the purchase 400.50$, will it increase or decrease the balance?


increase?


absolutely


would  i 2540.90 400.50


hence you see unpaid balance is increased 400.50 i.e. 2540.90 + 400.50 = 2941.40


kk


yes perfect, now let's move to line 3


its a payment, the final balance as per line 2 2941.40, the payment 638 will increase or decrease the balance?


oh nvm i did the math wrong i thought you 2540.90+291.40


it'll increase


once you have added 400 50, the final unpaid balance 2941.40, now we will forget aboyt 400.50 and only look at it when we move to the next line


ohh ok


As per the line, a payment decreases the unpaid balance


we add that to 2941.40?


what should you do?


think about it again, its a payment


oh it decreases


so subtract


not a purchase


yes perfect


im confused unpaid balance means it increases


i thought we add


so what will be the ans here


oh nvm unpaid decreases


just go by the question, a purchase increase the unpaid balance and payment decrease it.


yes absolutely


wonderful


line 4


now we add for the next one


yes!


very well


and is the 12 days part correct


look at the line one on the days part


from june 1 through june 7 = how many days are counted?


its 12 for 8-20


how do you think they calculated 7?


im just counting from finger


what fomula they used?


add


when you are counting on finger did you count both 1 and 7?


or both day 8 and day 20?


i did 8 to 20


so 9,10,11,12,13,14,15,16,17,18,19,20=12


but you missed day 8


thats not how u add


for instance if u add 6+2 you do 7,8 not 6,7


if you look at line 1, there are 7 days from June 1 through june 7


so its 13?


you don't seem convinced, let's look at line 3 - hopw many days are from june 21 through 24?


oh i see


they counted 21


now we 2540.90 times 7


2941.40 times 13


Yeah, so a general rule when you need to include both the start date and end date you do : 20-8+1


if you come across any problem where it's asked to find out the no. of days from x through y (both x and Y included) = y-x+1 is the direct formula


Only if both first and the last date are to be included in the calculation


are my calculations correct


yes absolutely


all the ans are perfect


now for total do i just add all of it or


just add


k


Now b


Okay, how do you calculate average?


idj


idk


generally, what's the formula to calculate an average?


add then divide


so if there are 5 people with heights 1,2,3,4,5; average height would be?


i mean thats 15/5=3


yes perfect


so in this case - the formula will be ?


average balance =


would i add the unpaid balances?


let's go step by step, let's write the formula first


average balance = total balance/total days?


oh so 84643.06/30?


yes!


did you fully get it?


mhm


correct :)


now b


c


i mean yea


what do you deduce from the question? what will be the interest?


ummm


read the underlined


oh so add the interest amount


you just need to calculate the interest for c


rate of interest = 1.5%
amount on which interest will be applicable = average daily balance

value of interest would be?


would i multiply?


sorry idk how to solve this part its confusing


No problem


let's look at interest in terms of principal, rate and time?


I = P*R*T


ok


have you read this?


mhm


so its PRT?


oh nvm p=2821.44


yes


give me one sec movin to the other room


no worries


back


Okay, so P = 2821.44


R =?


absolutely


T?


look at the question again


oh daily


1.5% interest for the month of june on the daily balance


so it means that 1.5% is monthly so T=1


what is n?


I = PRT


n stands for the number of times interest is compounded per year


o


oh ok


yeah, but we are not looking at compounding


we only need to find the interest for the month of june


now multiply all of that?


Yeah, but did you get why T=1?


u said it was


u said so T=1


yeah, i am asking did you understand why i did so?


Uh no bc it says daily and not month and u said bc of month


it says - an interest of 1.5% on the 'average daily balance (P)' for june


so it implies that 1.5% is for the full month of june and not a daily rate of interest. i


if the question had said 1.5% per day on the average daily balance then T would be different


oh i see


In this case question says that 1.5% interest rate for the month of june. hence we took t=1 because we are only calculating for June


Hope this is clear, you can ask if there is any doubt


Now d


what do you understand from the question?


so


so we have to add 42.32 to something


what do you think is something here?


the 84643?


what should you pay at the end of june? the amount you have spent right? in this case - did the person spend 84K?


thats the unpaid balance


thats the unpaid balance X number of days


what's the unpaid balance at the end of june?


after the last transaction?


try again, when we calculated the last column = we did unpaid balance X no. of days


the question is only about unpaid balance


so after the last transaction what is the unpaid balance?


read the line 4


ok


what's the unpaid balance?


great, was there any transaction post june 25?


june 25-30


no transaction in this period right?


no purchase or payment?


so whatever is left unpaid at the end of july + interest will be the begining balance for july : is this understanding correct?


yes


so what do you think is the ans?


i would add the 32k to the 42?


it will be 3.234K + 42


ignore the K thing


yeah ik


let's focus 3234.16+42


perfect


you have done a great job with this one!


Hope this session helped


Do you need any other help


Yes I have anotherone


ok sure


let me look at that


giveme one sec


i have another 10-15 mins to spare


its exactly the same problem, you should be able to solve it quickly if you understood the last one. Give it a try.


yes


2 days


you can also find the days = 5+x+10+14 = 31


you don't need to count always


if there is only one blank in days and total is given as in this problem


2552.44 for a


yeah


take a look


yes 100%


u!


thank you*!


Hello!


What do you need help with?


i need help with some homework


sure


could i share my screen with you?


yeah!


huh it wont let me


ill js screenschot


ok!


can you see it?


yea


ik its a vertical shift up


is there a specific part u need help with?


yes that right


but i dont really know how to find the value of k


basically i need help with them all but 3


do u know waht the vertex formula of an equation is ?


parabola equation


i dont think so..


ill wirte it


deos that look familar


a little yes!


do u know what h and k represent?


no..


sorry i was absent when they reviewed this so im kinda lacking on this part


its oki


sorry my computre is being slow


h is left and right shift


its okay!


so what could k be?


uhhh could you do it by step for me?


wdym


i don't get how to solve it


Hello


Hi I am confused how to do this


No worries, for this question, to find the equivalent fractions, we can go 1 by 1.


For each number line we need to find how the space between each dash.


Do you know what the space between each dash is for A?


Almost, that's the number of dashes total.


How many dashes does it take to reach one?


What do you mean?


How many spaces are between 0 and 1 for A?


Yes


If two spaces make 1, how much does one space make


Almost


In A, since two spaces make 1, one space must make 1/2


Does that make sense?


Ohh ok


So if each space is 1/2, what number is the dot at?


I can help you with this one


The dot is 6 spaces after 0, so we can do 6 times 1/2 to get 3


Ok


I actually have to go soon. But you just have to do that same process for all of the options and select the ones that get the same answer.


Hello


Need help with Trignometry tutoring.


do you have a problem that you are working on?


Hello?


It’s called trigonometric functions of acute angles


That’s the topic name


ok.  Can you show me a problem that you are working on?


Can you teach me topic wise my school just started


What have you learned so far?


Supplementary and complementary angles standard position quadrant of an angle


Sorry, I don't have a lesson planned for this.  As a tutor, I usually help students with their homework. It might be better if you made another request.  Sorry.


I can get back to you tomorrow with the homework


Sounds good.


Have a good evening.


You too thanks


you are welcome.


bye


hi! how are you?


Liam!


good how r u?


I'm good too


what do u need help with?


I was wondering if you could help me with an algebra assignment


yea sure


do u know how long it will take


aprox


I only have one question I need help with


oh ok


what is it?


can u make it a ittle bigger?


thanks


do u know what to do to find x-intercepts?


she didn't really explain it well when I was in class


set y=0


or in this case f(x)


ok


so u can solve for x


ill write it


can u see that?


yes


can u solve for x?


k


7/3 and -3


yes!!


so thats ur answer for A B and C


does it make sense?


do u want to try doing D by urself?


or do u need help?


Yes!!


u got it!!


thank you!


does it make sense tho?


ok :)


I hope you have a good night


u too


hi could you help  me out with this?


Hi  How are you?


good


Ok. Let's see your integral.


this is all ive got so far


Ok. Give me a couple of minutes to think on this.


ok


It's clear that the base can be represented by r^2 + y^2, since it is a circle.  Do you agree?


yea


Now each "square" It seems to me, has a side equal to 2r.  What do you think about that?


yea i agree


Ok.  So I think we need another relation ship to set up the integral.  Any thoughts?


that area of the squares is s^2


So.  In this case each "square" has an area of 4r^2.


why


Well, if we agree that each side of the square is 2r, then the area of a representative square would be (2r)(2r) = 4r^2


ohh yes ok


Now.  We already know that r^2 = x^2 + y^2


What we need is some relationship between x and y so that we can integrate over one variable.


Give me a couple of minutes to ponder that please,


Alright.  I think we were close.  Just a bit off.


So the circle is x^2 + y^2 = r^2


But the side of each square is really 2y, not 2r.  r is a constant, so that doesn't work.  Do you follow?


ohh yea i see


so the vertical y values change


Exactly.


So let's set up our integral to be a(x) = (2y)^2 = 4y^2 dx.


But y^2 = (r^2 - x^2)


So.  You get Int(r^2 - x^2) dx over the limits.


Would you write the integral on the whiteboard please?


ok


like this?


Excellent.  Let's talk about the limits now.


im still kind of confused why we got 2y again where did the 2 come from


Ok let's back up.


Take a look at the diagram again and focus on the squares.


Each one varies as shown by the vertical slices in the diagram.


yea


Now.  If you focus on a typical square, especially the one at the center, you will see that it is the same as the diameter of the circle.  That one is 2r for each side.


The other ones are smaller, as you look at slices off the center.


The relationship to determine the length of the other ones is (r^2 - y^2)^(1/2).


Is that making any sense?


yes so that's = x?


Yes!


Very good.


We can use either x or y to integrate here.  We just have to choose.


The limits for the x must run from -r to r


Think of the circular base as centered at the origin.


wait but how does that relate to (2y)^2 being the area??


That is precisely the integral you set up.


(2y)^2 = 4y^2 = 4(r^2-x^2)


Then you sum up each thin slice of an area over the limits.


I'm not sure I'm addressing your concern.


but why is it 2y and not 2r?


r is a constant.  Like 4, 16, etc.


It does not vary.


why couldnt it just be y?


It is the radius of our given circle


why can't the entire height just be y then


if it vaires


If you imagine the view from the top and think about the center slice...


It is exactly 2r by 2r


yea


But other slices are shorter


They can be represented by 2y by 2y.


That is 4y^2


so are we saying r=y?


and just not using r because it's a constant


Let's back up.  I feel like I'm not answering your questions.


ok


Think of the circle.


It's the at bottom of our structure.


It is sitting with a center at the origin and has an equation x^2 + y^2 = r^2


Now if we construct a very thin square over the origin, it would be 2r by 2r.  Do you see that?


yes


Now.  This the leap of faith.


