I've scored perfectly on back-to-back SAT Math sections and in today's video I'll be doing a walkthrough of the digital SAT practice test ones math sections this is going to include both Section 1 and section 2 in that order so with that being said make sure to like subscribe and turn on notifications and let's go and get started with question one so question one States what is ten percent of 470 to solve this all we have to do is 470 and multiply it by 0.1 that'll give us our answer of 47 which is B so let's go ahead and move on to question two which equation has the same solution as the given equation all right well I see all my answers are 4X equals something so I'm going to go ahead and subtract 6 from both sides that'll leave me with 4X is equal to 12 and I don't actually have to solve for x because as we can see our answer there will be C let's go ahead and move on to question three we've got the total cost in dollars to run a surfboard consists of a 25 service fee and a ten dollar per hour rental fee a person rents the surfboard for T hours and intends to spending maximum of 75 okay so it's gonna be less than 75 or I guess it's maximum so it'd be less than or equal to to rent the surfboard which inequality represents the situation it gave us t for hours I put in h so just keep in mind we'll have to switch that to T option A not correct option b uh we know that t is our variable here it's not our one-time cost option C is incorrect option D is correct we have 25 one-time charge plus a ten dollar charge per hour which is represented as T it has to be less than or equal to 75 so D is our answer there let's go ahead and move on to question four okay it's going to take me a little bit to scroll there uh let me get the right side screen there we go all right question number four the function G is defined by G of X is equal to x squared plus nine for which value of x is G of x equal to 25 all right so we just gotta set this equal to 25 so that's 25 is equal to x squared plus nine we'll subtract nine from both sides that'll give us 16 is equal to x squared take the square root of both sides that's going to give us four is equal to the value of x we're asked for which value of x is G of x equal to 25 so that would be 4 so our answer is a notice that at the end after I got my value of x I went back I checked what I'm asked to answer with in this case it is just the value of x sometimes maybe the value of 2x plus 1 or something like that so always make sure you are paying attention to that all right that being said let's go ahead and move on to question number five we've got each face of a fair 14-sided die so it's a fair 14-sided die it's labeled with a different number 1 through 14 with a different number appearing on each face if the dies rolled one time what is the probability of rolling a two well two is only on one of the 14 faces okay so our answer here would be one out of 14. it's not two out of fourteen two is just representative of one of the 14 faces and only one of the 14 faces has that number two on it so the answer there is going to be a 1 over 14. let's go ahead and move on to question six all right so you got printer produces posters at a constant rate of 42 posters per minute at what rate in posters per hour does the printer produce the posters on the SAT Math section always pay attention to anything that is underlined in this case we have a unit conversion so we are converting our 42 posters per minute which I'm gonna represent as p over M those aren't variables those are just representative of our units now we have to convert this into posters uh per hour all right so to do that we need to get rid of this minutes so what we're going to do is we're going to multiply by the fact that we have 60 minutes per hour and this will give us our minutes will cancel and we left with posters per hour so let's go ahead and put this in our calculator so that's going to be 42 times 60. keep in mind this is the digital sat which means you can use your calculator on all portions of this digital sat so we have 25 20 as our answer there okay so that'd be 25 20 posters per hour as you can see we have p over H so 25 20 is our answer for number six go and move on to number seven once again anytime we are kind of switching sides it will take me a minute because of the screen recording software I'm using I have to switch um the part that is recording so let's go ahead and get to number seven there we go all right number seven the function f is defined by the equation f of x is equal to seven X plus two what is the value of f of x when X is equal to four in this case pretty simple right we just have f of x when X is four we put in 4 for X that'll give us 7 times 4 which is 28 plus 2 28 plus 2 is 30. so our answer is 30. all right so that one right there is pretty simple moving on to number eight now a teacher is creating an assignment worth 70 points okay I'm guessing that is going to be a total uh the assignment will consist of questions worth one point and the questions worth three points which equation represents a situation where X represents the number of one point questions y represents number of three point questions okay it's going to Total out to seventy because that's how much the whole assignment is worth these are going to sum together it says y represents three point questions okay so we have our equation here a is not that b is not that c is uh C has these two mixed okay watch out for that it's got the the wrong Y and the wrong X coefficient it has them switched around sound and then D it looks like we got the right answer I'll quickly check to make sure that we do have X representing the number of one point questions that is true y representing the number of three-point questions okay so there we go all right so D is our answer always watch out for this right here where they flip the coefficients on you okay that's a simple mistake you can make so always pay close attention to what x represents what any sort of variable represents in the question in this case we get our answer there is going to be D let's go ahead and move on to number nine right triangles LMN and pqr are similar okay so we have similar triangles L Corp l and m correspond to p and Q okay so as you can see first one first one second one second one which means third one third one so that's perfect angle M has a measure of 53 what is the measure of angle Q well we see that these are similar triangles M A corresponds to Q therefore they're gonna have the same angle measure and our answer there will be 53 which is answer Choice B okay moving on to question 10. once again this will take me a couple seconds to switch the screen side in this screen recording software so let me just get this over in this case we are going to there we go all right so number ten solution to given system of equations is X Y what is the value of x all right immediately what I'm looking at whenever I have stacked equations is either plus minus or substitution sometimes we'll have to multiply the top or the bottom equation by some number in this case it's clearly going to be substitution and I I guess maybe I shouldn't say clearly but it is going to be substitution in this case and the reason why is because we have y is equal to negative 3x okay that's an indication I'm probably going to end up substituting in that negative 3x for y if I take a look at the question it's asking for the solution to the systematic equations X Y what is the value of x okay so we need to solve for x we don't really care about solving for y in order to solve for x we want to actually get rid of Y and get everything in terms of X so this works out perfectly we have 4X plus negative 3x that will end up leaving us with One X left and we would get that X is equal to 215 because 4X minus 3x leaves us with x x is going to equal 15. our answer there is going to be C once again pay attention what you're asked to answer with in this case only just the value of x not 2x plus 1 or anything like that so our answer there is just C all right moving on to number 11 now all right so I'm going to actually cover up the question numbers because I don't have much room on my screen which of the following equations is the most appropriate linear model for the data shown in the scatter plot all right uh first thing I'm going to check is my axes I see I've got zeros both here so that's good to know I see that my y-intercept is going to be somewhere roughly around 10 um and obviously we have this negative slope here okay so in this case we want most appropriate linear model for the data shown in the scatter plot okay keep in mind linear model all right we've got option A and B both have negative slopes that's good but option A has a negative y-intercept so I can get rid of that option b has got the positive Y intercept looks like it's probably got the right slope I'll quickly check C and D C