Don't worry if you're studying for the SAT last minute because after you watch this video, you'll understand that you can use Desmos for literally every single question on the math modules. Module one, module 2, every single question. Okay. So, if you just follow along and you watch the video, you're going to understand how easy the SAT is. Okay. All right. We're going to get started with module one of math. Okay. So, now let's read the question. bird is flying 16 miles per hour whatever 4 seconds. So what we're going to do always maxim maximize desmos 16 * 4 is 64. Cool cool cool. Now it's asking for slope of four and it passes through the point 0a 6. So let's go this. So 0 comma 6 and then you know the slope is the rise over the run. So that means it rises four and then it goes one. Now what we can do is we can use linear regression 4x plus 6. So a lot of people don't know what that little button means but now you know. Oh, just click this button. Okay, 4x + 6. Okay, so now that we know that the equation is 4x + 6, that means the answer is d. Next question. So now it's going to ask you how do you do this huge thing in desmos? So it's asking you which one is equivalent? Which equivalent which expression is equivalent to this huge ugly number? So, first what we're going to do is we're just going to do 5 x to the 5 plus - 6 x 4 plus 8 3. So, let's see which when it's equivalent, it's going to have the exact same slope and everything. So, it's going to look like a like a little Okay, so let's see which one's right. Let's try x 4 5 x. Oh, that is so wrong. You see how it kind of matches and then over here nowhere near matches. So, let's try the next option. Perfect match. Right, right, right, right, right, right, right. Yeah, perfect match. So, it has to be V. Okay, next question. So, it's basically saying there's 1440 total minutes of daylight and it's saying x is the number of minutes of day of non-daylight and then y is the number of millions of daylight. So, it's saying x + y = 1440. And if y is 6 oh my gosh, it's 670. Then what's x? So, let's zoom out. You know what? Let me teach you guys a trick. Instead of zooming out like an idiot, why don't you just go like this? So, we're can do the mi the the missing number. We can make it m for missing cuz we don't know it. You know what you can do is just do this and it gives you the answer. 770. This is a idiotic way to use regression, but now I don't have to zoom out and go like this, you know. So, the answer is 770. Remember this. It can save your life. Yo, I'm going to call out actually. No, no, sure. Okay, now read the question. Scott, 20 out of 40. Okay, no. He says 16 out of 20 people um enrolled in the courses. So now he wants to make a general generalization. So how Michael, how do you use how do you use Desmos for this statistics question? That's a great question. So he interviewed 16 out of 20 people or 20 people and 16 of them said three three classes. Okay. So that we can we can use the till day and we can do another regression. So now we want to find hey how much of this applies to the total amount of people. So I can go t over 400 and the answer is 320. So 16 is to 20 as t is to 400. So it's it's 320. You see? So that's another way you can use regression. Very very easy way to use regression. In fact, I've only ever told one person how to do that. Yo, did I just ungate keep the method or what? Okay, no, I'm just kidding. Yeah, that's pretty easy. So, now for the next question. Um, of course you could just divide both sides by seven, but why use brain when you can use Desmos? What? So, for this one, we're just going to see which one gives us the same line. Is it 2x - 3 = 9? Oh, gives me the same line. Perfect line. But let me just show you what would happen if it was wrong. Equals 56. Oh, where's the line at? Boy, completely. This that line is not matching at all. So, it has to be a next. Oh, this question guys, I'm about to ungate. This is the guys. I know it looks easy, but you Okay, watch watch. So, first what you're going to do, you're just going to type out the equation as is. And you're probably wondering, "Oh my goodness, there's so many constants." Wait a second, it doesn't say constants, it says positive numbers. Aha, so what you can do is you can exploit the fact that it only says positive numbers and you can just put random numbers. So I can make C1, P1, and K1. Okay, so um now you're probably like, yo, what did you just do? Like that basically did nothing. So the next step in becoming Desmos academic weapon is to just completely subtract everything. You don't want to see the equal sign. So how do you how do you remove this equal sign? So me what I would do is I would isolate everything. I would just add seven on both sides. This equal sign is making your life very very hard. And then I will subtract minus C. And then now you're like yo what good did that do? like be honest. So now what you can do is as you can see it gives you an answer, right? So let's just do the same for all these other answers. Let's do 25 P + K + 7. And now let's do minus C 32 and 32. So that's the right answer. You see what I mean? By exploiting the fact that these numbers can be anything. You see how they're always the right answer. So let's just see what would happen if you put in the wrong answer. 