Each of the squares have sides that get smaller as we move away from the center.


Their sides are like 2r, but smaller.


The relationship is expressed as 2y by 2y.


That is the area of a "representative" square.


It's not just y^2


so y is just a smaller rep version of r


When compared to the very center slice.


Yes.


could it also be (2x)^2 if i wanted to take the integral in terms of x?


Yes.  Then the integral would be using the y variable and dy


It is the same.


ok


Now.  If you buy all that..


We must set the limits of integration.


ok i get it


The lower limit for x is -r and the upper limit for x is +r.


So.  If you buy that, change a and b to -r and r


The reason for this is those are the smallest and larget values of x.


largest


Questions?


It may take a while to "sink in."


no i dont that makes sense


Ok.  Let's finish the easy part and inegrate.


integrate.


Let's change a and b to -r and r


Good.  Want to take a shot at integrating?


not really the 2 variables is throwing me off


Remember r is a constant.


There is only one variable, x


So the integration would be as follows:


4[(r^2)x - (1/3)(x^3)]


isnt it 4/3


not 1/3?


or (4r^2)(x) - (4/3)(x^3)


ok


There are two terms to integrate.


The first is simply a constant.


So, it becomes 4r^2(x)


The second is as you said.


Ok. Now we plug in the upper limit of r to give 4r^3 - (4/3)r^3


From it we will subtract the lower limit evaluated at -r


Give me a minute to calculate


i got this


Should give a final answer of (16/3)r^3


oh what did I do wrong ://


The last term should be negative


8r^3 - (4/3)r^3 - (4/3)r^3


8r^3 - (8/3)r^3


(24/3)r^3 - (8/3)r^3 = (16/3)r^3


Just simplify what you have and you will get the same answer


ok got it


That was a lot.  You hung in there!


I think it will be easier to visualize as you get more experience.


I like that you questioned things!


thanks :))


it made sense thanks for explaining


I do have 2 more like this though :(((


These are not easy!


Let's see another.


ok :))


Let me think for a few minutes.


Ok.


what are the length of the major and minor axes for the ellipse?


not too sure


So the ellipse in standard form is x^2/2^2 + y^2/5^2 = 1


So. the ellipse runs from -2 to 2 on the x axis.  And -5 to 5 on the y-axis.


Does that make sense?


how did you get there


to the standard form


divide 100 on both sides


Right.  Give me a couple more minutes please.


ok


All right.  This is going to be similar to the last problem.  Put on your thinking cap!


So.  We can picture triangles just like the squares we had last time.


And you are right that area is (1/2)bh.


We actually know that each base of the triangles is exactly 2y.


Do you see that?


Think of the largest triangle at the center if that helps.


Jamie, are you there?


yea


sorry i went to the bathroom


Let me take a break also for a couple of minutes, ok?


sure


I'm back


So.  We've got all these isocelles right triangles that have a base of 2y, does that make sense?


yes


Good.  So we want to get the area of a representative triangle and then integrate over each thin slice, dx.


Now.  We need to formulate the area of a representative triangle.


Let's call the each leg length b.


Then, by the Pythagorean Theorem b^2 + b^2 = (2y)^2


wait isnt b the base ie the hypotenuse


Think of these triangles coming to a point at the top wthe base being the hypotenuse.


We can use another variable if that confuses you.


yes please


Ok.  Remember that each triangle has a base (which is the hypotenuse) and two congruent legs, let's call them s for sides.


ok


Then for each triangle, (2y)^2 = s^2 + s^2


By the Pythagorean Theorem.


Tell me if that makes sense.


makes sense


Good.


So 4y^2 = 2s^2


and s^2 = 2y^2


Right?


yea


But the area of a triangle is (1/2)(s)(s) = (1/2)s^2 = y^2


Ask questions if it is not clear.


that last part didnt make sense


glad you stopped me


So.  We are visualizing all these very thin triangles with bases lying on the floor which is shaped like an ellipse.


We know that the hypotenuse of each of these triangles can be represented as 2y.


Now each of these triangles happens to be isoceles right


So.  We want know what the side are.


The Pythagorean Theorem says that (2y)^2 = s^2 + s^2 for each of these triangles.


ok


They have congruent sides


4y^2 = 2s^2 simplifiying.


s^2 = 2y^2 further simplifying.


But notice that if we multiply each side of this equatio by 1/2, we have the area of a representative triangle


Do you see this?  It's okay if you don't


no i don't


Glad you stopped me


I think you followed to the point where we said s^2 = 2y^2.  Correct?


yes


But the area of a representative triangle is (1/2)(bh) = (1/2)(s)(s) = (1/2)s^2 = y^2.


oh so the height isnt like what i had in the drawing


on the board


its s?


s is the leg of the triangle.


h is not involved in the calculation.


You have the two congruent sides - each is s


is bh=ss?


(1/2)(bh) = (1/2)(s)(s) = (1/2)s^2


We are not using the h you have marked on your triangle.


We are using the legs of a isosoles triange.


We are kind of going around in circles


ok


Please ask me some question.


s


why the legs for b and h


and not the general height


Please draw me an isoceles right triangle on the board.


this?


Yup!


Now label each side s


Great!


Now calculate the area of that triangle, please


The base is s and the height is s


So what is the area?


ohh ok


What is the area if the base is s and the height is s?


Right.  (1/2)s^2


But since s^2 = 2y^2, (1/2)s^2 = y^2, the area of our representative triangle.


ok


makes sense


I hope I'm not confusing you more than helping.


no this helps


Ok.  Good.


Now we are ready to set up our integral.


Since y^2 is now the area of a representative triangle,  We can integrate it with respect to x.


First would you solve for y^2 from the original ellipse equation, please?


this?


I think y^2 = 25 - x^2, if you go back to the original equation for the ellipse.


I'm sorry.  YOu are right!!!


Now let's think of the limits for our integral\


Recall that the x-axis runs from -2 to 2.


ok why is that?


When we standardized the ellipse equation, we got x^2/2^2 = Y^2/25 = 1


ok got it


That means the left most point on the ellipse is at -2 and the right most point is 2.  Do you see that?


Great


Let's write down our integral with limits.


ok


You've got most of it right there.


let me paste in my answer


i 200/3


Let me calculate for a minute


You got it!


That is correct.


yay!


i have one more and it seems easier than these


if that's okay


OK


Let me read for a few


Ok.  Have any thoughts?


Great start


im stuck


Too complicated


Let's think about the representative squares.


ok


Write me an equation for the line that connects the x and y axis.


please


Super!


Now.  Isn't true that y represents the side of the square we want?


length


yes


So,  isn't it true that the area of a representative square is simply y^2 = (5 - x)^2


so a(x)=(-x+5)^2?


Indeed!


What are my limits for x?


0 to 5


Fantastic!!!!


Crank it out my friend!


i got this :))


Yes you do!!!  Great job. :)


thanks so much for explaining all of this with me :DD


This was my last question so I shall take a break now


YOu are quite welcome and very deserving


have a nice rest of your day :))


Bye


Hello! I need help with this.


Hi Alex!


Hi!


I solved this a little but idk if this is correct


Or if this is the correc way to solve


for the 9%


Because we are given the total interest, I think that we should combine the two accounts into one equation


Oh it says "each"


So I thought seperate


That is a good point, but we want to solve the combined equation first and then we will get both parts


Ok how would I do that then


Let's start with the 9% account: We know that the 1 year interest will just be 0.09 times the amount invested


What should we use instead of x for the 10% account


oh


ummm


b?


Keep in mind that x and this must add to 15000


ok


we can actually use 15000 - x, because 15000 - x + x = 15000


That way, we simplify the problem into only one variable


And finally, what does this equation equal?


perfect


How should we solve this equation?


distribute


That is actually 1500 because we distribute the 0.1 to the 15000 as well


o


And that should equal because 1500-1432 is 68


Nice job!


So that is the amount invested in the 9% account. How should we find the amount for the 10% account?


yep


would we add that number into x?


6800 is our x. There is something that we can do with substitution here


hmmm


oh


put it in the parenthesis?


So close! We do use the 15000 - x. However, 6800 is our x value. So, the amount invested in the 10% account is 15000 - 6800


Ohh I see


Yes! 6800 was invested in the first account, 8200 was invested in the second account


yep!


I have another one that looks confusing


like i dont get it


I think we will be able to do it :)


it says "find the union or intersection of the given intervals. Write the answers in interval notation."


Ok! I always like to use a number line for tricky interval problems


ok


Could you draw the first interval on the number line for me?


-5 and 3?


oh nvm its not negative


they are already on the line


5 and 3


I will show you what I mean


this?


Just so we can see the interval


Now, it is a lot easier to see where these two intervals intersect!


why is one open and one closed like the circle


We have an open circle at the 5 because, if you look at the interval, there is a parenthesis as a bracket. This means that the number 5 itself is not included in the interval


Ohh ok


There is a closed circle at 3 because of the "hard" bracket in the interval in the question. This means that 3 is included


let me write this on my paper


so 3 is closed 5 is open


Yes


ok


oh bc 3 has bracket and 5 has parenthesis ok gotcha


Right


ok now what do we do next


Now that we have the intervals lined up on the number line, we just need to find where they overlap


at 3


Yes. And where does the overlap end?


it ends at 5?


Exactly. Is 5 included in the overlap?


It actually isn't because of the open circle on the first interval


oh so 5 starts it off


gotcha


oh nvm


no


5 is overlapping 3


The overlap goes from 3 to 5, but 5 is not included


oh


why


As you drew on the line, the overlap only happens where the two intervals are on top of each other. We know that 3 is included, and that the numbers between 3 and 5 are included.


However, 5 is not included because, while the second interval includes it, the first one does not (because of the open circle). To be in the overlap, both intervals have to include 5 which the first one doesn't


Ok I see


so the overlap ends at 5 because that’s where the two intervals stop overlapping?


this is why 5 is not included?


For it to be overlapping, both intervals have to include a point. They don't overlap at 5 because of the open circle (the first interval doesn't include 5)


yeah so 3 starts it and it ends at 5?


Yes, and 3 is included and 5 is not


yep got it


so it should be written as [3,5)


This is actually problem 87b*


Exactlu!


i thought we were doing the first one


bc im writing this on paper in order to turn in


let me just erase it rq


I missed a detail with the symbols they gave (union vs intersection


The problems aren't very different, so you can keep the two interval lines on the number line


Sorry about that!


its ok i fixed it


what does the upside down U mean


That means the intersection between the two intervals, which is the problem that we did


Ok


now for A


Problem a wants the union between the two intervals


ok


lets start


What do you think we should do to find the union between the two intervals?


draw the lines again?


Yep. Now the union means that we essentially combine the two intervals into one.


