, should I just check your answers?


okay


just let me know where your done checking the 1 page


The answers are correct, next page


next page ?


so in no 4, instead of saying it has both legs, I will suggest you write "this is an isosceles trapezoid because its legs are congruent and its base angles are congruent."


otherwise, it looks good.


yes next page


this are the 2 last pages after this there is 1 more and thats it


just telll me when your done checking if my answrs are right


okay, 5 and 6 correct


let me check 7 again


ok


CBD should 100 degree, I can be wrong though


can you double check?


for what question


question 7


180 - 80 equal 100 for tjhe Trapezoid obtuse angle and the other acute angles = same as triangle base angles = 80°


okay


But still think it should 100 degree


let me explain


okay i will change that from my side


so angle ABC+ angle CBD =180, if angle ABC is 80 degree, then CBD would 100


so fix number 8 according to that


so is it right how i put it like 7 on question in the text box


so the rest looks good


would you show me what to but for 8


is what i but in the new text box good in question 7


for no 7, it's okay what you wrote


for number 8, it is, 100, 80,80


so this is right The base angle being 80 degrees and so it will be for 100 degrees


yes


and for question 8 is this correct So 80 degrees and another 80 degrees for the top
The button angles of it will be 100 degrees and - 80 degrees = 100 degrees and it will then be for the trapezoid angles: 100°, 100°, 80°, 80°.


The base angle is 80°, so angle CBD must 180−80=100


could you do tell me what to write in question 8


i am lost


and for 7 also


so this is for 7 >The base angle is 80°, so angle CBD must 180−80=100


okay got it now for 8


so for 8, you can write> The top angles are both 80. The bottom angles are supplementary to 80°, so
180−80=100
so, the trapezoid has angles: 80, 80, 100, 100.


okay got it is question 9 good


yes, rest of them are good


so what i wrote is is good in question ?


let me double check


yes, it is correct


the idea is Alice’s 9-stone drawing gives 80° angles, but the actual stone has 84° angles.
Because the angles don’t match, her theory is wrong.


and you wrote that


so its right ?


yes


okay now check question 10 and 11


then there is one more page and thats it


okay, checking them again


okay


just let me know bc there is one more page left


okay after double checking I think, for 10, G and H (top) should both be 84.
E and F (bottom) should both be 96.


okay got it is 11 right ?


fix 11, according to 10


both 96


G= 84 H=84 E=96 F=96  for question 10


question 11 JEF=96 JFE=96


now can i add the last page


last page just let me knwo when your done


okay, on it


looks good


is it good ?


yeah


okay done i need to head out


good luck


okay thank you


its good right i need to turn it in


yeah, it is good


Hello!


Hi Sam!


What do you need help with today?


So im having trouble with congruent triangles, I dont know if its the way my teacher teachs or just math ingeneral i dont understand but i need some help like figuring out how to solve my homework


It questions 30 and 35


Sounds good


I see that the triangles might be confusing but when we go over it, you will know how to answer these questions


woohooo


Give me a second to go over the questions


okay take your time


Okay let's go over 30 first


Okay


What do you think congruent is?


When something is equal or liek the same as another thing


Good job! that's correct


What about isosceles triangle?


only 2 sides are congruent


That's correct!


So the statement in question 30 is that <PQT is congruent to <SRT. Can you show me on the board which angles this statement telling? or in other words, show <PQT and <SRT on the drawing I have on the board


those angles


okay that's right


If those angles are equal to each other, then what about the angles <TQR and <TRQ?


they are the same


Perfect!


Earlier you said isosceles triangle has 2 equal sides right?


yes


Therefore, now you proved that since <PQT is congruent to <SRT; therefore, <TQR and <TRQ are also congruent which means triangle QTR is an isosceles triangle!


I am not sure how your teacher answers these types of questions so let me know if you have insights to the way I answered above


its usually like this but we have to put it into a proofs chart


like that


oh okay


so when the question says given on the statement side i would put that <PMN is congruent to <ONM and the reason would be because its given


okay let's start with what is given


woohoo


do you want me to type it out?


so you dont have to draw


Yes


that's much better haha


wait what happened?


is that better


That's question 35


ohhh


I thought we were going over 30


But that's correct for 35


we are my brain is  just malfunctioning haha


haha


Good that's correct for the first part


so for number 2 we said that , <TQR and <TRQ are also congruent but what would be the reason for that?


or did i jump a step?


Then, we need to have some statement to why we think that TQR and TRQ are equal


the isosceles triangle theorem?


we can say that these angles form a linear pair meaning that since straight line 180 degrees


i see because all triangle angles add up 180?