25p + k - 7 minus c. Oh, that's the wrong answer. What about 7 25p + k 182? Also the wrong answer. So you see how these two match up. As long as there's no equal sign, you're chilling. Okay, next question. Oh, did I even select Okay, I didn't select the answer. I think it's a. Yeah. Okay, next question. So this question is basically saying, hey, if there's 2,000 animals at a zoo and each year it increases by 3%. Which one is a function? So the function is just a fancy way of saying like a, you know, like how do you model it? Like an equation basically. So what you need to understand for this one is that increasing by 3% is not the same as 3% of. So let's just do an example real quick. 3% of 2000 is 60. But 3% increase would be doing 2000 plus 3% of 2000 which would be60. You see how there's a huge difference there? So now that we know this, this is how we express increase in 3% increase. So which one of these functions will give us the same answer? So let's try f ofx= 2,000. So what's f of what? 6,000. Does 6,000 equal 2060? I'm afraid not. What about 1.97? Nope. Completely wrong. And now let's try 1.03. 2060. 2060. Bang. Power. Guys, drop a comment if you know who Jeremy Fragrance is. Next question. So, this one, guys, why does College Board keep making me do the test? So we're going to do this type exactly what we see. Exactly what we see. So which which one of these interesting looking expressions will give us the same line? Is it A? Please be A. I don't want to write out all these. I don't know the answer, by the way. No, it's not a bro. Are you serious? Just kidding. It's okay. 96. Is this Oh my gosh. Yes. You see how it lines up perfectly? It lines per like Watch. Hi. Now you see me. No, you don't. So, SPB. Oh, and you're probably wondering, how do I delete all? You just click the setting and you click delete all. Okay, next. Is this a physics wish? Oh my gosh. Ping pong physics. We're back. We're back doing physics in the SAT. Okay. Anyway, let's let's just do it. Okay. So, first I don't like how it gives you H and T. Me personally, I would just use y and x. You know, whatever floats your boat. 9 x + 18. So, what this is basically what this basically is, it's just a graph of the egg. So, he throws he throws the egg all the way up and then the gravity carries it down and it splashes down. So, the question is saying, what is the height from which the egg was thrown? Now, if you've never taken AP physics, this might be the hardest question of your life. But if you're me and a former physics former physics guy, you can just see that the x axis is time and you can't have negative time. So when x is zero, it's going to be 18. So the answer is 18, which basically means that boy was 18 ft off the ground when he threw the egg. Okay? And you're probably like, "Hey, isn't it zero? Isn't it zero?" But then you would be in the negatives for time, isn't it? 13. Nope. This then you'd have negative time. Okay, next. Oh, this one is so Oh, guys, guys, guys. What? Yo, what are we doing here? What are we doing here, guys? 4 2x = 16. And our answer is, see, you see how the equal sign always makes our life so difficult. Yeah. So, what you're going to do is you're going to want to remove the equal sign. So, you're going to do minus 16 on both sides. And then, now you remove the equal sign. And now, boom, it gives us a nice little point. That is our answer. So, it's going to be 8 comma 0. Oh, whoa, whoa, whoa. It's asking for 6x. I almost got that one wrong. So, you do 6 * 8, which is 48. Okay, next question. So, this one, it says it's a linear equation. Every time you increase x by one, value of y increases by 8. So, oh, and it gives us a value. So, let's just make a table here. So the way you add a table is you write table. So when x is 2, y is 18. And then how do we make that little regression symbol here? Well, we need one more data point. And how do we get one more data point? It says when you increase x by one, so let's increase x by one. So when you make two into three, the y value of y increases by 8. So let's increase 18 by 8. That's 26. And now, boom, the regression makes our life so much easier. Click the button and then it now gives us the answer, which is 8x + 2, which is C. [ __ ] next question. So, this one immediately I already know it's no solution because you can never if you want to find X, you have to take the root of a negative number. But that's not the purpose of the video. You have to be like, huh, let me just Desmos everything. Huh? So, as you can see, x^2= 841. And it has solutions, right? Cuz you have the the red lines. But this one is negative. And as you can see, the line disappears. So