We use the word "or" to describe unions, and "and" to describe intersection


So the answer will be the interval of all points contained in either interval


would it be 3,5 again or?


Here, we can use the number line and want to find points that are not included in either interval.


Are there any points that aren't in either interval?


uhhh 12


4 is included


That would be correct for intersection. For union, we want to find points that aren't in EITHER. For example, 1 and 2 are included in the first interval. So, they are fine


let me redraw my line


a lot of numbers are included


Yes. Are there any numbers not included?


Let's try putting the intervals together to visualize this scenario better


ok


its like 1-10 are included


Actually, everything is included from -infinity to infinity.


The combined line never ends. The only interesting point is 5 because of the open circle. However, we only need one interval to include 5, which the second one does


ohh yeah


I am glad that makes sense! Union is a very difficult concept to understand. Nice job with it!


Wait so


I'm still confused bc idk what the answer is like


is it 3,5 again?


So because the combined line never ends (all points are included in the union), the interval is (-∞,∞)


Does that make sense?


so for the steps we


combine the two intervals into one?


Yes, that is a great way to look at it


step 2. see if any numbers are not included in the line


Yep, and the answer is the interval of numbers which ARE on the line


step 3 every # is included


For this problem, all numbers are included


yep


i have one more left


if you Ben have time


Of course!


ok


lets work on A first


Sounds good! Do you want to try to draw the intervals on the number line for this one?


sure


done


The second interval should go to positive ∞ actually


oh i see


from -4 to positive ∞


so this way?


and closed circle?


Yes


Now, this question is asking for union again. Try to solve it using our steps!


That is correct, but that is for intersection which is problem b


ohhhh


so combine the intervals


into one


yes, and then look to see if there are any places not covered by the line


kk


all covered


so negative infinity, positive infiny


exactlu!


and thats it?


for a?


yes


now B


For b, we look at the overlap, which you correctly said was the interval [-4,-1].


find where they overlap


mhm


starts at -4 ends at -1?


Yes


thanks so much for your help! :)


Of course, great job with that material!


Hi, how can I help you today?


hi!


I need help with this one problem


Great!


What's confusing to you?


everything


Ok, let's see if we can find a starting point!


Are these two images part of the same question?


yes


Okay, let's start by defining the question


What is the problem asking?


to find the angles of m<a, m<B, and m<C


and to round our answers to one decimal place


Okay, and we have all the side lengths


Sorry, do you mind if I ask what the dropdown menu says on the first image>


oh yea


Law of Cosine or Law of Sine


Ok! Can you tell me the difference between sine and cosine?


If you can't, that's okay, we'll go over it together!


I got it


I'm typing them rn


Sounds good!


Sine (0) = opposite/ hypotenouse


Cosine (0)= adjacent/ hypotenuse


Ok, those are perfect!


I'm a little confused because the triangle in the picture doesn't have a right angle, so it wouldn't have a hypotenuse


We can't use either theorem because there isn't a hypotenuse


could we use Pythagoras


The trigonometric functions only work on right triangles!


oh


So sine, cosine, tangent, etc, don't work unless there's a right angle


I'm not sure what your teacher wants us to do here, did they ever bring up triangles with no right angle?


no


I'm doing geometry online through University of Phoenix


Hmm


You said the first and second images are part of the same question?


yes


Then I think the answer is going to have to be no solutions


ok


Wait, actually, hold on one minute!


Okay, I was mistaken about the Law of Cosines, sorry!


The law states:


a^2 = b^2 + c^2 - 2bc * cos(A)


b^2 = a^2 + c^2 - 2ac * cos(B)


c^2 = a^2 + b^2 - 2ab * cos(c)


I'm going to insert an image to help visualize it!


I see it


Ok!


Does it make sense to you?


So for the first question, you can say we'll be using the law of cosines


Then to find the angles!


Can you try plugging m<A into the formula?


um sure


15^2 = 15^2 + 17^2 ?


I don't know if that's even correct


To make it easier, I'm going to show how the angles and sides on your triangle align to the one in the picture, because it's really difficult to tell right now


And then we can do it together!


I'm just going to rotate your triangle so it looks like the one in the picture


well doesn't 14 in line with B on the picture and  15 in with a and 17 in with c


oh I was way off


Haha, I hope this picture helps a little!


it does for sure


So now, do you want to try plugging in again?


yea


17^2= 15^2 + 14^2 - 2(15*14) * cos (A)?


Ok, perfect!


Now, let's use a calculator to multiply out all the squares and do the multiplication!


ok


17^2 = 289


15^2= 225


so that would


289 = 225 + 196 - 2( 15*14) * cos(A)


is that right


Hold on! I'm so sorry, I gave you the regular Law of Cosines. Since we only have the three sides, we have to reformulate that into an equation I'll write on the screen. All that work is correct and we'll still be using it!


This is in order to find the cosines that we need to insert into the equation!


oh ok


So your work is still correct


But now we need to calculate cos(A) to put it in the equation


so Cos ( C) = 17^2 + 15^2 - 14^2/ 2(17*15)


you originally wrote 17^2 = 15^2 + 14^2 - 2(15*14)*cos(A)


And that was correct, there no need to change it!


oh


But using these new equations, we can find cos(A) to substitute it into that equation


so then I can continue solving it then


So now let's use the equation for cos (A)


yes!


so cos(A) is (b^2 + c^2 - a^2)/2bc


or (225+196-289)/2(210)


does that make sense?


yes


Can you finish doing that out, please?


sure


I need to solve ( 225+196-289)/1(210)? or  the other one


Sorry, yes, please solve that equation you just wrote


That equation will give you cos(A), which you can then plug into the first equation


ok, just double checking


Sure!


Perfect job, amazing work!


yay


Now, we plug that into the earlier equation


Wait, I'm so sorry, I have to go now, but I think you understand the problem, right?


yes thank u for ur help


Ok, glad I could help! Good luck with the rest of your work!


Hi!


How are you doing?


Fine


Great!


How can I help you?


Need help with my assignment my problems have two variables and I have to solve for one


Ok


can you upload the question


or copy and paste the question?


Hello?


Are you still there?


Yes


And I got 2-5x over 5 = y


Am I correct?


I'm going to solve it to check.


You done?


Not yet


Sorry


I wrote my answer on the board


So I forgot to simplify it


Yea


So do you get the concept


Or should I explain it.


Yes I get the concept


Thank you


Thats awesome!


Do you need help with any other questions or topics?


No not right now


Ok.


Bye


Have a great day!


Hello


Hi! What do you need help with?


Um


I need help with it's, uh, like comparing real numbers.


I have a question. So if you want me to write it down, I can.


yeah you can write it on the board and we can work through it together


OK, just give me one second to write it down.


ok


OK, there, I wrote it down


and it's kind of like you have to compare the numbers.


what does the number on the right say? I'm having trouble reading it


sorry


It's hard to write on this thing.


I'll write it, um, cleaner.


no worries


is that better?


yep thanks


No problem


how did you go about figuring this out?


Um, so what


I get of it is


the 10


I don't think you can like.


change how it is.


and then


for the fraction


I don't know what you would do.


I think I need help with all of it, more or less.


are you allowed to use a calculator to see what the square root of 10 is?


Um, so for some parts were allowed to use a calculator, but like on our notes it tells us like what the perfect squares are.


but on the list it doesn't show that 10 is up there.


yeah the square root of 10 isn't a perfect square, so it would be easy to figure out what it is by using a calculator


ok


So


like I was trying to think of it in my head and


I'm going to real quick write it down.


You can't go any farther with 5 and 2 and the only other factor pair that like can get you to 10 is 1 times 10.


thats a good strategy to simplify the radical but we want to know the exact value of the square root of 10


OK, so how do we do that?


do you have a calculator near by? if so, you can plug it into the calc


you'll get a decimal if you do so


Yeah, I have a calculator.


Oh, how?


do you want me to put it in?


are you using a hand held calc or an online one?


And


hand heled


right


right.


I'm going to pull up an online calc so I can show how to put it in


ok


the website that I'm going to use is called desmos scientific calc if you want to follow along


can you see my screen on the board?


yes


ok so you see the second button beneath main tab?


that's your square root button


and then type in 10 to get your answer


okay


I put that in my handheld calculator.


ok great


so the square root of 10 is about 3.16


Makes sense


So now do we turn the fraction into a decimal.


yep do you know how to do that?


I'm going to try and I'll do it on the screen.


alright sounds good


great job so far!


ty


So would I finished there?


Oh yes


yeah perfect


So now we can pare them.


Compare them, question mark.


Hm


yeah exactly


OK


you're close


Is it the opposite way


If so


yeah


why would that be? Because I would think 16 is bigger than 6.


3.6 is the same as 3.60


go


Oh, OK. Cause you would add a 0.


yeah also 6 is bigger than 1


does that make sense?


Oh yeah


that makes a lot more sense. Thank you.


no problem


is there anything else you need help with?


I think that's it


Thank you


Have a good day


you're welcome


you too


Hello!


hi


Hello


question


right now


do that


I need help comparing real numbers


ok great!


Can you hear me when I talk?


yes sorry


How do I show you what problems I NEED HELP WITH?


do I draw it?


you can draw it on the whiteboard type it in the chat or screenshot it and but the screenshot on the whiteboard


this is a fun problem


the best way to do it would be to estimate squaroot 13


Be it up with it right now.


Yeah


Did you do that?


so root 9 is 3 and root 16 is 4


I don't know how to estimate the square root


so it is somewhere between 3 and 4


OK


between the


16 is 4


times 3 times


pi is 3.14 so it is also between 3 and 4


we can manually square 3.14 and see if the result is bigger or smaller than 13


so find 3.14 times 3.14


I don't understand how to do the first part


oh ok we are just finding between which integers the squareroot of 13


so we know that the sqaroot of 9 is 3


and the squareroot of 16 is 4


because 13 is between 9 and 16


This is too confusing


we know that the squareroot of 13 is between 3 and 4


You know the square root of 9 and 16 but I don't


oh, ok


so the square root of something means what times itself is that something


3 times 3 is what?


therefore the squareroot of 9 is 3


because 3 times 3 is nine


so try and guess what the square root of 4 is


good!


and guess what squareroot 16 is


good, look at the board


there isn't anything on the board


try scrolling down


thanks


does this diagram makes sense


so its like inbetween


exactly


and brobably about 3.5


so would my answer be greater than, lesss than or equal


because it is halfway between 9 and 16


well you tell me


is 3.5 greater than less than or equal to 3.14


then I think it's greater than


Yep!


this is the next one


I think I need to change the % to a number or decimal but I don't know how


percent is super easy to change to a decimal, 25% equals .25


1% equals .01


100% equals 1


good!


now do long division to find 4/7


so move it over two places


yeah, .55 is correct


so it is equal?


no


you did the division wrong


I will try again


do I stop now?


yeah


how do you know when to stop?


when you have enough digits to tell which one is bigger


so now you know that .55 is less than .57


ohh


So 0.57


is bigger


umm, yeah


its the same of 55 and 57


of which 57 is bigger


ok


Give me a second


to get the next problem


Maya!!