That's true that Triangles adds up 180 degrees, but also straight line is 180 degrees


yes


ohh i see


What do you call it when something adds up 180 degree?


Guess what the reasoning 3 would be


supplementary


Good job!


Can you think of what we should say for 4?


uhh


<TQR and TRQ are congruent


I was thinking of rearranging the equation we have on statement 3


okay


how?


Algebraically


okay so what would it say?


Can you fill in the second equation on the board?


wdym?


I wrote the first equation on 4


and we need to have the second equation


i just see 4 blank?


how about now


nope


Do you see it now?


yes


Okay I will fill it in and you will help with the reasoning


oh, okay you actually did the reasoning


That's correct answer!


yayy


What should we say for 5?


transitive?


or definition of congruence


Yes!


wait which one is it?


definition of congurence


wouldnt that one be transitive property?


ohhh


Leo


Oh you are right that it is transitive but also we are defining congruency here


ohh i see


I think I like the transitive property rather than substitution so I will have that in the reason instead


ookay


What do you think the reasoning for 6?


congruent angles theorem


You can say that


You can also say this is a transitive property right?


yes


What is the reasoning for 7?


congruent angles theorem?


Almost there but not quite


What are we trying to prove?


that the triangle is isoscoeles'


Therefore the reasoning is what theorem?


converse of the Isosceles Triangle theorem


Mia


wooohooo


One last statement you can have is the triangle QTR is isosceles and then say definition of isosceles triangle for reasoning


i see


Good Job!!


thank you


Do you still want to go over 35 or you will try it yourself?


i can try it myself but that might not go very well lol


haha I understand


Do you mind if I erase what we have on the board for 30?


go ahead and erase it


35 seems complicated


just a tad


Let's to work it out together


okay


What is given in this question?


<PMN is congruent to <ONM


and <MPN is congruent to <NOM


correct


yayy


so would LM and LN be congruent


Sorry I had to go grab water


I am back


helllo


You mean the side LM and LN?


yes


So, we cannot prove that yet


Can you write the statement you had earlier on  1st statement slot


sure


like last time can you write the statement for definition of linear pair?


like that


Hi again.


hi  ijust wanted to ask about double digit decimals


Sure.


What do you want to know about them?


Are you working on that?


yes but where would i put the decimal


Are there any decimal places in the numbers you multiply?


infront of 72


Yes. And the number of decimal places will be whatever the total of decimal places is in the two numbers you multilply


ok thats all


So in this case, 56.16


That's a general rule you can always use.


thank you Sarah


0.78 x 72 = 7.8 x 7.2 = 78 x 0.72


have a good day


OK, you too.


hi Alex


Hello


I’ve gotten this much done of this function, though I’m having some trouble graphing it


the first one is wrong


Oh I see it


a good start would be to plot those points, one with closed circle and one with open


Alright that sounds good


good start


now we'll graph the function for x<=3


what kind of shape is it?


I’m not sure


is it in the form y=mx+b?


I think so


you need to know for sure


f(x) and y are the same thing


if it were that form, what would m and b be?


X


no


now do you see m and b?


below the graph image


are you gone?


your status shows as "is away," meaning you are no longer looking at this page.


I'll close the session in 2 minutes if you aren't back by then.


Bye


Hi Liam: How are you this evening?


i am good


hru


I need help on solving this question


Fine thanks, give me a sec plz


ok


i am stuck after here


OK, arcsec is the inverse of the secant function


yeah


and the sec is the inverse of the cos function


sooo arcsec and cos are = ??


I remember how to do this


Do you have a sheet of trig identities?


Look up secant


ohh yeah i remember that


can you solve it from here?


but isn't this arc sec


soo would arc sec = normal cos


howwould we solve cos of -2 if my logic is correct


arcsec is the inverse of sec, so if we are looking for arcsec(x), then sec (theta) = x


Multiply both sides by cos(theta)


and then divide both sides by -(2)^.5


i am confused


Plz go back to what I wrote and manipulate the equation to solve for cos(theta)


Basically, you just switch positions of cos(theta) and -(2)^.5


i am still confused


Can you ask a queston?


question


cause the answer key says that i was supposed to get 3pi/4


You will get that if you work with what I wrote


Can you rationalize the denominator of the left side?


yeah


Good, now look this up on your unit circle


You should see that it corresponds to 3pi/4


Making sense?


ohh so if i add the negative it will be 3pi/4 because its in the 2nd quadrant


yup


thx


my pleasure, anything else?