that means there's no solution, which means there's zero solutions. Okay. Okay. Okay. Okay. Okay. For this one, you're going to it's asking for the range. So the range is going to be the highest number of books minus the lowest number of books. So the range from this one is five minus 0 which is five. So class A has range of five. Also you don't need to write it like that. That's kind of dumb. But class B, what's its range? It's going to be 10 minus one. So it's class B has a range of 9. So now it's asking for the positive difference. Low key, bro, there's no there there's no need to be doing all that, bro. Positive difference is just like absolute value. So it could be 5 - 9 and the answer is four. So the range is four. Okay. Next. Okay. This one is a geometry question. And you might be thinking, yo, you're cooked, bro. How do you use Desmos for geometry? So think, close your eyes, envision yourself a square. Okay. And then now make the square side length 6 m. Okay. So now what's the area of a square? It's 36. Good. So now it's asking for the volume. So a volume is a square, but it's 3D. And now it's a cube. So now the volume of a cube is equal to the area times the height. And we know the area is 36. So now we're going to set up another regression. So if you know the volume is 2880 and you know the area is 36, what would you do if you're in my situation? Me personally, I'll give you 5 seconds. Okay, so the answer is you do 36 times the height regression 2880 and now it gives you the height which is 80. Boom. fifth time using my sixth or seventh time using regression. Bro, Desmos is so useful. So now it's saying which one. Okay. Wait, what is it even asking? Oh, it's saying like what's the equation? Okay, so y equ= a b to the x. So we're kind of on to nothing here, but it's saying b can be let's just sorry 0.83. And then it says a is a positive constant. So I can just make it one. So is this does this look like that low key? No, it doesn't really look like that. Okay, let's try 1.83. Okay, that looks like that a lot less. So let's try 18.36. Okay, that looks like that a lot more or less. Okay, I think I already know the answer. I was just messing with you guys. Answer is a cuz it goes down. So that's our answer. Next. So now the answer or it's asking for cosine x. So cosine so toa ka adjacent over hypotenuse. So the adjacent is 11 over 28. So that means our answer is 0.3928. What doesn't let me type more digits. Are you serious? 3928. Okay. Cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool go cool. Next. Also, I'm not going to get marked down, right? Yes, college board's smart. They're not going to mark me down for not rounding. Next question. x + 2 x - 5 x + 9. So, I'm just What I'm doing is I'm just writing it down. Oh, you see how the equal sign made my life hard? I'm just going to remove the equal sign. But he really thought I was going to put the equal sign on the SAT. I'm just instant replay. You see how it doesn't have like that nice little circle I can click. Okay. Anyway, it's asking for the positive solution. So, the solution is just another way to say when does it hit the x-axis. So, this one hits the x-axis at -9. Is99 positive? No. Is -2 positive? No. Is negative is five positive? Yes. So, it's five. Boom. There's our answer. Oh my gosh, bro. Okay, I know what you guys are thinking. You're like, Michael, you're cooked. How do you use Desos for this stupid question? So, what I want you to know is first of all, these triangles are similar. How do I know these triangles are similar? Well, first of all, they have one angle that's the same. They have two angles that are the same cuz they're vertical angles. You know, if you don't know what that is, or go Chemtutor. And as you know, if a triangle has if two triangles have three of the exact same angles, then they're similar. So, we know that two of the angles are similar. And if two of the angles are exactly the same, that means the third angle has to be the exactly the same because all triangles must add up to 180. So, that means the triangle is similar. Okay, enough yip yap. Okay, now that we know they're similar, what does that even mean for us? So, first let's let's make some things clear. So, th this angle A, it opens up to XQ. This angle A, however, opens up to QZ. So, let's just write something. XQ is similar to QZ. Okay, I don't know why there's a regression. I don't want that. Okay, I'll just write this. XQ is similar to QZ. Also, I don't know if that's the symbol. Okay, it doesn't matter. What else? We know that these two are the exactly the same. So, now we know now we know WX is similar to YZ. What's our next thing? We know that this last one WQ because this angle opens up to this line and this angle opens up to this line. So that's YQ. Okay, so now you're like, bro, you just use you're on to absolutely nothing. Okay, which low key you you're right. You're right. So let's just it gives us the values, right? So 63 is YQ. is 63. WQ is 70. WX