Hi Olivia


Hi can you check my answer to this problem?


OK.


I'm reading...


Checking your result...


Your result is correct, but you can simplify it.


You can divide top and bottom by 3.


Anything else I can help you with?


Are you still there


Yes.


Can you read the chat?


Looks like you're away. Maybe you're having wifi connection problems? I'll end the session to help others. You can always make another request.


ok ai


-76-102 solve it with no calculator


Hi I am a human tutor


Let me show you the steps give me a minute please


oh I was talking to that bot


lol


Oh no problem lol


can i show the steps on the whiteboard


yes pls


Can you see the steps


I have shown all the work


If you don't understand anything please let me know


Hi Are you in the session currently


where did it go?


i have no idea


its back


yay


I hope you can see the steps with the explanation.


Please feel free ti let me know if you have any questions.


Okay thank you Mr. Smith for the help


bye


any more questions


can i end the session


yes


hope u have fun with algebra 1


hi


can we use mics today?


Yeah, sure. Hi, how are you?


Good, how are you


I'm good, thank you


Um, was there anything or interested?


or you need help on


Just the basics.


of in your math in general?


Yeah


OK, do you like maybe tell me what you're learning in school right now.


Um, like


um, multiplying and dividing negatives and positives.


Oh, OK. And then that's um like long division.


or just like the rules of negative positives.


Uh, just like the rules of negative fossils.


Oh, OK. So what do you know?


so far? Or what could you explain to me?


Well


I mean, I know how to like multiply and divide. uh


Yeah.


like,


negatives and positives


OK


And you just want more practice?


OK, so do you have any practice problems we could work on or should I maybe phantom.


Um, could you find some?


Yeah, yeah, sure.


Just give me a second


Our complex is the math you're doing in school right now? Is it just like


Um


80 divided by -8?


That's harder than that


So like algebra.


do you have like variables?


Yeah


So you need help with algebra.


I'm also, like I'm also starting to learn like pre-algebra.


Oh, OK, OK


All right, hold on


OK. Do you see the problem I've put on the um whiteboard.


Uh, yeah, I'm looking for it.


It's ready to go. Oh, it's right here.


Do you think you could solve that


OK


And then double one, actually you can.


Do you need help getting started?


No


Hang on


OK.


Can you see what I'm like doing?


Oh yeah, I see it. OK. It's, yeah, it's just a little sorry.


So X equals -1.


Um


wait, I can't see your work here


Oh, OK, I see. All right.


I'm just gonna move this.


OK, so


when you have


when you're moving, um, a number from one side to the other, what are you trying to do?


What


Oh wait


It's like, um, you have negative


There's a line in between there


OK. Um, but like


when you're trying to move, let's say -6.


from the right side to the left side


How would you go about doing that?


Oh, no, because um


I, um, took away two X and then the answer was -6, cause that's what was left.


OK, so then for the -2,


so you subtracted -2 from each side.


No, I subtracted to X.


But OK, so when you do this, what you're essentially doing is


you do it, you have negative 2 X, right?


Oops.


And then you subtracting to x.


So what does this give you?


What


OK. Here, do you see this?


OK, so right here


you had -2 X on the right side.


and you're trying to get rid of kind of the negative to X, correct?


hold on


Yeah, OK


OK, sorry. So


when I did -2 X, I meant to do a plus 2 X.


OK, yeah. So you add 2 eggs to each side.


Yeah, so


OK.


Um, so on the right-hand side, negative 2 x + 2 x becomes 0, yeah, and you're left with -6. That's correct. And then on the um on the left side.


on the left side here, you have Adex and then you're adding 2 eggs.


What does that give you?


OK, so you have 8X on the side. You're adding two to both sides, right?


Yeah


OK, so on, uh, OK, so on the left side you have Adex, and then you're adding


2 more eggs


What do you have in total on the left side.


Tenex


Yeah.


Wait, I can't edit it. Why isn't it letting me? Oh, there we go.


And then that would just be it, that would be divided by 1 or 10, and this would be just divided by 10.


Then the answer isn't that.


that would be


that would be 0.6. So yeah, there we go. The X equals 0.6.


OK, and 0 0.6 or positive?


Is this the level of math you're doing, or is it like too easy, too hard?


Uh, that's like the level of math undoing.


OK, so is this helpful or do you want to do something else?


No, this is helpful


OK, so you wanna do more like this?


Yeah


Yeah, all right, OK


Um


OK. I'll just make one up


Is it easier if we use the whiteboard for you instead of typing it, cause I think you said it was hard to edit.


No, that was only because uh my computer was lacking up.


Oh OK


Um hm.


Oh


it's fine. We can just use the right, uh, the whiteboard if it's like easier.


That's it, do you see the problem


OK.


Do you wanna try it


Um, yeah.


OK, so


So we would


not


each side


oh


Uh-huh


So that would be sniff 7 next.


Um


2X minus 9 would be


would be me.


they can't


When you subtract numbers,


they have to be like terms


right?


yeah, um, yeah.


I managed the wrong number.


Whoops, you, um, I really like.


Oh, could you like rewrite the problem, please.


Oh yeah


OK, do you see it


Um, where? Oh, there.


Hm, yeah, I see it


A little back to down.


for


Wait, I'm sorry.


Good ****. Ow sorry. Why did you hit me?


Yeah, I think it


OK, um, I, I think I have to go.


Oh, all right


OK. I hope this was helpful.


It was


OK


All right, bye


Hi


Can you help me find the points on this graph? I see -2,2


but I can't find the one


0,5didn't work


Okay so do you know what quadrants are on a graph?


Is this it?


Not quite


But that's okay


Let's work through it


ok tyy


the boxes


Do you know what quadrants are on a graph


Yes! So do you know which boxes are negative and which ones are positive


It's okay if you don't. Let's just refresh


I think rising to the left is negative and falling to the right is negative but rising to thr right is positive?


I think


Yes! That's correct


So quadrants go in a clockwise direction


The first quadrant is on the upper right


Then the second one is on the lower right, then the third one on the bottom left, and the 4th on the upper left


Do you get this so far?


yes


right?


Perfect job!


So quadrant 1 will have coordinates with a positive x and y value


so is it that 1 and 2 are positive and 3 and 4 are negative


ok


So 1 and 2 have positive x -values


But what about the y-values, do you think they are both positive?


Idk


Let me help you. For quadrant 2 the coordinates would look a little like this, (+ x-value, - y-value)


Do you know where the x-axis and y-axis are?


Good Job!


So when you go from top to bottom on the y- axis it goes from prositive(top0 to negative (bottom)


So now do you think the 2nd quadrant will have positive or negative y values


negative if its going clockwise right?


Exactly!


We are looking for (-2,-2) correct?


im looking for  points


i only found -2,-2


Okay! So now let's follow the line above (-2, -2). Can you find another coordinate or point that goes through a number not a decimal?


oh it can go through a number


I thought the points always had to be here.


Yes my apologies, they do! I'll do better at explaining next time


Ok :)


If you follow the line above (-2,-2) you can find another point that your line goes through. Let's try


ok


So the line does not directly pass through any whole numbers on the graph except for (-2,-2) and one more point.


Can you tell me which one?


I tried 0,5 but it didn't work for the slope


Okay. Let's try again then


k :)


I will try it again too


Can you write the formula for finding the slope down just to make sure your understanding the formula.


Perfect!


So far you equation is looking good!


y = mx + b, does this look familiar?


TYYYY


Kinda


let me try


Your so close!


hmmmm


But pay attention to how the graph is labeled


i got it


Would the y-intercept be 5?


yes


Yes your correct and you fixed the negative! Nice job!


Yes! :)


My apologies for the lag! I hope you were able to value this session!


I do vaule it. :)


Value*


Unfortunately I can no longer stay on the session, but I hope I helped!


hi how may i help you today


Hello, I need a little help ty! Let me upload the assignment


okayy


I know how to find the slope but how would I write it in standard form


can you make the pictures a little bigger pls


so you need it in terms of y=2x+3?


hellooo???


are you still here?


Im here


so do you need it in terms of y=2x+3


I will log back in later


okay as youw ish


Hi Emma


How can I help you


How do you become a worker for this job


Like can you be more specific?


How can you get the tourer job


Like tutor for math.


Ye


For this app


So for that you need to be good at math and see how far you want to be to work on specific math job title.


For this the role needed is completely voluntary


This is not paid


You will just have to sign up like always


What jobs pay


And then try to explain if you are prehighschool graduate


Do u know


Employment based you would want to look out for ones that pay back.


Like TutoringWorks


Is that a app


Emma that is a good one.


That is onsite.


You would have to take the test and pass.


What do I type in


But that is one example.


Just google search and try to search for the job of your interest.


Does this make sense are we good here?


Mr. Lee good bye


hi


how are you


Hi Chloe


I'm well, thanks! And you?


im well


im taking a screen shot of the promblem now


Which question do you need help with?


c


the funtion one


OK. Can you give me 5 minutes to solve, and then I'll explain?


ok


We can start. Have you learned about geometric series?


yeah so long ago


We can solve it in two steps. The first step is to see the "pattern" of the series. I'll write on the board.


I'm writing below your upload. Do you see it?


yes


After the first dose, we have Q_1 = 500 mg, correct?


And after the 2nd dose, we have Q_2 = 500 + 500(0.2).


right


The pattern continues. As you can see the "500" is multiplied by increasing powers of 0.2 as "n" increases.


Using Summation notation (Σ), we can write the geometric series as I've shown.


The second step is to find the "formula" for the series.


Can you find the formula for Qn ?


i thought it was just qn=500(0.2)^k


What you wrote is the "kth" term of the series, but not the sum.


I can show you the general formula, and you can apply it to your problem if you like.


Looking at the series, can you find what are a = ? and r = ?


is r for rate


Yes. r = 0.2


The formula is correct. For example, if n=3, we have Q_3 = 500(0.2^3-1)/(0.2-1) = ?


Exactly.


So your formula works.


whats this formula called?


It's the formula for a "geometric series". You could also simplify it to read: Qn = 625*(1-0.2^n)


so long term the amount of anitbotic that remains as n approaches infinity


No. For question (d), to find the remaining amount in the long run, you calculate the limit of Qn as n→∞. Can you find it?


infinty


Use the formula: Qn = 625*(1-0.2^n). As n→∞, 0.2^n → 0, correct?


oh i just plugged in infiny for n


I can show you on the board if you wish.


yes please


Did you learn about "limits" ?


yes


anything to the infinty power


is o


Because 0.2 is less than 1, 0.2^n goes to zero as "n" goes to infinity. So (1-0.2^n) goes to "1".