and D both have positive slopes they're going to be wrong B will have to be our correct answer we're going to move on let's see okay once again I've got to switch the side of my screen so just give me one second to do that all right there we go question 12. okay we've got a graph uh graph y equals f of x is shown where the function f is defined by f of x equals ax cubed plus BX squared plus c x plus d where a b c and d are constants for how many values of X does f of x equal zero okay so how many values of X does f of x equals zero well let's find all the points where f of x equals zero f of x equals zero where we're crossing our x-intercept okay which we see happens at three different points so for how many values of X is f of x equals zero that'd be three because we have three of those points where we cross that x-intercept so our answer there is going to be C when down to question 13 now we've got Vivian bot party hats and cupcakes for seventy one dollars okay so that's a total between the two that she spent uh each package of party hats cost three dollars so we have three dollars per package of party hats I'll represent that as H for hats and each cupcake cost one dollar so we'll have uh just C for cupcakes uh if Vivian bought 10 packages of party hats okay so we'll probably be substituting in that H equals ten how many cups Gates did she buy okay should we know she spent 71 we know that's the sum of three h plus C we can plug in that 10 for H that'll give us 71 is equal to 3 times 10 which is 30 plus C therefore we subtract 30 from each side 71 minus 30 leaves us with 41 is the value of C quickly double check what we're asked to answer with okay we see that we're asked to answer with how many cupcakes she bought which is 41. moving on let's go and go to question number 14. okay once again I've got to switch the side of my screen so just give me about five seconds to do that okay there we go question 14. what is one of the solutions to the given equation all right well immediately what I'm going to look to do here is go ahead and Factor because we have it set equal to zero another option you could use here is Desmos but in this case I think it's probably faster just to go ahead and a factor all right so if I'm factoring this out looking for numbers that multiply to get me negative 24 and sum to positive 10. uh cbda z uh six and four would make sense here let's see if that would work be um no six and four wouldn't work uh 12 and 2. that would work so we could have X Plus or Z plus 12 and then we can have Z minus two it's going to equal zero so what is one of the solutions to the given equation all right well one of them would be positive two so we can just go with that we could also go with a negative 12 as well so those would be the two possible solutions we only need to do one of them so I would just put in two um personally but you could take your pick there and if you want to see how this factors I'll just quickly foil it for you see you have that plus 12z you also have this minus 2z okay and then you also have that minus 24 and then you obviously have that Z squared so the key thing there is that plus 12z minus 2z gets you plus 10 Z and then you have negative 2 times 12 equal to negative 24. all right anyways there's question 14 question 15 bacteria are growing in a liquid growth medium there were 300 000 cells per milliliter during an initial observation the number of cells per milliliter doubles every three hours okay so we got our initial amount three hundred thousand we are doubling every three hours how many cells per milliliter will there be 15 hours after the initial observation okay so I'm gonna actually write this a little bit bigger so you can kind of see that this is indeed an exponent okay so the reason that we have 15 or I guess I'll kind of explain this whole thing okay so the equation for exponential growth we have our initial value right this initial observation at which we have 300 000 cells per milliliter okay so our initial value and exponential growth equation will go here right it's just the initial value stays there next thing we have is going to be our growth factor our growth factor is two because we are doubling so since we're doubling growth factor is two growth factor goes in parentheses here now what are we raising our growth factor to what power that comes in where we have the fact that we are doubling every three hours okay since we're doubling every three hours a good way to think about this is the following we have 300 000 growth rate or growth factor of two if we're doubling every three hours and we had three over three as you can see we'd have three hundred thousand times two which gives us 600 000 so we'd be doubling right so that's why we need to have that um that denominator of three so we're doubling every three hours not every single hour okay so with that being said we have to ask ourselves that how many cells per milliliter will there be 15 hours after the initial observation well that's where we get that numerator of 15. so now we get that 15 over three all right so from here we can go ahead and put this in our calculator so let's go ahead and do that so we've got 300 000 times two raised to the power of 15 over three fifteen over three is the same as five and that'll get our answer of 9.6 million so our answer there would be D okay moving on to question 16 which expression is equivalent two and then we've got all of this right here so first thing I'm going to look to do uh in this case we've got addition I see that we've got 6 and 12 so I can probably factor out a six um I see I've got y squared and Y squared I've got x squared and I've got x to the power of 8 which we could actually break down into x squared times x to the power of 6 because that would then sum to x to the power of 8 so that works out great for us let's go ahead and factor out six we know we have y squared because that's in both we know we have x squared because that's in both now we have to figure out what we're also going to multiply that by all right well in order to get this first value of 6 times x to the power of 8 y squared we would have to multiply by x to the power of 6. and then over here with this plus 12x squared y squared we would have to also multiply by 2 in order to get this 12 but the x squared and Y squared are already taken care of over here okay so we've gone ahead and factored this now let's go and look at our options we've got option A let's actually just see if we have one that matches up perfectly with what we got 6X squared y squared it's the same as 6y squared x squared and then we have the X to the power of six plus two okay so our answer there will be C I could go through and I'll show you why a b and d are wrong but I'm not going to do that just because that's just it's kind of pointless right you saw how I factored this we see C is equivalent um I just don't feel like showing you why the all the other ones are wrong there all right let's go ahead and go on to 17 I will go ahead and switch sides on my screen there we go and if you're wondering why I'm not using Bluebook to show this it's because you notice how I'm switching sides on my screen here um it's way easier for me to actually do that than to screen record Bluebook because Blue Book the questions like Jump Around left and right all the time and it would take me way longer um to like set up the screen capture so anyways that's just a side note on why I'm not doing this through Blue Book even though this is the digital sat it's just way easier for me to screen record on this even though it takes a couple seconds to switch sides anyways question 17 a neighborhood consists of a two hectare Park and a 35 hectare residential area the total number of trees in the neighborhoods 3934 equation 2x plus 3 5y our 35 wise 394 it represents the situation which the following is the best interpretation of X in the context all right well what does X represent uh we see here it's getting multiplied by two which we know it's a two hectare Park okay and this is ultimately being used to give us our total number of trees so it would have to be the number of trees per hectare in the Park Okay so we've got option A the average number of trees per hectare in the park that would be correct a quick show you why BC and Dr wrong B says average number of trees per hectare in residential area that would be representative of the value Y and then we have C total number that'd be 3934 and then a d total number of trees in the residential area or I'm sorry total number of trees in the park sorry C would not be a three nine three four C says the total number of trees in the park um that'd be representative of 2 times x and then D would be representative of uh 35 times y okay anyways I want to show you why those are wrong let's go and move on to 18. once again I got to switch sides here so just give me a couple seconds on