is 60 and XQ is 120. So now what can we do? It's asking for YZ, right? So now what we're going to do is we're going to do this. We're going to say 63 is to 70 as YZ. I'm just going to call it Z is 260. So what this is doing here, it's doing another regression, right? And it's basically saying, hey, these two are similar. Okay, so now you're just going to divide on both sides and then what what's Z? And it's going to give you 54. And that's our answer. Okay, next. Okay, G. Okay, we're just going to copy down the question. X + 14 and then T minus X. T is a constant. I know some of you guys that's like a trigger word. You know, you just get just get annoyed when you see that. So, don't fear. It passes through 24, 0. Let's let's label that um Tyrone. So, we know we know it passes through Tyrone. So, now let's add the slider. So, oh, so when does it touch? When does it touch? Does it touch? Does it touch? Does it touch? Stop. Go back. It touches at 24. So, it touches when t is equal to 24. So, now it's asking what's the value of g of zero. G of 0 is 336. So, that is our answer. You see, but if we didn't make it touch, then it would be completely wrong. 18.2 is not the answer. So, it's be 24. Okay. Okay, next. Ah, dude, I just love percent questions. You know why? Cuz you can use Desmos. Let me tutorial time. Okay, so first of all, let's just assign a couple of variables. So, it's saying number of zebras in 2018 was blah blah blah. So, let's just write 2018 zebras is equal to a. Okay. And then it's saying population of zebras in 2014. So we're going to write 2014 zebras is equal to B. Okay. Now let's set up a system of equations using let's yeah using regression. So we're going to do the two brackets and then we're going to write till day then another two brackets. So what it's saying basically if you were paying attention it means that whatever's in here is equal to the stuff in here. So let's let's go by this one by one. So it's saying 2018 zebras which is a is so anytime you see is that means equal sign. So equal sign so we put it go on this side 1.27 times the number of zebras in 2014 and like we said 2014 zebras is B. So it's 1.27B. What's the other? So I said system so there has to be more than one equation. So what's the other equation? Um, it's going to be B is P% of the number of zebras in 2018. So, we're going to do B is comma is equal to P% of A. Okay. So, what exactly did I do here? What I basically said, I said A is equal to 1.27B and I said B is equal to P% of A. And how does it know that? Because I added the commas. Okay, don't never forget the commas. So now it's asking for the value of P. So as you can see P is 78.7 and it's asking for it to the whole number. So it's 79. Okay, that's our answer. Last question. This one's lowkey the most annoying one cuz we have to check which one translates it down six units. So this is our nice little boy right here. What's the midpoint? I don't know. Okay, don't need to worry about that. So, which one translates it down six units? So, let's try a squared + y + 6 2 = 36. I'm just going to Does this look like it transferred down six units? Yes. Does it look like it doubled the radius? Yes. But how do we prove this? Let's try proving that the radius was doubled. Actually, let's just try this option. Number B. 2x + 2^ 2 + 2 y + 6^2 = 9. Does this look like the radius was squared? Definitely not. So, it definitely can't be this one through. And let's try this one. x + 2^ 2 + y - 6^2 = 36. Does that look like it went down six units? Definitely not. It looks like it went up six units. So wrong. What about this one? 2x + 2 + 2 - 2 = 9. Does it look like it went down? Nope, it didn't. So our answer is a cuz none of the other ones went down and none of the other ones or I mean this guy went down, but it's radius decreased. So we're done. Okay, next. Okay, so for this first question, it's saying that there's 4,500 cups to start and then each day you use 70 of them. So, how many days will it take for you to get to 1,700? So, what you're going to do is you're going to use a quick regression and we're going to say D is the amount of days and if each day you lose 70, how many will you take until you have 1,700? So, look, it tells you 40 days. So that's going to be our answer for one. Two. So it's saying there's a triangle. One of the measures is 63. Which one could be the one of the other one? So here's what you need to know. In the triangle, it has to add up to 180°. Okay. If it's more than 180°, then it's not a triangle. So let's see which one of these are more than 180°. 63 + 116 179. So this one could work. So I'm just going to click it. What about 63 + 118? It's greater than 180. So it can't be a triangle. And then what about this one? 126 greater than 180. And then this one greater than 180. So it has to be a. Okay. Next question. So it's saying which one of these tables satisfies this inequality. So we're just going to type out the inequality in Desmos and then we're going to see, hey, which table is in this area? Actually, I'm going to make it green because green means good. Green means good. So you want it to be in the green. So let's try a. So it's going to be 2 comma 19. Oh, 2 comma 19, 430, and then 641. Is it in the green? Yep, it's in the green. So I already know it's right. But just to make sure, let me just double check. Let's see if B is wrong. 