For example, if n=1, then 0.2^n = 0.2. If n = 10, then 0,2^10 = 0.0000001024.


its going closer to zero


Yes. And the final limit is: 625*(1-0) = ?


Right.


thanks


You're welcome. Is that all for today?


i have one more question


OK.


I need to step away for 3 minutes, and I'll be right back, OK?


ok


I'm back. Can you give me 5 minutes to solve, and then I'll walk you through the solution?


We can start.


Let's say the original area is A_0 = 1, correct?


right


I'll write below your upload.


Now let's find the next area in the sequence, A_1. How much area is removed from A_0 ?


Correct. 1/9 of the area is removed. So A_1 = ?


Yes. We'll write this as 8/9.


Now look at the second carpet, circled in yellow. How much more area is removed from the previous carpet?


8 small squares


the center of


Yes. We have 8 remaining squared (boxed in dark blue), and the center is 1/9 of it.


So the area removed from A_1 is (8/9)*(1/9), correct?


Now let's simplify a bit.


We have 8/9 - 8/9^2. If we add the two fractions, the common denominator is 9^2, correct?


So we can simplify A_2 = (8/9)^2.


We have A_0 = (8/9)^0, A_1 = (8/9)^1 and A_2 = (8/9)^2. Do you see the pattern?


increase in exponet


Exactly. In general, we have An = (8/9)^n.


Is 8/9 less than or greater than 1 ?


less


Right. So what is the limit of An as n→∞ ?


Correct. For example, A_1 = 8/9 = 0.889, A_100 = (8/9)^100 = 0.00000000000.


The limit is zero.


This is not a geometric series. We have a limit of zero because (8/9)<1.


ok


its heading to zero


That's right.


would you say any term less than one always heads to zero when the limit is going to infinty


Yes. If you look at the limit of r^n as n→∞, the limit is 0 if r<1 and the limit is ∞ if r>1.


right


are you a  math major?


No. I'm an engineer who studied a lot of math!


i bet


thats basically all yall do


A lot of math, and physics too.


That's all the time I have. Any quick question before I go?


no thanks for the help


You're welcome. We can end the session. Enjoy the rest of your day.


alright you too


bye


Hi! How can I help you?


hii could u recheck my answers and make sure i get a 100?


Sure. Is this your homework?


yes but can u garuntee me a 100 if we work on it together?


I can’t guarantee a 100, but I can definitely go over your answers with you and help explain anything that seems confusing. That way you’ll understand the material really well, and your chances of doing great are much higher.


ok.


Ok so do you have an idea on how to approach this question?


the answer i got for this was


Ok, I got a bit of a different answer. But if you think about it logically do you think 25 makes sense relatively?


Let's go step by step, what equation did you use?


no it would be 26


Ok, could you please explain what you did?


Hey! I'm jsut asking so we can go through it.


Hi Jamie, how are you?


good


That's good! How can I help you?


my homework


Ok, what are you working on?


math


Ok, can you be a little more specific please?


What kind of math?


.rounding whole numbers  .estimating


Ok, like rounding 9.7 to the nearest whole number?


no not exactly


its like round 4,587 to nearest thousand


Ok, I can help with that


Do you have any specific questions?


What questions do you have on rounding?


Or would you like to do some examples?


no I have every rounding question done ?


Awesome! Do you need help with anything else?


no actuallyy


but thank you


Ok! In that case, feel free to end the session, and if you have any other questions, feel free to request for another one!


ok


Hi Maya!!


How can I help you today?


Hey! I was wondering if you could check my answers, some questions are not answered and I was wondering if you could help me with them


Yeah, we can do that


Is it okay to share my screen with you?


Of course


Also you can add pictures on the whiteboard, if you would love to!!


Can you see my screen?


Yeah I can see, thank you for sharing your screen!!


Okay!


Can you please let me know if I made a mistake?


Of course!!


Thank you!


I am glad to inform you that you have answered to all of the questions correclty (from 39 - 45)


Is it okay for me to move on to the next page?


Do you have any questions so far? I'll be happy to answer, if you have!!


Yes it's totally okay to move on !!😊


Ok so let's start of 46


Do you have any ideas how can we solve this problem?


If you are not sure just let me know, we will break this down together!!


I'm not sure sorry


You don't have to sorry, everything is fine, I am here to help you!!😊


okay so now I have a question!!


Yea?


ok so we have this information that y is a function of x, each output is half the corresponding input, and when the input is -2 the output is -1


now, what do we have to find? Did you get the statement of the problem? Or do you have any questions about the problem?


Hello?


Are you still there?


So You did absolutely correct, you have chosen the right coordinates based on the information provided, and drew the correct line!!


But now I cannot see your screen


Can you share that one more time, please?


Yea I don't know what happened to my chromebook


Of course!


That's totally ok,


Please go ahead and share your screen, take your time !!😊


It won't let me share my screen


Omg I don't know what's happening right now


you can try to add the photos of your assignment


Everything will be ok, don't worry, and which is important don't panic, I'm here to help


I can see the screen!!


That's great!!


I uploaded the picture!


So I'm happy to inform you that you have answered to 46th question correctly


Do you have any questions about this problem?


Or are there anything you would love to be explained?


I have some more questions but I do understand this one thank you for asking :)


Can you help me solve #47 please?


Yeah now we will break this down together!!


Okay!


Would you like to draw a picture of that triangle?


If you don't want to do that I am here to help and I can to that as well!!


If you are not sure just let me know!!


Can you draw the triangle? I'm so sorry it cause right now I'm on my bed and it's gonna become crooked


It's 4:30 am here that's why


That's totally fine, you don't have to be sorry, I am here to help!!


Thank you so much!


I think it will be better if I draw than use already existing shapes!


It's okay take your time!


What's your zodiac sign?


Gemini!!


Thanks for asking!!


OMG me too!!


Great happy to hear that!!


Wait stop I love Gems


June or May?


I'm June


I love Gems too,


I'm May


Ooo


Is it 4 am there too?


No it is 12:31 pm


Oh


Yeah I know


It's 4 am here


Do u like math?


I like it a lot, I'm passionate about math


Ooo!


Ugh I wish I could feel the same about it


I'm terrible at math I only like it when I understand it


Wait omg have you watched Love Island?


I pick Noah


I used to hate it until I got involved in math olympiads, the way that I have discovered the real beauty of it


Omgg really??


Omgg and was it hard? Who got you into it?


I haven't watched that, sorry, but I will


Omg you should its so good!


I just started participating nationals and go to olympiad math clubs


At what age did you go to the math Olympics?


I started pretty late, I was in tenth grade when the first time I took part in!


Ooo


Wait what grade are you in now?


Springfield Academy


Major?


yup


I was supposed to be a rising eleventh grader too but I wasn't born here and I had to do first grade again


That's totally fine!! We have so much in common!!


Omg I know right?!!


What's your favorite series or music?


Ok so do you mind if we go back to our problem, solve that cause I finished wrting about that, and we can take time and talk later, if you want to


Oh yea I'm sorry I usually get distracted and start talking


That's fine!!


It happens everytime like my teacher has to move me but either way I'll still try to find a way to talk to the person next to me lol


ok so do you know what is the meaning of area?


That's totally fine, I'm here to help!!


Like 1/2?


And you have to add all the parts?


Base x Height?


Almost ok so to be more certain, do you know what is the meaning of perimeter of a triangle?


If you are not sure just let me know!!


Oh yes!


1/2 (Base x Height)


Ok so that's the area of the triangle


Oh


but the perimeter is the sum of the lengths of all the edges of the triangle!!


Ohhh!


Do you have any questions about the perimeter so far?


I don't!


We can do some practice problems to deepen your understanding


If you want to!


Sure!


ok so if we have a triangle ABC and know that AB=3 BC= 2 AC=4


can you tell me what's the value of the perimeter of triangle ABC


How did you get that?


I added 3 and 2 and 4


correct


so You get the idea I guess!


Yay!


That awesome!!


OK so now we have to look at the problem


so is it okay if I named the length of EF as x ?


Yes


I mean that I have written that EF=x


then we know that DE= 2EF = 2x


Do you have any quesions about that


Mane I'm so sorry but I am getting a bit sleepy since it's about to be 5 am here


If you want I can explain it more detailed!!


Is it okay if I can come back later and work with you?


Yeah that's fine, Go and sleep and come back later!!


Also one question is sophmore slump a real thing?


Yea I think I would feel much better if I slept good!


At what time will you be connected?


Good Night or Mosrning!!


Oh


Sophmore slump is very personal, but it can be!!


What do you mean?


I hope that I will be connected!!


So what do you mean by saying Sophmore  slump?


I understand this by saying that a decline in performance or motivation following a successful or promising initial period


Like getting really bad grades sophmore year


Yes that


Like when you give up of doing something


You know what I mean?


hmmm


I guess


but can you explain that once more, if that's ok?


Of course!


Also if you are tired, you can go and sleep and then we will continue talking that's totally ok


general exhaustion and lack of motivation students face during their junior year which causes you to have bad grades


a lot of people are talking about it and saying most of the people that were in junior year got sophmore slump


ooh  Now I get it


Yea


So a little info , Springfield Academy is only 3 years, also we cannot choose our classes


Wait ur not in Texas?


But I guess that junior slump can be true for some people, and cannot work for others


Ooh


No I'm not in Texas


Where are you?


I'm in uSa


I'm in Georgia!! But I don't know if I'm allowed to be more certain or not!!


Sorry about that!!


Oooo


Is that a country?


Yeah!


Ooo!


I mean during classes I don't know if I can be more certain or not


Otherwise I can be certain about that!!


It can contradict to Privacy Policy, I'm sorry!


So Maya do you have any other questions?


No I don't and thank you so much for your time!


Thank you Maya


Have a good night!!


Georgia!


Bye!


hey can you check my answers for me


Hi Marcus! Post the questions on the whiteboard so I can check them.


Alright. The first answer to the multiple-choice question is incorrect. You're close with the factor part and correct with the reflection part of the equation.


whats that mean


The answer to question 4 is 4th option available.


As for the graphs, I have noticed some mistakes. Would you like to go over them together?


but don't you need to have a recipricol because its over the x- axis


No. The reciprocal is applied when graphing perpendicular functions.


oh okay


yeah we can look over the next one


Yes. Let's first start with the dotted yellow one.


Here, our function tells us we have a vertical translation, not horizontal.


yes


is it the y=lx+4l for the yellow dotted


Yes, if you were to take the horizontal version.


As for your work on the green graph, I noticed it is correct. Nice work! However, moving on to the blue graph, we will actually flip the equation we had with the yellow graph to get the correct function description.


would it look like this


Close! Make sure that you add a plus sign to the yellow graph. After adding this minor correction, we can begin talking about the red graph.


how do I add a plus


Add a positive sign (+) to the yellow graph so it looks like: y=Ix+4I


so just switch it with the red then?