nope


actually


OK, take care


hello!


hi I have no clue how to salve a geometry question


show me it and I can help you!


ok so I got some of it right but to be honest I have no clue how I did


okay give me a sec to look at it


okay thank you for drawing the picture!


this is pretty how far I got


okay so the orthocenter is the point of intersection of the altitudes of the triangle. The altitude of a triangle is a perpendicular line from a vertex to the opposite side.


first we need to find the equations of the altitudes


I don't know how to do that


I will show you don't worry


could you guide me through it step by step


yes


ok so if I understood correctly first you need to find the slope of the segment opposite of the vertex and then you need to find the perpendicular slope


now I am finding the equation of the altitude


that's the part that I don't understand


so I don't understand why it would be y-5=1(x-0)


so I used point-slope form


where did you get -5 from


I used point M


the coordinates (0,5) x=0 and y=5 so you just plug it into the point slope formula I wrote in blue


so now you do the same for the other two sides


how do you solve the point slope form formula?


you just plug the x and y values in from a point


I don't really understand why we are doing this


the orthocenter is the point of intersection of the altitudes of the triangle.


so first we need to find the altitude


so we need to find the altitudes and then what point they all go through


yes I am finding the equations of the altittudes right now


so to find the altitude we first need to find the equation which you use point slope form


yes!


so the red is one separate equation and the blue is another one


yes


the red is for the altitude of JK and blue is for altitude of LM


now, we will find the intersection of the altitudes


you only need two lines to find their intersection


ok


now since both equations equal to y, we can use the other side and say they are equal together


now we will find y


by plugging x in


will the equations always equal to y?


or not necessarily


since we wrote them in slope intersect form yes


ok so if you use this method you don't necessarily need to graph the picture?


sometimes graphs aren't really accurate so calculation is more guranteed for a correct answer


I don't really understand how you got -6


im sorry I am really struggling with the ortho center


okay since in equation1, y=x+5 and in equation 2, y=-3x-19


they both equal the same thing, y


that means the values of  x+5 and -3x-19 are equal too


does that make more sense?


oooohh


but then why did we do y=x+5


you can use either equation and plug x in


since we know x we can use it to find y


ok so first you  find x and then you plug in x to find y?


yes!


ok thank you so much.


I'm going to write a step by step for you real quick


I get it now


yes please!


okay that should be it


this is great thank you so much


you can take a screenshot or you will be able to see it after the session ends in the session recap


ok thank you so much


of course! i''m happy to help!


thank you have a nice day


you too!


Hello, what did you need help with?


i need help with i ready


Okay do you have a specific question you want me to help you through?


You can either tell me it, draw it on the whiteboard, or import a picture


white board


okay great you can start drawing


do you know how to start the problem?


its okay if you dont


done


what was your answer?


i dont know yet


that's okay


since 13 can be written as 5+5+3, we can separate the fraction into these


5/5=1 so those can be 1s


and then just add the whole numbers


Do you understand it better now?


Okay I see that you are away so I


l  see that you're are away so I'll end the session here


You will still be able to view the whiteboard after the session in the session recap


Hello!


Hello


Did you need help on a question?


Yes, please


Do I need share my screen?


Yes


That or take a photo/screenshot and upload it to the white board on your left


Shared my screen


Ok one moment


I'm sorry I cant see your screen. Could you take a screenshot of the problem and upload it to the white/graph board on the left side of the screen?


Can you see it?


Yes I can see It! Can you explain to me what about the question your stuck on?


I have an idea on how to solve the question


But I need to know if I'm misunderstanding the question.


Alright! Can you start by trying to solve the question


Sure, in the chat or on the whiteboard?


The whiteboard


Is that the answer?


Yes! That is the answer


Great Job! :)


Could you help me with the second part?


It's a graphing portion.


Yes I can!


Just upload a screenshot of the second question


I tried to do it on my own


Hence the line


So, I'm just checking if that correct.


You're close! The Y intercept is correct but the line is wrong


An easy way help graph this is by inputting the Number of months into the equation


Since the plant's height started at 9 centimeters if we add 2 months the plants heigh would be 11 centimeters


I got the question!


Thank you!


Its no problem, Thats awesome!


Have an awesome day!🥳


You too!


Hi Liam


How can I help you today?


hi


can you estimate 0.76 x 62


Sure is that your question


yeha


show in standard form


Ok are you familiar with these kinds of questions?


kind of


ok I'll take it one step at a time


ok


first I'll be breaking the 0.76 into 0.75 and 0.01 ok?


why