2 8 4 16 64. Is this in the green? It is not in the green, which means it's wrong. Okay, next question. So for the next question, it's going to be it's giving us an equation. So I'm just going to type out the equation 9 over 7 x + 8 / 7. And it's saying when does it equal 5? So let's just do this. So let's say f of a and then we're going to have a slider a. So when does this number equal 5? Let's see. It's going to equal five when a is equal to three. So that's the answer. It's three. Okay. Next question. So for this one, it's saying uh a plane only goes between 150 and 170. So which one of these satisfies that? So A says that it's less than 20, which is wrong. B means that it's less than 150, which is wrong. C means that it's less than 170, which is right, but D says exactly what the question is asking. So it means it's the better option. So it's D. Next question. So this one is saying that this is the this is the end of November 2012. Okay. And then it's saying that as the months passed as the months pass it's going to increase in projects and then slowly decrease. So it's saying that in December it's going to have seven projects and then in January it's going to have eight and then February it's going to have nine. But they don't the question's not asking that. The question is asking at the end of November 12, how many projects do they have? And it we can just see here it has five. Correct? So the answer is five. Okay. So this one what you need to do is you need to see hey which function when you input 28 it gives you 15. So let's try. So h of x= -2 over 7x + 23. So does h of 28 give you 15? It does. What about h of 26? Does it give you 22? If it doesn't, then we need to try a different one. And this is wrong. So now let's try B. What's H of 28? 105. That's not 15. So that means it's wrong. What about this one? Oops. Don't do that. So this one is -7 / 2x + 23. So what's h of 28? Is it 15? Nope. What about + 113? Is h of 28 15? It is. And what about h of 26? Does it equal 22? It does. So click next. Okay. And then now is the next question. So this one is saying when you plug in the number of cars for C and then the number of passengers for 9, will it equal 9? So let's see. 55 * 3 minus 174. Does it equal9? Oh, it does. So that's our answer. But let me just show you why the other ones are wrong. Does 553 minus 174 equal 9? Does it equal 9? No, it equals 9. So, this is wrong. What about 55 174 minus 3? Does that equal -9? No, it doesn't. And the reason why I'm plugging in 174 is cuz that's the number of passengers. P is for passengers. So, yeah. And this is completely wrong. So, it has to be a. Okay, next question. So this one I know it says W. So you might be inclined to write W ^2 + 12 W - 40. And you see how it doesn't work in Desmos. What you want to do is you want to just use X instead. Okay. So now it's asking which one is a solution. So as you know a solution is when it touches the X-axis or yeah like it's a root or it's a zero. So, um, which one are which one of these numbers represents one of these two numbers? So, let's just copy these two numbers down. So, and let's just pay attention. Do any of these numbers equal this? So, this is -2.7. Do any of these numbers have -2.7? Nope. So, this one's wrong. What about 2 19? This one's 8.7. Do any of these numbers have 8.7? Nope. What about 19? 4.3. None of these have 4.3. So these two are wrong. So it means it has to be d6 + 2 19 2.7. So this one matches which means it has to be d. Okay, next question. So now we're just going to type in the function 3x over 7 = -5 y over 9 + 21. And now it's asking what's the y intercept? So the y intercept is when it touches the y ais. So it's 37.8 as you see here. Okay. Next. So now it's saying which one demonstrates the linear these these lines. So let's just type them out. Well, they look the same. And if the answer is yes, then that's our answer. So this one kind of looks similar. Kind of looks similar. Let's double check though. This one intercepts with what? 6.67. 