that uh drop a comment um or like the video anyways moving on to number 18. we've got the graph shows relationship between the number of shares of stock from company a which represent by X number of shares stock from Company B which represent by y that Simone can purchase which equation can represent this relationship all right once again keep thinking to take a look at as my axes always make sure I've got zero zero otherwise you know I need to make note of that in this case we got company B company a c y intercepts right around 40 so we have negative slope okay let's go and move on which equation can represent this relationship all right so it's a pretty simple question looking for the equation represented first thing I'm going to take a look at is the one that are in slope intercept form because those are easier to interpret we have y equals 8X plus 12. I know that that's the wrong y-intercept and then if I take a look at C we have 12x Plus 8 wrong y-intercept now I'm between B and D between these two they're both in standard linear form so I'm going to use this equation here m is equal to negative A over B if you don't know what that is we can apply it to questions that are in standard linear form standard linear form looks like B and D where you have a coefficient in front of x a coefficient in front of Y and then that being set equal to some constant like this all right so that being said um your a value is going to be what's in front of your X and your B values can be what's in front of your y so option b would have m is equal to negative 8 over 12 which would equal out if we're simplifying down to uh would be negative two over three now if I'm going to go up to my graph I see that we've got we start at this 40 Value and then we go down so we go down 40 and we go over 60. so down 40 over 60 simplify that down that is also going to be negative two-thirds okay so that's also negative two-thirds so put a check by B I'll Quick Check D just check its slope um real realistically the answer is going to be B here and we know that because it's got the right slope and we see that these two are flipped around okay but I'll just quick show you why that has to be the case Okay because and I guess I'll actually just explain it all right so I know it's going to be B because we have the correct slope and you glance you literally just have to glance at D and you know it has to be wrong because it's got the same signs here but it's got the coefficient in front of Y and X flipped so you really don't have to calculate the slope here just by glancing you should be able to tell that it's got to be B but I'll quick show you um how you can calculate this just for practice so you would have negative 12 over 8 and as you can see that would end up being negative 3 over 2 which is not the slopes so you could write out that but realistically if you see that you've got you know B has the correct slope here and then you just glance at D you can see it's got you know the 12 and 8 flipped um so obviously B would have to be correct but anyways uh getting lost a little bit in the weeds there aren't I moving on to number 19 we've got Circle A's got radius Three N Circle B's got radius 129 and where N is a positive constant the area of circle B is how many times that of area Circle A okay so we got Circle B over Circle A and the reason it's over Circle A is because we want to know how many times it is greater than or how many times it is how many times Circle B is um to Circle a right so that's going to be Circle A's got three n uh for its radius now keep in mind the area of a circle is pi r squared so Pi 3n squared okay and then on top we're going to have same thing it's also a circle but in this case we have a radius of 129n and always pay attention to if it's radius or denominator okay they could flip that up on you so always pay attention there now from here gotta recognize a couple things obviously our pies are going to cancel next thing I'm going to do is I'm actually going to write now that our pies are canceled I'll quick show what this can equal out to you could write this also as 129 squared times N squared over 3 squared N squared and as you can see your n squareds are going to cancel as well so then you just have 129 squared over 3 squared which we can put in our calculator so let's go ahead and do that 129 squared divided by 3 squared that's gonna give you 1849 so that'd be answer Choice d all right let's go ahead and move on to number 20. once again I gotta switch sides here so go ahead and take this moment to drop a comment on videos that you want me to make next or videos won't make want me to make in the future um anyways let's go and move on to number 20 switches uh it's there you go all right frequency table summarizes the 57 data values in the data set what is the maximum data value in the data set okay key thing here is maximum data value in the data set as we see our data values are lifted in this left side of or this left column okay what is the maximum data value we see it's 14. the mistake that some people would make here is they would see maximum data value they would look in the frequency table and they would say it's got to be 11 because that is the one that has the most um that's the data value the highest frequency right that's the data value with the highest frequency but we need the maximum data value not the data value of the highest frequency those two things are different pay attention to that on the SAT all right anyways 21 Circle and XY plane is a diameter with n points two four and two fourteen okay immediately what jumps out to me is two and two and then four to fourteen the reason that um and what immediately jumps out to me is two and two is because if I have the same x uh the same x coordinate in my circle and I'll actually just quickly draw this out so you can see what goes on in my mind here we've got x value two and we've got y values of all right 14 and 4. okay well if I know that they are both at that two for their endpoints and I draw this circle right it looks something like this okay I know that to get the radius all I got to do is take the difference of the Y's right so 14 minus 4 would give us 10 that's our diameter and then our radius then is going to have to equal 5 because it's ten over two anyways uh an equation of the circle is x minus 2 squared plus y minus 9 squared r squared where R is a positive constant what's the value of R okay we already have that's going to be five so just quickly elaborate on what I look for here I look for if the X values are the same and if the or if the Y values are the same because if they had different X values but the same y values right you can pretty much do the same thing it's just um in that case your points would be like here and here and you draw the line like this so yeah anytime you have a circle like that and you have end points look to see if the X values are the same or if the Y values are same and then that'll save you a bunch of time as you can see it did here I didn't really even have to mess with the circle equation just because I could tell that we had that 2 and the two for the X values uh anyways moving on to number 22. okay once again I gotta switch sides to my screen so go ahead and take this moment to turn on notifications and subscribe okay there we go question 22 the measure of angle R is 2 pi over 3 radians measure of angle T is five pi over 12 radians greater than the measure of angle R what is the measure of angle T in degrees okay so we know angle T I'm just going to call that t is going to equal the measure of angle R which is two pi over three and then it's going to be 5 pi over 12 greater than the angle R so plus 5 pi over 12. okay from here I'm going to go ahead and get a common denominator I'm just going to make the common denominator 12 um so I know that I got to multiply my numerator and denominator here by 4 okay so 2 times 4 is going to give me 8 so I'll have 8 Pi there from there I'll go ahead and add 8 pi to 5 Pi that'll give me 13 pi over 12. now keep in mind we have to answer with degrees always pay attention to what your ass answered on the SAT and pay attention to anything that's underlined in this case degrees so we got to convert these radians to degrees to do that we'll take 13 pi over 12 radians we're going to multiply in a way that gets rid of this pi value by doing 180 degrees okay that's not to the power I guess I'll just write uh deg for degrees dag okay degrees per Pi radians per Pi radians okay as you can see our PI radians are going to cancel out we're going to be left with 13 over 12 times 180. I'll quick put that in the calculator 13 over 12 times 180 that's going to get you 195 as your value for angle T in degrees so the answer there's going to be C moving on to question 23 now certain town has an area of 4.36 square miles what is the area in square yards of this town one