I cant add things its just a box and I put them where they belong


Yes. If you switch the two functions, the matching will be correct.


so this is how its supposed to look


Yes, you got it! Need help with anything else?


On the question asking to analyze the effect of compressions, the first option you picked appears correct.


Yes, the 3rd option picked for the translation is correct.


okay thanks that it


Alright! Thanks for tutoring with TutorEase, and have a great day:)


hello what seems to be the problem


Find the inverse of the function f(x) = 6x-1/x+2


do you know what an inverse is


No


so a regular function is f(x) = y right?


so an inverse should give you f(y) = x


so with that we say that y = 6x-1/(x+2) we need to find the function such that we put it in terms of y instead of x so how would i go about that


I don't know


so
wehave this right?


correct


Yes


So want it in terms of y instead of x right


so we then have


where y is our input and x is our output


so how do you think we should go about doing that


change all the x's to y's?


kind of


so we need to rearrange so that we have y as an input and x as an output


Got it, how do we do that


you should rearrange it using algebra


do you know how to do that


No


Do you know what to do to cancel out terms?


No I don't


like if had a subtraction do you know what to do to cancel it


To make it be the same


you add to cancel out subtraction


do the inverse


Okay got it.


Can you help me? Or could you just do it so I can see how it's done


I can try and help you but i am not sure how exactly to


Could you show me how to do it


lets look at a differen tprolem


Okay


so this is a functino of x in terms fo y


so you try the actual problem now


No idea


so how would you cancel division


multiply


yeah


so then how would u cancel a division by (x+2)


x - 2


or just -2?


no you mutiply by the inverse which is x+2


x times 2?


no (x+2) as a whole


so we have to do to one side what we do to the other right?


Do the same


yes


so write it out


I don't know how


so now you have to rearragne it so that you can get x alone


So you should divide?


you need to group everything together


all the variables


How do we do that


Hello!


i need help with a question on my hw that im not too sure on


so -8 is less than -6


so f(-8) is (-8)^3-4


which is -512-4


which -516


-516 i mean


-2 is between -6 and 1 and therefore f(-2) = 2(-2) + 7


= 3


3 is greater than 1, so f(3)= (3) all over (3)^2 + 2


so 3/11


That was very quick, so what questions do you have?


so those values you got is the answer for each a, b, c?


-516 , 3, 3/11


a. -516,   b=3  c=3/11


yes


so basically theres 3 statement and i will have to fill in a b c into each one/


yeah,its basically three different questions within the same one


so three different answers


OHHH thats how to do piecewise??


im sorry i got to go


bye!


oh Mike


Hi Alex!


Hello! I need help with solving this its difficult


Okay! Can you start by writing the 17 numbers from smallest to biggest?


Mhm


Done


Thanks


Obviously you know what the minimum and maximum are now so let's start with the median


Do you know what the median means?


mhm the middle number


Yeah! So what do you think the median is?


Yeah


Do you know what the first quartile and third quartile are?


uhh


would it be 40?


third would be 42?


No but I get where you got that from


Each quartile is a quarter of the way through the numbers so the first quarter is the middle of the first half and the third quartile is the middle of the second half


so how would i like find it then


You already separated the halves with your underlines so you have to find the number in the middle of each of the underlines


oh i get it


If the middle is between 2 numbers then the quartile is just the middle of those 2 numbers


wait Mr. Smith


39 for Q1


See how the 3 lines you drew split it up into around 4 even parts?


mhm


oh i see 36 is the middle number


That means each line is a quarter of the way through so the quartiles are right at the lines


Can you double check your last line on the right though?


yep i did


The second line should be on the 41 since 41 is in the middle


That will move your 3rd line to where it should be


You only need 3 lines because 3 lines splits it into 4 areas


oh ok


is this right


The median/Q1 is perfect but the lines are still a little off


ok can u help me then bc idk


Sure of course, do you get what I mean by you only need 3 lines?


i'm doing 4 on each side


Can you see what I'm drawing?


I mean like on the actual numbers


This isn't what the box is gonna look like but I just wanna show you what I mean


Bc I still don't know where to draw it since itis wrong each time


You're trying to split it into 4 areas like this box I drew so the middle line should be through the 41 because that's straight down the middle


Does that make sense?


mhm


wrong or right


It's close but do you see how the numbers from 25 to 60 are split into 5 sections instead of 4 the way you drew it?


Can we start over with the lines and I'll try to explain it better?


can you do it then bc i reall don't get it


i thought it was 4 each box


Each box is supposed to be a quarter of the set of numbers


Sure I can show you and you can tell me if this makes sense


ok


The box represents the whole set of numbers by the way from minimum to maximum


i get that but i need to actually see it visually for the numbers


Yeah I totally get that if you're a visual learner that'll probably help


The line I just drew is like splitting in half through the middle since 41 is the median like you said


When I split the box into quarters I split in in half and then drew a line in the middle of each half to split the box into 4


I'm gonna do the same thing with these numbers


I get why you thought 4 each because it looks like the sections each have 4 but you have to start by splitting it in half and then splitting in half again because you have 17 not 16


The 41 isn't part of any of the 4 sections


Does this make sense so far/


my laptop died


Oh ok no worries


ok i get it


so u split the median


so then which is the Q1


Yeah you split in half at the median/Q1 and then split each half in half


mhm


Now are you able to figure out Q1 and Q3?


39 is Q1?


Q1 is where I drew the line so it's in the middle of 30 and 31?


Mr. Smith


im counting the numbers in it


like in that box


im not looking at 30 bc its in the other box


Wait wait wait


ok


I think you accidentally wrote down a 60 instead of a 50


There's 2 50s in the number set and no 60s


ugh yeah your right


can u check all the numbers now


Sure


that changes the median now


Yeah sorry about that


its kk


There's no 30 either


At least for me it helps to cross them out while I go through them so that I don't miss any


agreed


There should be 2 36s too


let me reorder it


Okay


ok can  u check now


Looks good


ok


median 41


Yeah


Let's see if you can remember how to get Q1 and Q3


ok now lets split it


k


this?


Yeah nice job!


The Q1 line is a little trickier than the Q3 but it's in the middle of 31 and 36


is Q1 39?


Can you tell me how you got that?


i looked at the numbers in the mix


its in the middle


Q1 is directly on the line labeled Q1 because that's right in the middle of the left half


You drew the line perfectly between the 31 and the 36 so that means Q1 is in the middle of 31 and 36


Does that make sense?


so everythings in half


so its 36


so should i look at it like this, : 31, 36,36,39?


You should think of it like this: the median is 41 so that's the middle which means everything to the left of 41 is one half and everything to the right is one half, that means one half is 25,27, 28, 31, 36, 36, 39, 40


Since that's 8 numbers the middle of that half is between 31 and 36 because that's 4 on each side


25, 27, 28, 31 and 36, 36, 39, 40


yeah so would it be 31,36,,36,39?


What is 31, 36, 36, 39? Sorry I'm a little confused


By the way I don't know if I made this clear but Q1 and Q3 are also numbers just like the median


They're not groups of numbers if that's what you were thinking


You mentioned its between 31 so would i include that number when finding the middle number


bc originally i wasnt looking at that i was looking at the numbers in the actual box but we split 41


It's the number in the middle of 31 and 36 so it would be 33.5


thats cnofusing


how would you know its 33 is there math to solve that?


Yeah I'll show you


Thank you


No problem, there's 2 ways so you can choose whatever's easier for you


Ok


You can either find the distance between the numbers which is 5 and add half the distance to the smaller number so 31+5*1/2 is 33.5


Or since the middle of 2 numbers is their average you can add the number and divide by 2


31+36 is 67 and 67/2 is 33.5


ok i like that


and do that for the rest?


Q3 is between 50 and 50 so you don't have to


No we don't have to do it for everything because we just need the min, Q1, Median, Q3, and Max


ok


i have to put these points so u sure its 41 nd not 41.5? bc we did split it


and Q3 is just 50


We were just trying to split the numbers in half but we don't have to split like that because we have 8 on each side of the 41


Now you have the 5 numbers you need: 25, 33.5, 41, 50, and 59


ok let me plug this in


its correct ill try the next one on my own and then can you look over it


Oh it checks it for you?


That's cool


Sure I'll check it


done


38 is the median?


It is but I think for a different reason then you think


See how the section on the left has 7 and the section on the right has 8


mhm


That means the first 38 should be part of the 1st half so each side is 8


So it is 38 but that's because that's in the middle of the 2 38s not because the 38 is in the middle


well when i see it as 7 and 8 on the side i know its the middle even tho one isnt equal but itis close


so 3 for each?


The line you drew still isn't in the middle because it doesn't have the same amount of numbers on each side


If there's an even amount of numbers like 16 you can just do 8 and 8 instead of excluding the middle number


You only exclude the middle number if it's an odd amount like 17


ok


Now you have to find the middle of 32 and 35 for Q1 and the middle of 42 and 44 for Q3


is that Q1?


Q3 is at this line


Remember that it's a number not a region


here?


or like the actual middle line


It should be on the actual line yeah


kk


now Q3


is this right?


Yeah


so median is 38


58.5 is Q3


Median is 38 yeah


Do you see how the line you drew for Q3 goes between 42 and 44?


mhm


oh we do it that way


and then 32+35/2


which is 33.5


Yup good fix!


So now we have everything we need


so 33.5,38, and 43


gonna plug it rn


Okay!


i have one more problem


Okay you can put it up when you're ready


66 is the median


Yeah


so 18 is an even number


i tried to do 4


but it aint even enouh soo


You know how earlier when it was 17 we had to exclude the middle number to split it into?


Since you have 9 on each side and 9 is odd you take out the middle number to make Q1 and Q3


mhm


yeah i had a feeling we do it that way


stillwont be evn


Can you start by making the middle line and erase the rest for now?


Make sure there's the same amount on each side of the middle line


Did you count how many numbers are on each side of the line and they were the same?


You have 8 numbers on one side and 9 on the other right now


If you draw the line between the 66s you'll have 9 on each side


Does that make sense?


yes


so 3 groups?


Right now we're just splitting it in half


ok


oh so 4 groups but Mr. Smith


last time?


Yeah


but 85


is on its own


Sorry if I sound repetitive but you have to fix the line that splits it in half or the rest won't be right


this?


That line should be between the 66s so that there's 9 on each side of the line and it's splitting the 18 numbers in half


like this?


It should look like this


o


Now it's the same size on the left and right


Now that we have 9 in the first half, are there the same amount on both sides of the second line you drew?


oh i see


mhm


yepp


do 3?