6.7. Anyway, and this one intersects with 0 and 16. So, it means that this one can't be right because these y intercepts are not the same. 8x - 4 y = 32, -10x + 4 y = -64. This one has nowhere near the same slope as this one, so it can't be this one either. Now, let's plug in C. 4x - 10 y = 328x + 10 y = -64. So, this one also has a positive slope, but this one has a negative slope, and they don't look anything alike. So, it can't be this one. Oops. Okay, that means last. Last one has to be right. I don't even feel like trying this, but it's all right. So, 64. Okay. I thought it was another number, but next question. So, this one is saying, so we're just going to write it down. Okay. And then you see now it's asking the solution is x y. So what's the value of the x - 2 * 6? So what's our x value? Our x value is 281.5. So what's 6 281.5 - 2? It's 1,677. Wait 1677. Okay. That's our answer. Okay. And then now for the next one. So we're just going to type in the function. Okay. And then now it's asking what's the minimum value. So the minimum value is the lowest y-coordinate basically. So what's the lowest y coordinate? So it's high and it's getting lower lower. Stop. 1728 is our answer. So that's the minimum. Okay. And then now for our next question, it's saying how many solutions does this have? So solutions is basically how many times will it touch the x-axis? So49x=98x. How many times does it touch the x-axis? Only one time, which is at 0 0. Right, right, right, right. Let me just double check. Yep, that boy is not touching me anywhere else. Okay, so the answer is zero or whoa whoa whoa one. Lock in buddy. Okay, next question. Okay, so this one it looks kind of complicated but we're just going to write it out first. Okay, x - 2 x + 6^2. Okay, now it's saying the value of g of 7 - w is zero. Okay, so basically it's saying 7 minus a number is equal to a root. So let me just give you an example. Okay, -6 is a root. Why? Because it hits it hits zero. It hits the x axis. Okay, so now it's saying 7 minus w is equal to -6. Correct? So let's just use some regression. So w is 13 in this case. Okay, so that's one possible value of w. What's another time where g of x hits zero? Well, it's at zero. So we're going to do the same thing. 7 - w zero. So it's seven. So that's another value of seven. What's the last value of the what's what's the last solution? It's two. So it would be 7 minus w is two. So why am I writing two over here not zero? Because when when the x value when the x value is two then it's zero. So that's why I'm writing it down. You get it? So now the sum of all the values of w is 5 + 7 + 13 which is 25. So that's that's our answer. Okay. A little tricky. Okay. So the next question. So I'm going to give you some time to read it and you guys should have 5 seconds. Okay. So it's asking a tree from one of these rows will be selected at random. And now it's saying given that the tree is 20 ft or taller. So that means 20 ft or taller will be in the denominator. What's the probability of selecting a maple tree? So this is going to be maple tree 20 ft or taller. So now let's just simplify. How many trees are 20 ft or taller? So eight trees 20 ft or taller. And then each row has eight trees birch trees 20 ft or taller. How many rows of birch trees are there? There's six. So that's 6 * 8. And then remember there's also maple trees. How many maple trees are 20 ft or taller? There's nine trees. 9 * 5. And now what is how many maple trees 20 ft or taller are there? So there is nine maple trees 20 ft or taller. Correct. And then how many rows? 45. So what is this? How do you simplify this? This should be plus. Oopsies. Okay. Um, so the answer is 15 over 31. Okay. Next question. Um, so this one you're probably like, "Yo, Michael, you're absolutely cooked. How are you going to use it for a circle?" But then you need to realize this first. It gives you the area of the rectangle. How do you find the area of a rectangle? It's base time height equals the area. And then in this case, it's equal to 1089 3. Okay. Next, what's some more information it tells you? It says that the diagonal of the rectangle is twice the length the shortest side of the rectangle. Now, if this doesn't ring any bells, that's okay. But now you know. If you go to the reference sheet, this reminds me of a special right triangle. As you can see, the diagonal is two and then the shortest side is X or is one, which means the diagonal is twice the side of twice the size of the shortest side. So now I know it's 30 60 90 right triangle. So now instead of writing base time height, I can write X * 3. So let's just do that. X or I'm just going to use um what can I use instead of X? I'm just going to say X1 3. And then instead of height, I know that there's an imaginary triangle like that. So it's square or it's a rectangle. So the height is going to be X. Okay. Okay. And then now what I can do, I can use a regression. So I can do instead of using equals I can go like this. So now I know the height of the rectangle is 33. So does this help me at all? No it does. Or yes. Yes. But no first because it's asking for the diameter of the circle. So how in the world do we get the diameter of the circle from the smallest side of the rectangle? Well, it tells us that the diagonal of the rectangle is twice the length of the shortest side of the re rectangle. So, we know that the diagonal, is that how you spell it? Yo, lock it. Lock it. Lock it. Lock it. Equals 66. Why? Because it's twice. And now, how do we relate the diagonal of the rectangle to the diameter of the