miles you could throw 1 760 yards key thing here once again pay attention to anything that's underlining the SAT the big thing you need to pay attention to is the fact that it is square yards square yards and square miles pay attention to units guys if you don't pay attention to units you're going to miss questions square miles and square yards all right so since we're converting square miles two square yards we're going to take this 4.36 square miles and we have to multiply it by 1760 squared because we have to keep in mind this conversion is only uh sort of a it's only one dimensional right or I guess I don't know if one dimensional is the right word but it's it's just one mile equals 1760 yards if we're doing square miles to square yards you'd have to square you know each of these so you have to multiply by that 70 1760 squared now if it was dealing with like um cubic yards then you'd have to raise it to the power of three because it'd have to be cubed so pay attention to that on the SAT that being said let's go and put this in the calculator so 1760 squared multiplied by 4.36 that's going to give us a one three five oh five five three six which will be answer Choice D all right moving on to question 24. once again I gotta switch sides my screen so go ahead and take this chance to share this video with a friend um if you want to post it to your Snapchat story with a link that'd be awesome would be much much appreciated all right let's go to 24 switching the screen there we go okay uh for line H the table shows three values of X corresponding values of Y Line K is the result of translating line H down five units in the X Y plane all right this right here is what's going to get a lot of people on the SAT to get questions wrong is you're gonna you absolutely need to on the SAT pay attention to translations and questions it's fairly common for them to give you something like an equation or a table or a graph and then state that a different equation or line or graph is a translation of the graph that they gave you okay in this case we're given line H in this table but we're asked questions about line K right what is the x-intercept of line K we're told line K is line H translated down five units the X Y plane so always pays super close attention to your translations on the SAT Math section it's really really crucial anyways question 24. uh let's go and take a look so we need to First find what line uh what line H is so let's just quickly do that so we see we go over by five we go up by 30 so our slope is 30 over 5 which is equal to six okay so I'm going to write line k on K is y equals six x since it's a line in case we have the slope now we need to get y-intercept okay well if you know that our slope is six we see that we have this x value 18 I'll just go back 18 6 times 18 in my calculator 6 times 18 is going to be 108. keep in mind I have 130 as this y value so I do 130 minus 108 and that's going to leave me with 22. okay now keep in mind that this is not plus 22 that would be incorrect because we have to move it down by five right because we have it translated down five units in the X Y plane so if I was to write the equation for line h i could write line h is y equals 6X plus 22 therefore line K is translated down 5 units and it's 6X plus 17. all right now the reason that we got it to here is because now I see that in my answer choices I've got y values that are all zero since my y values are all zero I just set this zero is equal to six x plus 17 from there I see track 17 from both sides negative 17 equals 6X I divide both sides by 6 and I get X is negative 17 over 6. option A is not that option b is not that option C is not that option D is that so D will be our correct answer there let's go and move on to question 25 once again I gotta switch sides to my screen so go ahead and take this moment to post your Instagram story this video or my Channel or text it to a friend on WhatsApp all right now we got question 25 let's go ahead and switch the screen there we go all right and the X Y plane the graph of the equation y equals negative x squared plus nine x minus 100 intersects the line Y equals c at exactly one point what is the value of C okay so if we know know that this quadratic is intersecting at exactly one point all we in this case this is actually a great question for Desmos and the reason why I say that is it's not a super easy thing to factor this out so I would literally just put this into Desmos so let me go ahead and show Desmos okay there's Desmos and the reason that we're using Desmos is here is because on the digital sat in Blue Book the testing environment you have access essentially to Desmos right it's available within Bluebook so let's go ahead and graph this out so it's negative x squared plus 9x minus 100 let's quickly put this in negative x squared then it's negative x squared plus 9x and then minus 100 now always make sure that we put equals we can put equals y that's fine um always make sure that it's typed in correctly you don't want to actually make mistake typing and not catch it that being said go ahead and zoom out okay so we know that intersects at exactly one point so that's going to be where the vertex is so I'm going to zoom in so you can see this clearly okay as you can see our vertex can be right here we can kind of click on it and we see that the x coordinate for that is 4.5 now keep in mind here that we're not looking for the x coordinate we are looking for the y coordinate because it says intersects the line Y equals c okay so that y coordinate is negative 79.75 okay so what we can do is we can get rid of B we can get rid of D because that's obviously not a then we're between uh A and C so we can just quickly check I guess obviously 481 over 4 would be something that is in uh the I guess I'll just put in the calculator whatever 48 1 over 4 that'd be 120 something so that's not going to be right option C 319 over four we'll just quick check that that's gonna be some yeah okay perfect yep negative 79.75 is what that is equal to which as we can see in Desmos is that point where it would intersect only once okay so key thing here that I want you to notice is that you got to pay attention to what you're asked to answer in this case the value of C right it's not at the point x right it's in order for the line Y equals c to intersect at exactly one point so you're looking for I'll actually quick graph this as well on Desmos I can show you if we were to put in the point Y equals negative 79.75 as you can see intersects at only one point so always pay attention what you're asked to answer with moving on to 26 go ahead and take this moment to share this video with your teacher so that they can show you more of my videos during class and I can get more views okay question 26 right there let me go ahead and hide Desmos now all right sweet so question 26 see if I can get over there there we go all right perfect for each real number R which of the following points lies on the graph of each equation in the X Y plane for the given system okay so stacked equations once again I've talked about this before but you would typically look to add subtract um and then you know maybe multiply one of those equations or use substitution now in this case what I see is I've got 2 to 10 3 to 15 7 to 35 all of those are multiplied by five to get what is below so 2 times 5 is 10 3 times 5 is 15 7 times 5 is 35. so that's good because we know that if a solution is if it's a solution if any of these points is a solution to one of them it's also going to be the solution to the other because it's just multiplying the top equation by five now keep in mind that for this question it really is just a substitution battle so you want to be smart about the way that you do this or the order that you do this and the reason why is because substitution takes the most time pretty much out of any question that you'll come across in the SAT and you'll notice especially that if it's a substitution question that's coming towards the end it's probably going to be a bit of a Time suck and because of that you want to be selective in the way that you go about it so what I'm going to do is I'm going to pick the equation that is more simple which is 2x plus 3ys equals seven and that's one that I'm going to use and if it satisfies that it will also satisfy the one below it so that's great because we've already cut our time in half now the next thing I'm going to do is I'm going to look for which answer choices are having an x value that is has a 2 as the denominator and Y values that have a 3 in the denominator or ones that are just extremely simplistic on their own like a whole number that's between like 1 and 10 or something okay so if I look at option A I see that that's going to be over five and over five that's not very simple to do so I'm not going to do that one First Option B's got an x value over 