You're still making 4 groups but we're gonna split the 1st half and then the second half


We're splitting the first 9 right now and since 9 is odd we have to exclude the number in the middle of the 9


Ok


lik this or?


sorry im rlly trying to understand


hello?


Sorry I had to do something real quick


its ok


Do you remember the 1st problem we did where it was 17 numbers?


yes


41 was split


Yeah


We had to do that because it's odd so to split it in half we don't include the middle number


Here since we're splitting 9 numbers into half it's the same thing


We have to take out the middle number like we took out 41 earlier to split it in half


ok


so split 66?


Splitting the whole thing in half was splitting 18 so we don't split any numbers, after that we're splitting 9 numbers so we split the 59


If what you're splitting is odd you split the middle number if it's even you don't


can you do it on the board bc im still not getting it


Okay


We started by splitting the 18 numbers in half and since 18 is even we don't split the middle number and just draw a line between the 66s


Now there's 9 numbers on one side (50 55 56 57 59 59 60 65 66) and 9 on the other (66 69 70 72 74 75 81 81 85)


Ok I see


Now we split the first 9 numbers in half and since 9 is odd we split the middle number(the first 59) so one side is 50 55 56 57 and one is 59 60 65 66


Same thing with the second half


ok I see


58 for 57 & 59?


This time the line is on 59 so Q1 is just 59


samething for 4?


Yeah


ok so its


50, 66, 74, and 85


You forgot Q1 but those are right


i mean 50, 59, 66, 74, 85


Yeah that's perfect


thank you!


hello


Hi, I wanted your help with a question like Find (f⋅g)(x) when f(x)=x^2+4x−21 and g(x)=3/x^2−9


okay give me one moment


Wait how did you do that?


give me one sec im going to write it out then explain


okay so in step one we multiple the numerator


so 3 * x^2 +4x-21


Why 3?


the g(x)= 3/x^2 -9


the numerator you provided shows a three


Right will that be it all the time?


yes


Okay got it


if it makes it easier you can also do this


so you see how i wrote a one under the f(x)?


Yes


I'm sorry, I am getting a call. I'll be back in 2 minutes


if you make it into a fraction it is easy to remember to multiple across


no worries


ill be here


Okay I'm back


welcome back


Thank you.


so you see how it is easy to multiply across when you make the f(x) a fraction also


okay so then we need to factor (x^2+4x-21)


do you know how?


or would you like me to explain how


Right I have problems with factoring. I can never remember how to


oh okay well what we are looking for is two number which can add up to "B" or in this situation 4 and those same numbers must multiply to be "C" or in this situation -21


7 and -3


so if we take 7 and 3 that would multiply to 21 but it would not add to 4. thus we need to make the 3 negative so we get +4 and -21. if we did it where the 7 is negative then we get -4  and -21 which would be incorrect


does that make sense?


Yes


okay so you would do the same with the denominator which is (x^2-9)


Right how do we do this since nothing equals x^2


3 x 3 = 9 but we need it to be negative thus we make one of the threes negative


so the important thing you need to learn moving forward is the formula


so x^2+bx+c


so since the 9 has no x next to is we know it is c


does that make sense


Yes what is bx though?


there is no bx so if it helps you understand it better you can make it a 0x


so then you need two numbers which would add to 0 and multiply to -9


thus 3-3=0 3 * -3= -9


Okay got it


do you want me to write it out and explain it on the board?


does it make sense?


I think so.


im going to continue explaining but im going to return to this when we finish so i can give you another example to help you get it


so then in step two we see what is the same and cancel it out


Right


which then leaves us with 3(x+7)/(x+3)


I understand that. Why does x not equal plus or negative 3?


so the best way to explain it is the denominator can never be 0


x-3=0 and x+3=0 is not possible thus x cannot equal - or + 3


does this make sense


Yes


okay so going back to the example


Could I try this one on my own


yes


okay so in fx what is b and what is c


5x and -14


perfect


So it needs to add to 5 and multiply to -14


add to -5 and multiply to -14


you have to be careful with those thats how they like to trick you on a test


okay you can continue


let me know if you have questions


Is that right?


youre doing great


Would it be (x+4)(x-4)


correct


Got it


I have nothing to cancel


you need one more thing for your final answer


that is okay sometimes there wont be anything to cancel out


Is that correct


so what you have would stay the same and then you would also state the x does not equal + or -4


you got it


Okay great. Can I try one more


sure thing


there you go


Is that correct?


yes


Good job


great


That made it alot easier. Thank you so much


Do you have anymore time?


no problem im glad i made it easier to understand


yes i have a bit more time


if you dont mind when we finish our session please leave a positive review for me :)


Determine the domain of the function: x-7/4x^2 -3x - 10


Of course, you are great


thank you! so are you!


is it okay if i clear the screen?


Give me one moment to put the equation down on my paper


okay no problem let me know when it is okay to clear it


Done, you can clear


the first step is to make the denominator equal to 0


do you know the quadratic formula?


Maybe


this is the formula


does it look familiar?


Yes a little


okay so first lets identify what is a= b= c=


so similar to earlier we are going to look at the denominator is step one


so A= 4 B= -3 C= -10


does that make sense?


Yes because it just goes in order, that doesn't change right?


correct


Okay good


easy way to remember even if the did try to change the order


is x^2 is always a


x is always b


and then number with no x is always c


okay do you think you are able to condense this down or would you like help?


I can try


Do we do in the sqaure root first?


you can


is that meant to be a 4 or 9?


explain how you got 4


Sorry I did mean 9 lol, not sure why I wrote 4


all good


remember the denominator is for the whole equation


Now what do we do?


we can condense some more


also the sign you have next to X is incorrect


so -4(4)= -16 X -10 = 160


How did you get 13?


okay so if we do the square root 169 it is equal to 13


Oh wait


I know


okay


so now you must solve for both of the following


does this make sense how i set it up?


Yes


so it can be written this way


there is also the way with the infinity signs but idk if you have seen that in class


Yes I do, how do I do that


so the way you set it up if the left is the most - and as you go across it becomes more postive


do you see that or does it make sense?


I don't understand


- infinity is the most negative


then followed by -5/4


then -5,4 to positive 2


then 2 , positive infinity


Why the 2 though?


it make sense if you use your graphing calculator to see it


we got 2 from earlier


will highlight it in pink


Oh right


What is the u?


so those are our two x's


the U is a symbol it just connects the intervals


so like if they ask you what are the intervals it would just be


Got it


think of the U like "and" or like a comma if that kinda makes sense


it is just a connector


okay I do now have to go to class but great job


have a great day!


is there anything you need before i leave?


No, thank you so much


you're welcome :)


Hi Mia


hi i am confused what to do


Ok let me see


ok


Ok imagine you have 9 apples


And want to arrange in 3 rows


How many apples you will have in each?


Correct! What operation you will need to get your answer 3?


multiplication


Not much. From the perspective of having 9 and you should get 3


Multiplication of 9 and 3 will get you 27


not 3


You want to get 3


Are you here Mia?


Pleasantville


Hello! How are you?


I'm great! Thanks for asking


Alright so we have arrived at the inequality unit


Ok


lets do this problem


Yep! I think I know the concept, I am just a bit stuck


oh ok


would you mind telling me what exactly you are stuck with, or should i go throught this problem step by step


Can I work it out on the board? I think it would take an hour if I tried typing lol


ye thats true lol


sure


one small mistake


-1/-6 is positive 1/6


everything else is great


Oh okay


And that would b e the correct answer? (So far?) I thought that it was wrong (since it is a fraction)


no


oh nvm, so far yes


thats the right answer


However, it is not the final answer


Did you learn about how to use brackets and parentheses for inequalities


Yes, for this one, I think it would be (positive infinity, 1/6)?


close


it's negative infinity, 1/6


think about it, if the inequality is h< 1/6


then positive infinity wouldn't work right as h would go higher than 1/6


Ohh okay, that makes sense.


Yup


One second, I am going to input that into the box and see if it is correct


okay,


It's correct!


YESSSS


Anything else


Thank you for your help!! I was so confused at first 😭


lol


no problem


That will be all


Okayy


Alright see you later


Have a great day, bye!


Emily


Hi!


Hi Jay


Im uploading the page


Can you tell me how to find the points of these lines?


so that I can thenfind the slope


Denver


Ok


Do you know the formula to find slope?


Something like this right?


I can't remeber the formula but  can look it up


You've got the general idea


Ok tyyy. So whats considered the numerator?


We have to pick two points on line 1.


ok so for line 1 is it -7,9


and


I never know if im choosing the right points


You can choose any points on the line. (-9, 9) is a point, but (-7, 9) is not. (-7, 7) is.


Are you able to plug those numbers into the formula?


Yes but im still kinda confused to where to look to fin the right points


ohhh


All the red points are on the line (they are not all the points on the line, but they are some)


Oh I gave you negative -7,7 but thats on line two sorry


(-7, 7) is on line 1. It's the orange point.


and thats not a point?


(-7, 7) is a point on line 1. (-7, 9) is not a point on line 1.


got that now.. tyyy soo much. ok now with the slope


I dont really understnd what the numbers next to the letters mean


It means it's the y coordinate from the second ordered pair minus the y coordinate from the first ordered pair. I wrote each letter below its corresponding number.


Ok please give me one sec to plug it to mak sure I understand


Ok


oh you already did it.. Let me look at it and compare it to the graph


would it become a positive?


Yes


simplify?


-9 + 7 is -2


would I still subtract? with the plus sign? lol


The answer then would be -1


Yes, that is the simplified answer. You are adding 7 to -9 in the denominator, which is 2.


ohhhhh


i have to remember that


getting points for line 2


Yes, you can use those


k


I did something wrong


-2 - 6 is -8


-3 - 3 is -6


Help me with that part please


im not subtracting


When you subtract, you move to the left on the number line


So 6 to the left of -2 is -8


oh if im already negative 2 and i add a negative 6 it's negative 8


Yes, you can look at it as adding negative six or subtracting positive six


but it say minus so i guess that confused me


You can subtract numbers from negative numbers, you're just starting to the left of zero and moving farther to the left of zero


hmmm ok makes sense


would the answer be 4/3 simplified


Yes


yaayy!


I do want to make sure I got the negative and positive part right.


tyyy


Nice work. I like how you persevered through this problem.


Tyyyy :) :) now I know how thanks to you!


Can you give me an example that I can subtract to find the slope to make sure under stand the negative portion?


well a problem not example


Do you have other practice problems you can use, or do you want me to give you one?


Let me look in my classkick


line 1- (4,-4)


can i use those? for line 1?


Hmm, be careful. Those aren't points on line 1 (green line). You can use (-4, 2) and (0, -1)


ohhh.. -4,2 didn't seem like a point. I will try these you gave


It's the point at the intersection of lines 1 and 2


ok the intersection makes the point, right?


No, that's just where this point is.