circle? Well, here's the thing. The diameter is going to equal the diagonal of the circle. I'm going to have an image right here, and you can see what I mean. Okay. So the answer for the diameter of the circle is going to be 66 because it's going to be equal to the diagonal of the rectangle. Okay, next question. So these these ones are really easy because anytime you see this anything with dec or with percentages, you can just use Desmos. So watch. So first I'm going to set up a system of equations uh regression on Desmos. So the way you can do that is first put in two brackets and then two brackets. So what you're basically telling Desmos is that whatever is equal in here is equal to this. So let me just do an example. I can say a is equal to 67. And now it's going to say yo Michael A is 67. And I'm thank you. So now how do we do this for this question? First we need to know vocabulary. Is is another way of saying equal sign. So just remember that. So when it says A equals 2241% of the sum of the positive numbers B and C, anytime you see an equal sign, you're going to get out of this U bracket and then go to this one. So A is 2240% of the sum of the positive numbers B and C. So the sum just means the match together. So B plus C. And then now is the interesting part. You're probably like, yo, you said system of equations. I'm only seeing one equation. So how do you add the second equation? So what you have to do is you have to do comma on this side, comma on this side. And then you get to add whatever you want. Now I can still write B or no whoa whoa whoa. I can write Z is equal to 67. And then now you see it says Z is 67. You get it now? So that was just an example. What what are we actually supposed to write? Well, what's the second equation it gives us? It says B is 83% of C. So, we're going to write B is go to the go to the comma 83% of C. And then now what you're probably realizing is, yeah, Michael, this is a scam. You don't you can't use Desmos on this one because it just 00 0. But what you can do is you can you can tell Desmos um you can tell Desmos that B and C are positive because that's what it says, positive numbers B and C. So you have to be like yo desmos b is greater than zero and yo desmos c is greater than zero. Okay. Now what percent of b is a? So let's just guess and check. Bro, I'm I'm too I'm too Yeah. 23 24% of b. Is that a? Nope. If a is 44, we need to see which one is equal to 44. What about 49.41%. So this is 0.44, 44, but it's not 44. Okay. So, what about 2324? This is 20. So, we're And then now let's try 4,941. And then this is exactly the answer of A. So, it's got to be D. Okay, next question. So, for this one, it's asking for um the value of P if there's no solution. So, an easy way to do this is just writing 7 8 y 8 x = 47 - 7 over 8 y. And then you're just going to write the other equation down. Okay? And then now you're going to add a slider. So, this one says it has no solution. So, you need to see which one of these makes them not intersect. So, you know that if they intersect, that means there's a solution. Okay. I feel like it intersects right there. Okay, they do. So, if you just drag the slider and see when do they intersect and when do they not intersect, then you should be good to go. Okay, let me try 3.5. Okay, and then as you can see, they're perfectly parallel. Like, they never intersect at all. Even if I zoom in at like 400, they're still parallel. Okay, so that's the answer. 3.5. Next question. So, I see a table. So, I'm just going to write down a table. -27 39 0 21 and 5 and now I'm saying now I'm seeing that g of x is actually f ofx over x + 3 what is f ofx well no they don't tell us but a simple way we can find this is by saying that y1 so y1 is equal to g ofx so we're basically saying g ofx is equal to f ofx x or f ofx over x + 3. And right now you see nothing correct, which is good or which is normal because we still need we have extra information. It says it's a linear function. So the equation of any linear function is always going to be mx plus b. So we're going to type in mx plus b. And then now it should work, right? But we need to realize that Desmos only works with it doesn't work with variables. You need constants. So you need write mx1 and then x1. So now you see or yeah the regression it works when you have x1 and you're basically saying that hey it's not x itself it's a value x. Correct? So now it's asking for the y intercept of y= f ofx. So you might be thinking, hey, it's just 12. It's right there. But that's not f ofx. That's g of x, right? Because y1 is g ofx. You're really trying to find f ofx, which is mx plus b. So what's m? 4x 4 x. And then what's b? 36. So now what's the real y intercept? So it's this blue line. So what's the x y intercept? It's 36. Okay, next question. So, this question, it's going to take a it's going to take a minute to do on Desmos, but I'm going to prove that it's possible. And this is how you're going to get that 800. Okay, so