2 which is good because that would simplify because that 2 is going to cancel and then it's got a y value it's not over three but it's very simple it's just R so that's a good one to check early on if I look at C I've got my y values that are over um three so that's good and then it's got simplistic x value as well so B and C would probably be the first to check I'm going to take a look at D D um okay so D has these twos but they're in the Y slot and the Y slots can be multiplied by three so I would check that one third I would check this one fourth and I check these ones one and two and you could kind of just take your pick here in this case I guess I'll just pick C to start with um anyways all right let's go ahead and let's go ahead and put in uh R for the value of x that'd be 2R Plus we got 3y so that'd be three keep in mind our threes are going to cancel here with that three y so we'll end up with two R plus seven so plus two R plus seven is equal to seven okay we know that this isn't going to be right because that's going to end up leaving us with 4r plus 7 equals seven so that's not going to work because we have for each real number R so obviously that can't work we have to get rid of R uh so let's go ahead and test this that this B option right here so once again these twos will cancel out since we have that two in front of that X so that's going to leave us with negative three R I believe that's plus seven yeah plus seven and then we have that would be plus 3 times our y value which is R is equal to seven okay well we have negative three R and three R ourselves will cancel we'll be left with 7 equals seven so our answer there would be B keep in mind like I said earlier that since this bottom equation is just the top equation multiplied by five it will also satisfy that right there okay so that means let's go and move on to question 27 go ahead and take this chance to subscribe if you have not already and also drop a like um also oh you can give super thanks yeah give please send super thanks please please send super thanks if this video is helpful all right question 27 the perimeter of an equilateral triangle is 624 centimeters okay so perimeter 624 height of the triangles K times root three centimeters or k is a constant what's the value of K all right let's draw this out anytime you question on triangles or on um circles try to draw them out it's usually pretty helpful let's go ahead and do that we know it's equilateral triangle so let's just pretend that that looks equilateral um because it's supposed to represent that we have right angles here and here um we also know that Nickelodeon or triangle we have all the same angle measures right of 60 which means that this top One's Gonna Get split into two 30 degree angles and then we have 60 here and 60 here this is important because now we have a 60 30 90 triangle if you aren't familiar with the 60 30 90 triangle I'm going to quickly show you what a 60 30 90 triangle has for special properties okay so 60 30 90 triangle looks like this um the Key properties are that it has values of X where it's across from that 30. x times root 3 where it's across from the 60 and then 2x is the hypotenuse all right that means that's going to talk about this problem in particular so we know that our height is K root 3 so K root three okay and I know that this is a maybe I can zoom in a little bit let me see if I can zoom in to show you guys a little bit clearer all right there you go okay so K root 3 is there now from here we see that that's across from the 60. so since that's across from the 60 we know across from the 30 must be K and we know that our hypotenuse must be 2K well this makes it really easy because it's equilateral so all the sides are the same okay this would be K and K which would sum this to 2K right so now you have your perimeter must also equal 2K plus 2K plus 2K which is 6k therefore 6 K is equal to 624 divide both sides by six and K is going to equal put it in a calculator real quick six two four over six is going to be 104 for the value of K so our answer there's gonna be 104. okay I'll quickly zoom out so you can kind of see the the whole question there okay there it is all right so answer there's gonna be 104. okay so now we've just finished section one um let me see how long that took that took okay looks like around um actually I'm not sure how long it was because I started this recording uh earlier where I was getting everything set up but anyways um that's the first section obviously like it's gonna have taken longer than it would if I'm doing on my own because I'm giving you a bunch of explanations and talking about certain strategies tips things like that but anyways we'll go ahead and keep going on to the next section okay there we go let me go ahead and switch the side again okay there we go we're on the right side all right go ahead and take this moment to send a super thanks or uh comment at your friend or something anyways go into number one now until he earns P dollars for every W hours of work which expression represents the amount of money in dollars totally earns for 39 W hours of work all right well Sharon's P dollars for every W hours of work uh she works 39 W hours okay our W's will cancel and the amount she earned then is going to be equal to 39p okay that's the amount that she earned 39p that's gonna be answer Choice a moving on to question two now for training program one rides his bike at an average rate of 5.7 minutes per mile which function models the number of minutes it will take one to ride X miles at this rate okay so we don't know the amount of minutes it takes them to ride X miles well we know that he's riding an average rate of 5.7 minutes per mile so if we take 5.7 we know X is the amount of miles that he's riding okay so minutes per mile times number of miles gets us his total number of minutes M of X therefore answer there's got to be D moving on to question three now okay once again I gotta switch sides go and take this chance to comment some video requests let me know what videos you want um whether that's courses whether that's YouTube shorts whatever I'm going to switch the side there we go question three solution to the given system equations is X Y what's the value of y all right immediately I got 3x and negative 3x that jump out to me also quick no I want to pay attention to what I'm asked to answer with that's the value of y so I do want to get rid of these X's I want to isolate y I'll add these together that's going to give me Y is equal to 12 plus negative 6 12 minus six is six thus I'm left with Y is equal to six I'm only asked for the value of y not 2y plus anything so uh very easy to answer that one that one's going to be B moving on to four equation gives a speed as the miles per hour of a certain car T seconds after it began to accelerate what is the speed miles per hour of the car five seconds after it began to accelerate well we know T is representative of the seconds after it began to accelerate we're asked five seconds after began to accelerate we plug in 5 for t five times three is going to give us 15 40 plus 15 is going to give us 55. so our answer there will be D all right go ahead and take this moment to drop a comment and let me know what your goal score is on the SAT keep in mind the SAT is out of 1600 points all right here's question five for the right triangle shown a is equal to 4 B is equal to 5 which expression represents the value of C well let's go and write this in a is 4 B is 5. well we know that this is just a squared plus b squared plus c squared right so that's going to be a squared which we'll just call A4 right so 4 squared plus b which is 5 squared is going to equal value of c squared keep in mind we need the value of C not c squared so we have to take the square root of both sides which means that we'll get C is equal to the square root of 4 squared plus 5 squared which we see is going to be answer choice at D so D would be our answer for that question number six now what is the solution to the given equation all right so this is really simple it's just one sentence what's the solution to the given equation subtract 5 from both sides that'll give us 4X is equal to 160 divide both sides by 4 and that's going to give us x equals 160 over 4 which is 40 so our answer there is going to be 40. go and take this moment to like the video if you have not already and if you haven't liked the video by now after me having asked you like three times um I I take that as a sign of disrespect to be honest like if you're here this long go ahead and like the video why not anyways here's question number seven the x-intercept of the graph shown is X zero what is the value of x okay so graph shown or x-intercept shown as X zero What's the value of x well that's going to be where our Y is zero which we see is right here value of x there is seven so that one's really easy