I marked each point on the graph so you can visualize it easier


I looked closer there is a point


ty


doing the problem now


does it look correct so far?


No, I think you mixed up the numbers


sheesh


let me look again


what about now?


working on the next one


Correct!


next points (-3,4)(-6,-1)


Close. The first one should be (-3, 3).


im blind apparently. Sam


thats wrong. I wil figure it out


no 4/3


Close. The numerator is correct, but the denominator is not. -6 - (-3) is -6 + 3, or -3.


it say 4/3 is right


Yes


was it positive because the numerator and the denominator was negative?


Yep


ohh yeah tyyy!


that is all :)


Ok, have a good night and keep working hard!


TYYYY enjoy your night.


Hi!


Hi! What can I help you with?


I’m having issues with this problem


Okay I see it!


So start with the definition of complementary anggles


angles*


Ummm a 90° angle that’s been bisected by a ray?


Idk


Almost! Two complementary angles add up to 90 degrees


And you often see them represented as you described


OHHHHH IS IT ONE OF THOSE 180° ONES?.


Where it’s straight across?


Or wait no


It's just like those problems but you want them to add up to 90 degrees instead!


Wait


How are the angles not connected by a point though in the problem?


What do you mean by that?


Like the vertex


Oh yes they would look something like that, I was just clarifying the actual definition of the angles


Oh


It'd be something like that, and I think that's what you drew (it was kind of blocked so I couldn't see all of it)


So knowing that UVW + XYZ = 90, do you know how we could start to approach this?


Set both equations equal to 90?


Yes!


Make sure to include both at once though to represent both angles adding to 90 degrees


Is this right?


Double check your work on solving for x, because those add to 50 instead of 90


That's the best way to check if you're right


I need to check my answers pls


hello!


Hi


What do you need?


I need to check my answer


okay


How did you come up with the bottom equation


1/7 x - 6/7


first I found the slope by doing (-2--8/-1--2) and then I put it into point slope form to find the y intercept


what is the problem asking for you to do


I uploaded it


Okay i see it


So the first equation is right


x+1 is correct


but the next equation is not


why?


The equation you wrote, 1/7 x - 6/7, what kind of equation is that?


Linear, quadratic, etc.


linear


And when looking at the graph


Does the part before 1 look like a line


I'm not too sure what that function would be x^3?


that's super close


cube root x?


Yep


but what would you put under it?


like under the cube root


just x


ooh ok and would the rule beside it stay the same or is that also wrong


The rule is right :)


yay!


do u have time to check more of my answers?


Yeah


Okay numbers 45, 47, and 49 all look good


Did you get 83 for number 51?


yes


Okay that's right


also how would u graph step functions? like for F(x)= step functions thingy -x, would it be like a -x slope but instead of line it would be points and to the left side the small line would go left and towards the right side the lil line would go right?


Yes it would look like that


ooh ok I get it


It looks kind of like stairs


Hence the name "step function"


got it


or atleast that's how I like to think about it


ok I think that's pretty much it for now ty sm!


Okay no problem


I don't know how to get this into hyperbole form


hello!


Hi!


I'm confused on what u would do, divide by 16? but that would not work bcz you have to have 1 on the right side so I'm confused on what to do


Ah, I see why you're confused! you can't divide by 16, but the first term can be divided by 1/16, since dividing by 1/16 is the same as multiplying by 16!


so u would have (x+5)/1/16 - (y-3) =1?


with added exponents that just takes too long to typw


close yeah! You'd just divide the y-3 by 1 to get it in the correct form


ok I get it!


Great job!


I have another question, do u have time?


Yeah, what's up?


I'm confused on 27


I got to the part of y/3 - x/4 =1 , but I don't know how to make it squared


Okay, so a simpler way to do that is to just square both sides and then move the x term over!


ohhh that was so simple ty!


Of course!


that's it for now Charlie and have a great day!


You too! :)


Hi!


Hii


How are you? What help do you need?


I’m alright I think and I’m kinda struggling with my homework atm..


ok! i can try to help out! i dont have much time but i can help you with the problems you need help with!!


whats the first question you need help with?


(-2)to the power of 2 - (3)(-4)(2)


ok so first you should solve  2 - (3)(-4)(2)


because that is in your exponent


what do you get?


4 - (3)(-4)2) ?


no 2


My bad


because -2 is the base


Oh


oh its ok!


youre doing good!


yes!


now you do (-2)^26


no, i think you have to use a calculater and put (-2) to the power of 26


Alright mbb


oh no! you did really good!


hey im sorry i have to go but please text if you have any problems and ill try to respond right away!


Good job today!!


I need help with like 18 math problems im not sure about how to do


No problem, can you show me them?


im confused on how to do this one


This one is interesting


Do you know the formula for average rate of change?


y=x??


or is it f(b)-f(a)/b-a


The second one


The first one you listed I believe is the slope intercept form of a linear equation


ohh okay!!


so how would I go about plugging the equation into the formula?


So this is a trick question but theres some reasoning behind it


The f(20)-f(10) / 10 is actually a rate of change formula since 10 can be rewritten as 20-10


and f(20)-f(10) / 20-10 matches f(b)-f(a) / b-a


So the question is effectively asking for the rate of change of f


by plugging that into the calculator I got an error, did I do it wrong??


The question doesn't need a calculator since the answer is already in the question


and the answer is the last one correct??


Well


The slope (or rate of change) of a linear function is the same across the entire function


So if the slope of f is 12/5 for one interval its 12/5 for all other intervals


And f(20) - f(10) / 20-10 is the rate of change of f across the interval [10, 20]


uh


The question is asking for the rate of change, not the interval


And the rate of change across the entire function is 12/5


this may be silly but would you mind solving an example problem similar to this one for reference


I wasn't sure that was the correct answer, but the way I read the message made it sound like that it was obviously simple lol


Alright sure


So lets say the rate of change of a linear function a is 4 across the interval [0, 1]


And you have to calculate the rate of change of function a across a different interval


regardless of what that interval is the rate of change will always be 4


so basically f(b)) - f(a) / b-a = 4 no matter what


as long as youre solving for something in that form for a function the answer will always be the rate of change


so in this case since f(20) - f(10) / 20-10 is the right form for rate of change


it will equal 12/5 since thats what the rate of change is for the entire function


if that makes sense


okay yes that makes sense


so the entire thing equals 12/5


Yes its 12/5


Do you need help with this one?


yes please :)


Casey


Could you try zooming into the question my eyesight is horrendous


oh lawd yes I can


tell me if I need to move it


Ok so this question is asking for if the rate of change is staying constant across the range of values


Are you allowed to use a calculator for this question?


yes


Graphing or scientific?


im not sure


I assume graphing


Basically what you have to do here is use the equation for rate of change


for two pairs at a time


Each pair is a number of servings and the total cost for that number of servings


how would I put it into the calculator


What model of calculator is it


If its not a ti84 I genuinely have no idea how to use it


im using the gauth calculator


I dont have one of my own


other than at school


Oh


yep...


Unfortunate


Theres a method you can use with the ti84 to cheese these types of questions


if you were to set it up how would it look though


like would you set it up as a fraction


To do it properly you basically have to calculate f(x2)-f(x1)/x2-x1


and then another calculation


and so on


because that calculates the rate of change between each pair


Im gonna do it myself just to make sure


do you have the right type of calculator


Any calculator works


If we do it the proper way that I described


The fast method only works with the ti84 so we won't be using that


the answer to the first calculation is 4.65 correct??


For the rate of change between the first two pairs yes thats correct


Now you have to calculate the rate of change between (5, 33.24) and (9, 49.81)


so f(9)-f(5)/9-5


and then after that you have to do the rate of change between (9, 49.81) and (11, 57.96)


its a long process


would the answer be 4.075


Well the question is asking for if the rate of change is increasing, decreasing, or staying the same


So  you have to compare the rates of change between the points


So if the rate of change is changing from 4.65 to 4.075 then that means its decreasing


okay so the rate of change is decreasing while the number of servings is increasing


As the number of servings increase, the rate of change decreases yes


what's the difference between quadratic and linear


Theres multiple differences


Linear equations are mostly in the form y = mx + b


but quadratic equations are in the form y = ax^2 + bx + c


how could I tell which one it is by just looking at h


By looking at differences


Basically find the difference between each value of h


so between 18 and -12


and then -12 and -29


and -29 and -33 and so on


are they all supposed to follow a pattern


Yes


if they are all equal the function is linear


If the differences of the differences are equal then the function is quadratic


aka second differences


I feel like its quadratic


It probably is


Ill check


difference between -12 and 18 is -30


difference between -29 and -12 is -17


difference between -33 and -29 is 4


difference between -33 and -24 is 9


yea its quadratic


If you look at the differences between the differences you can see that its 13


so its quadratic since the second differences are equal


You should also probably give an example


or i guess not


what you said is right but


what would be a good example


You should probably state that the differences between -12 and 18 is -30, the difference between -29 and -12 is -17, and the difference between -33 and -29 is -4, and the differences between those differences is 13


What you already stated there was right though


Also its less of an example and more of a reason


That was bad wording on my part


yea thats good


as long as you understand it


yes I do, thank you for explaining it to me!


no problem


I may ask my teacher for additional time to finish these


When are they due


we've been working on them for a few days (Jefferson High School tour) but she's giving us until 11:45


she's only given us class time until today


so its been hard to watching videos and apply it until today


ah


so we have 15 minutes?


yes...


very very sad


I guess we can speedrun


Ok so for this one the rate of change is calculated using the same equation


okay and is that the equation we started with


f(b)) - f(a) / b-a


Looking at the graph the points we have are (-3, 4) (-2, -3) (-1, -6) (0, -5) (1, 0)


Part A we need the rate of change between (-3, 4) (-2, -3)


-3-4 / -2-(-3) = -7


thats the answer to part a


part b is with (-2, -3) (-1, -6)


thats -3


oh wait i can just look at the graph


part c is 1 part d is 5


You can just look at the vertical distance between the points since the horizontal distance is always 1


is that what e is??


e is where you have to find the difference between each of those rates of change


you have to find the second differences


so its 5-1 or 1-(-3)


well


yes


buts asking for the rate of change of the rate of change


and thats constant at 3


or 4


its 4 not 3


okay I'm submitting it


I appreciate you helping me so much Liam!! normally I'm more knowledgeable but I'm very very tired. you helped me very well though!! I understood the way you described everything. this is a very helpful tool!!


your doing the lords work Liam


thanks


your very patient too


and smart


i thought most of my explanations were buns


your very nonchalant with your explanations so that was really good


10/10 epic experience


so when you sign on to this can you request people or is it just random?


No idea


Did you request me particularly or was I just randomly assigned?


just randomly assigned


but I think your teaching style thats why I was asking for future refernce


oh alright


I hope you have a nice night, thank you again!!