watch. So, first it's saying a circle. So, I'm just going to write down the equation of a circle= r 2. What's r you you uh you're asking? It's the radius of the circle. So, the radius is 168. So can write 168 and boom. Now we have a nice good circle. Now it's saying that M and N lie on the circle. So what does this mean? M are like physically on this red line. But here's the thing. It doesn't say that it's here or here. Here here. It could be anywhere. So I'm just going to define it. I'm just going to say that this is where point M lies. And I'm going to say this is where point N lies. Okay. And then this is where point G lies. I mean, we know it's the center. Then I'm going to label it. And I'm going to label this one. And I'm going to label this one. Okay. And then now I want us to visualize this really really good because it's ask it's it's asking us basically to imagine a point H. It doesn't tell you where the H is. It's just saying there's a point H here. So I'll solve for it. So the a good way to visualize this is to make a polygon. Polygon M G N H. So right now we don't know where H is. But let me just do some some dillydally and let me just assign H to be 500 comma 500. I know this is wrong. This is completely wrong. It's not at 500 500, but it's just for me to be able to visualize what the shape looks like, right? Because this is a quadrilateral. So, I'm just going to be like, hey, this is what the quadrat quadrilateral kind of looks like. It kind of looks like this. Okay. So, now we need to find the distance from G to H. Let me label H. Well, how do we find that? So first let's just find the distance from m to g and n to g. So if you're paying attention you would realize that these are radiuses correct the radius is from the midpoint to the outside of the circle. So these are radiuses. What's the radius? 168. So now we know mg is 168 and ng is 168. Right? So what's the what's the perimeter? The perimeter is 168 + 168 plus x plus another number is 3,856. So what are the what are these two values and are they the same number is what you should be asking yourself. Well, let's see. Are they the same number? Let's let's calculate. So we're going to do distance m to h. So that's 600. And then we're also going to do the distance from N to h which is also 600. So now you know that these two values are the same. So now we know that. So let's subtract both sides by 2 * 168. Okay, it's not. You see how I have to zoom out? So I'm just going to use regression so I can so it tells me. So, now that I know the distance from M to H and N to H is 1,760. Okay. So, is that our answer? No, it's not. Here's the thing. It's not asking for the distance between M and H. It's asking for the distance between G and H. So, how do we find that? So, what we can do is actually make a triangle. We can realize that we already have this side and this side, and we're trying to find the diagonal. So, we can use the Pythagorean theorem. Well, how how big is this side? It's 168 according to this, correct? So, it's 168 squared. And then we just found out that the distance from M to H is 1,760 and this equals the hypotenuse. So, we're going to write H for hypotenuse. And then we're going to use regression. And then it's going to tell us that the distance from G to H is 1,768. Okay, so that's our answer. And now for the last question. It's saying that f ofx is defined as f ofx or f ofx is defined as a of x squared. Yo, can I lock in? Okay. So for this question, it's saying we have a function f ofx and it's defined as a x^2 + bx plus c. Okay. Okay, so for this question it's saying that f ofx is equal to x^2 + bx + c. Okay, and now it's saying that when x is -7, y is zero. So let's just plug it in. And it also says -3. When x is3, y is zero. So how do we do this? We're going to use the the the concept that we learned earlier. We're going to use the system uh system of equations regression. So we're going to say f of 7 is equal to zero. And then we're going to do comma f of -3 is also equal to zero. And we're missing something. Hopefully you remember cuz right now the function is kind of useless. And it says a is integer greater than one. So we need to tell desmos a is greater than one. And then now boom it gives us the answer. It's asking for a plus b. So, what's a plus b? -6. And that's our answer. Okay. So, next exit out. So, now we're all done with module two. As you can see, we use Desmos for every single question. I hope you guys learned a lot. If this helped you in any way, shape, or form, um, please subscribe. Again, uh, comment down if you learned something. Oh, also comment down if you ate Chipotle. Do you want to see finish on Chipotle today? Pretty good, huh? Anyway, let's see what we got. Let's go. Okay, so as you can see, you can go back, but every single question will use Desmos in some way, shape, or form. And hopefully you can transfer this energy into your SAT this Saturday. Okay. Uh, thank you guys for watching. See you guys. until heyo.