answer there's seven moving on question eight we've got function F's defined by f of x equals one tenth x minus two what is the Y intercept of the graph y equals f of x and the X Y plane all right so y-intercept we know is where X is zero okay so 1 10 times 0 is going to be zero zero minus two is going to leave us with a value of negative two okay so we have zero and negative 2 as our answer there so the answer Choice B okay moving on to question number nine not gonna lie I don't know if you guys saw that but I got hit in like the I with a bug um yeah that kind of painful I'm not gonna lie all right now we've got question number nine function apps defined by f of x is equal to 7x cubed and the X Y plane the graph of y equals g of X is the result Shifting the graph of y equals f of x down two units okay you saw me talk about this in the last section Transformations pay close attention to them okay we're given that f of x equals 7x cubed but we're told y equals g of X is a result of Shifting the graph down two units which equation defines function G okay well that's going to be 7X cubed and now we're shifting it down two units so all we're doing is subtracting two then okay so a is wrong B is wrong uh C is going to be wrong as well and our answer there would be answer Choice d okay moving on to question number 10 which ordered pair XY is a solution to the given system of equations Okay so we've got X Plus Y is equal to 10 or I'm sorry X plus 7 is equal to 10 X plus seven squared is equal to Y well if X plus seven is equal to 10 then we can just substitute in 10 for X plus seven right stacked equations look to add subtract multiply or substitute in this case substitute okay so that'd be 10 squared is equal to Y thus Y Must equal 100 only has Choice with Y is 100 is answer Choice a so a is our answer there as you can see understanding that trick for stacked equation saves you a ton of time all right moving on to question number 11. if you want to take this chance to share this video with a friend that'd be much appreciated posting it to Snapchat or Instagram stories would be awesome and much appreciated question 11 which expression is equivalent to this expression here and look for common terms which we have as X cubed values so 7x cubed minus 6X cubed will leave me with one X cubed same thing look for common values here 7x and negative 3x so keep in mind this subtraction sign gets applied here so we have minus negative 3x which turns into a plus 3x so we've got X cubed plus 10x so we see that's going to answer Choice a go into 12. function p is defined by P of n is equal to 7 n cubed what is the value of N1 P of n is equal to 56 case p and N is 56 solve for the value of n56 is equal to 7n cubed divide both sides by 7. gives us n cubes equal to 56 over 7 which would be eight eight is equal to NQ we'll take the third root third root of each of these keep in mind third root of 8 is 2 so 2 is going to equal the value of N and our answer there is eight okay keep in mind 2 times 2 times 2 is 8. all right remember 13 is what we're on now go ahead and take this moment to subscribe if you have not already if you have ideas for what I should say while I change the side of the screen during these videos then let me know in the comments question number 13 and the figures shown line C in our sex parallel lines s and t what's the value of x all right so key thing to understand with intersecting parallel lines is this angle here of 110 is going to be the same as this angle here of 110k they're corresponding angles now from there it's really easy you're just going to look to get this 180 degrees right because it's sort of like that semi-circle so then you just have that 180 degrees and you subtract 110 degrees and that's going to give you 70 degrees as the value of x okay so your answer there for the value of x is 70. all right let me grab a quick Swig of water okay 14 a list of time values as shown what is the mean of these data to calculate the mean we're going to sum the data and then divide by the number of data values all right so let's go and do that we'll sum these together I'm going to use a calculator I'm not going to write it all out so just I'll talk you through it okay so you're going to open up your calculator clear it and then go six plus eight plus 16 plus 4 plus 17. Plus 26. plus 8 plus 5 plus 5 plus 5. okay that gives us 100 how many data valves do we have see we've got one two three four five one two three four five so we've got ten data values okay that's pretty simple 100 over 10 that's going to leave us with 10. okay so our answer for the mean is going to be ten so Circle our answer of 10. going on to question 15 now okay let me know what videos you guys want next okay question number 15. equation E of T is equal to 5 times 1.8 to the power T gives okay just quick thing I want to talk about if you see this where you have an initial value a growth a growth factor and that's raised to some power always be thinking exponential growth formula okay this is the initial value this is your growth factor and then this is the rate at which that growth factor is changing all right so gives or the rate at which um or how much time has passed right okay now gives estimated number of employees at a restaurant T's number of years since the restaurant opened which of the following is the best interpretation of number five that's the initial value okay so that'd be uh since this is all representing the estimated number of employees at a restaurant this would be the estimated number of employees at the restaurant when it first opens um which we see is answer Choice a when the restaurant opened option b increased an estimated number each year no c number of years it's been open no and then D percent increase in the estimated number of employees each year that is incorrect okay number 16. what is the minimum value of the given function okay this is super simple we have x squared that's always going to be positive and then we have plus 55 so the minimum value would be 55. okay that one's really easy um just recognize that X squared's got to be positive if you're adding a positive number to anything it's just gonna get larger so minimum value there would be 55. uh number 17 it looks like we're on now I'm so sorry I just did like like a massive hiss and anyone who's wearing headphones probably uh heard that so sorry about that I should have just told you all to subscribe one more time um but anyways moving on to question number 17. each year the value of an investment increases by 0.49 of its value of the previous year which of the following functions best models how the value of investment changes over time okay well it's obviously increasing because it literally said it increases by 0.49 of its value the previous year so decreasings are all wrong uh C increasing exponential yes D increasing linear no okay some you may be wondering about the difference between increasing exponential increasing linear um or the difference between all of these I'll quickly touch on that okay if the value of an investment is increasing by 0.49 of its value the previous year that means the amount that it's increasing is dependent on what it was the prior year and since since it is dependent on what was the prior year it's going to be exponential now keep in mind it we're told that it's increasing by 0.49 if we were told that it was decreasing by 0.49 then that'd be decreasing exponential increasing and decreasing linear obviously you're going up or down by the same amount every year regardless of what the value was the previous year all right moving on to question number 18. population of Greenville increased by seven percent from 2015 to 2016 and the 2016 population is K times the 2015 population what is the value of K well obviously you would take 2015 population which we'll call X is equal to 2015 population you would take that and you have to multiply that by that seven percent increase which we represent as a decimal of 1.07 in order to get that 2016 population so uh 2016 populations K times the 2015 population what's 5K 1.07 so against Choice C moving on to question number 19 the expression is equivalent to a to the power of 11 over 12. okay where a is positive anytime I see a is greater than zero or a is less than zero I just think positive or negative I just find that easier than sort of thinking about something like this so that's just kind of a sort of a mindset that I think you should have on the SAT but anyways getting back to this this question's specifics I see that all of these numerator values are 132 um and then the values out here are all what's different okay so let's go ahead and get this numerator value so to do that we need to get um we'll do 132 divided by 11 to see what we're multiplying by 132 divided by 11 that's going to give us 12 okay so that'll give us 12 so we have to multiply by 1 so we'll have to do 12 over 12. that's going to give us a to the power then of 1 3 1 over 12 times 12 which is one four four okay from there we could rewrite that as um I guess let's go ahead and rewrite it so that'd be a to the power of one three one and that's an a not a 9 a to the power of one three one and we're taking the 144th root of that since 144 is the denominator in the exponent and 131 is the numerator and the exponent so looking at our I'm sorry that should be one through two not one three one one three two quick check that yeah one through two okay sweet uh from here we find from matches this we're going to see that that's answer Choice B so B would be our correct answer for number 19. let's go move on to number 20. number 20. go ahead and take this this moment in time to like the video One More Time um but don't like dislike the video just like it if you haven't yet question 20 an event planner is planning a party it costs the event planner a one-time fee of 35 dollars to rent the venue and 10.25 cents per attendee I'll represent that as a uh the event planner has a budget of 200 what is the greatest number of attendees possible without exceeding the budget okay so we can meet the budget but we cannot go over the budget all right so we've got our equation down keep in mind 35 one-time fee so we just add that and then we have 10.25 times a um which that kind of looks like a q so I'll just rewrite that as an a all right there you go what's the greatest of our attendees let's go and solve this we subtract 35 from both sides that'll give us 165 must be greater than or equal to 10.25 a from there to solve for a we divide both sides by 10.25 165 divided by 10.25 is going to equal and keep in mind oh it looks like I forgot the a there there you go okay keep in mind this still has to be greater than there all right so let's go and put that in the calculator 165 divided by 10.25 it's going to be 16.09 16.09 okay keep in mind it has to be less than or equal to that so the greatest number of attendees then be 16. obviously you cannot have a partial person um sorry answer there is 16 going down to 21 absolute value question I don't think we've had an absolute value question on this test yet so it's going to be this one if uh absolute value 4X minus 4 is 12 what's the positive value of x minus 1. okay keep in mind like I talked about earlier you want to pay attention to what you're asked to answer with on the SAT some people here are just kind of answering with the value of x and they're going to get it wrong because you need to do the value of x minus 1. anyways a couple ways that you could look at this um one of it which would be looking at 4X minus 4 understanding sort of division by four to get to the x minus one in context of absolute value I really don't like looking for ratios on absolute value and absolute value I think it's smart to just play it safe and just go ahead and solve for x um it's just kind of my take on absolute value just kind of my gut instinct but anyways let's go ahead and solve for x here um and I I'll show you how to get both Solutions even though we only need one here okay that's gonna equal 112 I'll add four to both sides I get 116 that's equal to 4X divide both sides by 4 that means that X is going to equal I think that's 104 but I'll Quick Check once or not 104. um 116 divided by 4 29 okay yeah I don't know why I was saying 104. uh X is going to equal 29 positive value okay that's perfect then okay so we just take that 29 we subtract 1 and we're gonna get 28 as the positive value from here we could go ahead and move on but I'll quickly show you how you can get the other uh the other value of x this won't be the other answer would be the other value of x okay and that would be that you would take minus 4X minus 4 distribute that negative sign and this is because it's absolute value so it's absolute value you can get two solutions for the value of x the first being just how I showed you to set it up and the second being you put this negative sign out in front of everything that's in that absolute value and you apply it okay so then we'd have negative 4X plus 4 is equal to 112 we'd go ahead and subtract 4 from both sides we'd get 108 is equal to negative 4X then from there we would get that X is equal to 108 divided by negative 4 which would give us a negative 27 and as you can see that would give us a value of negative 28 which it can't be correct because SP the positive value but anyways I just want to show you that absolute value because we hadn't covered that yet on this on this test um I mean let me go ahead and erase this so that no one is confused later on um but anyway so going on to number 22. uh we've got a cube has an edge length of 68 a solid sphere has a radius of 34 inches and it's inside of the cube okay so 34 is equal to R to the nearest cubic inch what is the volume of the space in the cube not taken up by the sphere once again pay attention to anything underlined on the SAT okay so volume of the space in the cube not taken up by the sphere if we quick draw this I'm just going to draw it two-dimensional because I can't really draw very well okay we're looking for the value of the space that is not taken up so this is a subtraction question okay so we need to start by calculating the volume of the cube so that's going to be 68 cubed keep in mind length times width times height and a cube all those are the same so 68 cubed now we have the volume of a uh sphere which is four thirds pi R cubed our radius is 34 so 34 cubed now from here we can go and put this on our calculator let's see what that comes out to 68 cubed minus four thirds times pi times 34 cubed that's going to give us 149796 so our answer there would be a all right moving on to question number 23 go ahead and take this moment to comment your goal score for the SAT if you have not done that yet and also comment your test date so I can know how far out you guys are from taking the test here we've got question number 23 what is the diameter of a circle in the X Y plane with this equation all right I'll quickly go over the circle equation in case anyone doesn't know it x minus H squared plus y minus k squared equals r squared where R is your radius and your center of your circle is the point h k key thing to note here is that h k um note that there's negative signs in front of H and K but your Center is still H and K not with a negative sign um one to point that out anyways that being said we need to calculate the diameter of the circle we know 16 is the value of r squared 16 is equal to r squared from there we take the square root of both sides that gets us 4 is equal to R therefore our diameter keep in mind what you're asked to answer with on the SAT because 4 is an option here but it's not correct okay so our answer for the diameter is eight because it's two times radius our answer is B all right number 24 if exponential function f value of f of 1 is k k is a constant which the five equivalent forms of the function shows the value of K as coefficient or base all right this one's a little bit tricky um so if we take a look here we've got value of f of one is okay so we can just quick write F of one is k k is a constant which shows the value of K as the coefficient or the base k a coefficient would be something like 50 80 128 24.8 okay so let's go ahead and plug in one and see if that's the case anywhere okay if we put in one here we have 1.6 squared times 50 that's impossible for that to equal anything that's a coefficient or base and option a uh same thing in B it's 80 times 1.6 to the power of one there's no way that that can be a coefficient or base equal a coefficient or base that's in that that formula or that equation or that function sorry and then question C or I'm sorry option C we have 128 times 1.6 all right then we have one minus one keep in mind I'm getting this one from F of one equals K okay 1 minus one would put this to the power of zero for that 1.6 that'd be equal to 128 times 1.6 to the power of zero one point six to the power of zero is one so that would equal 128 which we see is a coefficient in that function so our answer has to be answer Choice C moving on to question number 25 now okay go ahead and take this moment to send a super thanks if this video is helping you out okay here's question number 25. all right a model estimates that at the end of each year from 2015 to 2020 the number of squirrels in population was 150 more than the number of squirrels in the population at the end of the previous year the model estimates that at the end of 2016 okay this is interesting we have 2015 to 2020 and then we have 2016. okay so at the end of 2016 there were 180 squirrels in the population which of the following equations represents to this model where n is the estimated number of squirrels in the population T years after the end of 2015 and T is less than or equal to five Okay so key thing I'm seeing is that we have this 180 swirls in the population but that's at the end of 2016 and our model here is starting at the starts at 2015. so we actually have to backtrack to get our initial value and our exponential growth formula so we know it can't be 180 because we know that's one year after and we know each year it's 150 more than the number of squirrels at the end of the previous year so we go and get rid of C and D um and now we don't actually have to calculate it because we know to be 72. now the difference is between one and a half and two and a half as for the growth rate now a growth rate of or a growth factor of 1.5 growth factor of 1.5 would be 50 increase every year a growth factor of 2.5 is 150 increase every year because keep in mind that if it was something like um I guess we can just use this as an example if it was 50 year over year that is just 1.5 right because one is if there's a zero percent increase over a year right so keeping that in mind always pay attention to if it's um something like 150 more than the number of the previous year things like that but yeah overall I think the big thing for this question is making sure you're paying close attention to dates um dates are really important on the SAT because you can come across a difficult question like this where you have um you know an initial population and an exponential growth formula where you have a date that is not at the start or at the end so always pay close attention to that it's really important because if you didn't catch that you'd answer with um I guess I should probably go ahead and circle my answer and so here's B because if you didn't catch that your answer would end up being answer Choice D which would be wrong so always pay close attention to that anyways go and move on to question 26 go ahead and take this chance or this moment in time to like the video if you have not already and also please comment something I should say while I'm moving things um from like well I'm switching sides of the test because I've just been saying like the same things for the past hour anyways question 26 and a given pair of equations A and B are constants the graph of this pair of equations an X Y plane is a pair of perpendicular lines okay perpendicular that's good which of the following pairs of equations also represents a pair of perpendicular lines all right so this first pair of equations is perpendicular in order for it to be perpendicular we need to have slopes that are reciprocals and opposite signs so I'll quickly show you what that means I'm actually just going to use this question as the example so I'll quick show this note that both of these are in standard linear form which is where you have a coefficient in front of the X um and then a coefficient in front of your Y and that's set equal to a constant that's important because your slope can then be calculated by m equals negative A over B where a is the value of the coefficient in front of X and B is the value of the coefficient in front of Y so let's go and calculate that for this first equation okay that would be slope equals negative a which in this case be negative 5 over 7 because 7 is that b value now the slope then for this equation down here is going to have to be the opposite sign so I have to be positive and then the reciprocal so be seven over five now if it's seven over five then we know that the a value here has to be actually negative seven right because keep in mind that the slope for standard linear forms negative A over B so to get that positive would have to be that negative seven okay and the value of B would just have to be 5. now key thing that you need to recognize here is that we have 5x and then 5y and then we have 7 Y and negative 7x now what you have to see is that the coefficients are switched right the coefficient in front of X is not the coefficient in front of Y the coefficient that's in front of Y is not a coefficient in front of x but there can only be one sign change okay so you'll notice that the only sign change here is in front of the coefficient in front of X right it goes from being a positive coefficient to a negative coefficient but the coefficients in front of Y stay the same because if there's two sign changes we're not going to end up actually changing sine in the slope equation there will be one sign change all right now that we know that let's go ahead and keep going through this so we know our value for a is negative seven we know our value for B is 5. so let's go ahead and run through these okay this is a whole new pair of equations here okay we do know the values of A and B right so we have to check each of these pairs of equations to see if they're perpendicular they are all in um standard linear form as well so we can still use m equals negative A over B all right let me actually write this a little bit higher up b equals five all right so 10x plus 7y we know that right there we've got negative a so negative 10 over 7 and then down here we've got our value of a which is negative 7 which negative negative seven gives us positive seven um actually you know what we can do let's just do this we'll just plug in uh this is going to be way faster okay so negative 7 and then B value is five so that'd become negative 10. as you can see we do switch our coefficients but we have two sine changes so a is incorrect and if we look at B we've got let's go and plug in our a values to negative seven here and then we have plus two times B Because five so give us plus 10y we do have the opposite coefficients and we have only one sign change so B would be have to be our answer okay so as you can see that's way faster okay um I accidentally kind of started out going down the rabbit hole of doing m equals negative A over B for all of these and then I remembered I literally like one minute ago just told you the trick of looking at the coefficients and then flipping the sign so that's all we have to do there on number 26. moving on to number 27. uh guys please like the video like I'm so dehydrated right now because I've just been talking this whole time continuously and very pretty loudly um so like the video because like my eyes are like watering from like how dehydrated I am um number 27 and the given equation C is a constant uh the equation has no real solutions anytime you're told something has two real solutions one real solution or no real solutions pay attention to it if C is greater than n what is the least possible value of n okay I'll quickly go over B squared minus 4AC for anyone who doesn't know it if B squared minus 4AC is greater than zero or in other words it's positive that means that there's two real solutions now if B squared minus 4AC is equal to zero that means that there is one real solution and if B squared minus 4AC is less than zero and that means there are zero real solutions or in other words there are no real solutions okay now you might be wondering what the value of B is I'll quickly show you keep in mind this applies for quadratics that are set equal to zero so if something isn't set equal to zero you have to set it equal to zero first the value of a is whatever the coefficient is in front of x squared so in this case a is equal to one the value of B is what's ever is in front of that x value so in this case b is negative 34. okay the value of C let me zoom in actually I just noticed this is pretty zoomed out okay sorry about that I feel like I've been zoomed out for a while that's my fault I should have caught that earlier um and then C is going to be that value of the coefficient which in this case is just C so C is equal to C all right from here we're told that the equation has no real solutions okay which means that it has to be set or has to be less than zero as you can see okay Less Than Zero just going to draw this out so we got negative 34 squared minus 4 times a a is just one so minus 4A times C this is what we get it's got to be less than zero all right from here we want to isolate C so let's go and do negative 34 squared see what that gets us that's going to give us 1156. so we got 1156 minus 4C must be less than zero I'm going to add 4C to both sides so now I get 11.56 it must be less than 4C from there I'm going to divide C by both sides I'm sorry divide 4 from both sides okay 1156 over 4 is going to give us 289. all right so from here we see that c must be greater than 289 which as you can see if we look back up here at C is greater than n okay we see that n would be 289 okay so our least possible value of n is 289. so our answer is 289. if you enjoyed this video please like subscribe and consider sending a super thanks to help support my channel additionally please drop a comment below letting me know what videos you want me to make in the future and if you are looking for additional Educational Services that it offer please check out my website Hayden roadie.com