The graph concept can be extended in several ways. In an edge-weighted graph, each edge is assigned a weight or a cost, or you might think about this as a distance. Taking the edge incurs the cost, and so a question we can ask, what path between nodes has the least cost? So let's introduce the idea of an algorithm. An algorithm is a systematic procedure that solves a problem. Taking an algorithm requires ingenuity and imagination. Following an algorithm, on the other hand, requires blind obedience to orders. Humans are good at ingenuity and imagination. Humans are also good at blind obedience to orders, but we don't want to encourage this. The important idea to keep in mind is that once we produce an algorithm to solve a problem, a machine can solve the problem faster, more accurately, and more cheaply than any human. What this means is that any task that can be reduced to an algorithm can and will be done by a machine, and so it is not worth learning algorithms at the expense of understanding. Now that doesn't mean you shouldn't learn algorithms, this will be on the test, but it does mean that you should also understand why they work, because understanding why something works is the key to making it better. The advantage of a human side is that humans do things without knowing how they do it. For example, find the shortest path. If we give a human the task of finding the shortest path, they can probably do it quickly without difficulty, but they would have a hard time describing how they do it. In order to create an algorithm, we have to consider how we make our choices. Now before we go on one important idea about our creation of algorithms, in 1950 computer scientist Alan Turing described what he called the imitation game, but would later be called the Turing test. Reduced to its essentials, we don't care if a computer solves problems the same way we do, it only matters that it gets the same answers we would. So we don't have to describe how we would solve the problem, rather we can focus on whether the problem has been solved. Now because computers can do things very, very, very, very quickly, it's tempting to use what's called a brute force algorithm, try every possible answer, and see which one works. Unfortunately most problems have too many possible answers for a brute force algorithm to be useful. It would take a computer longer than the lifetime of the universe to try every possible answer to certain questions. So one way humans make decisions is they look around and say what's the best possible decision I could make right at this instant. And this leads to what's called a greedy algorithm. In a greedy algorithm we make the best possible decision at the instant we have to make the decision. And what's important here is that we're not considering the long term consequences of our decision. Now in this case if we want to minimize the distance, this means we should take the shortest path from wherever we are. Now one risk that we have whenever we describe an algorithm, because an algorithm describes a sequence of steps to be followed without deviation, we do run the risk that that sequence of steps will trap us into a loop. And so to avoid cycling we'll also require that the vertex be one we haven't visited. So let's apply a greedy algorithm to find the shortest path from A to H. So we'll start at A, and if we want to take the shortest path from a node that doesn't go to a node we've been to, from A we could go to either B, distance 15, or C, distance 6. And since we want to take the shortest path we'll go to C. Now we're at C. Well if we're at C we can go to B, distance 7, E, distance 8, G, distance 15, or F, distance 12. And since we're being greedy we go to B which has the shortest distance. Now from B we can go to D, distance 12, or E, distance 6. So we go to E which has the shortest distance. The only path from E that takes us to a new node is the path to H which is where we want to go anyway. And so our last leg is going to go from E to H and our total distance A to C is 6, C to B is 7, B to E is 6, and E to H is 10 for a total distance of 29.


is dedicated I'm back with another video make sure you put me on your big screen video and if you're in the car turning up on your exterior you see the title you see the thumbnail guess what new app alert baby we got a new app it's time for us to get to this money no cap now i do not know what to expect i don't know it's going to be good or it's going to be bad i'm going to tell you guys everything and how i feel about the app but we're picking up some parcels so we we we uh scheduled this last night at joint pop thub we scheduled it now the one thing i will say about this app is you get the schedule the time you want to come so we picked between 6 30 a.m and 7 a.m we got here around 6 45 and we still have not pulled into the building yet so already right now i don't know what's going to happen now it says we're supposed to pick up 18 to 24 parcels and we will receive a payment between $55 and $93.50 and we also will receive a $15 bonus for doing this for our first time we are here in the garage now we got a line we got people lined up right now i don't know when we're going to go inside but i want to tell you guys all the info we already pulled up it's time to get dough let's go oh we finally got to win all the way there but if y'all can see right there look this how they set you up baby they bring the route to you and just load your car from there so it's a huge warehouse and just bring your route to you then you got to load the car from there and i want to say this we did put snow white on there but these boxes are seeming kind of big them doors looking huge i ain't gonna lie and we're supposed to be able to fit 18 to 24 boxes in this car so i don't know if it's gonna be ever done it's a corolla right here too so they seem to think they over there getting right but we're going to see what happened baby y'all gonna go when i go it's time for us to pull up we are already about to go let's go my name is Don trail those the check off that you're doing is just uh they just telling you where to deliver or what not to deliver so if you don't feel safe don't deliver the box all right please try not to throw like over the fence anything try to just put it in front of the address take a picture they want to see the actual po d the information of the the label right once you take a picture correct um if for any reason you have any issues you like no need to get in touch with someone hit your ss blood at the top that's this batch all right they'll direct you on what next to do okay in terms of um some of these do have like the um the ice packs that you have to have your window down just slightly just so that you obviously won't fall out anything dry ice right and then in terms of routes so these are your stop numbers right here this number seven yep so you want to load up from highest to lowest because obviously the lowest lowest number is what you're pulling first that's going to be your stop number all right any questions no pretty good pretty well check it out baby look at this this joint is critical you can really breathe about this joint your pack to the brim let's go to the trunk for me i'm a trunk this is trunk baby 23 packages if you want you can have it let's go and just like that i think we are here at the first address oh here you go right here i'm getting that joint mixed up mix it up get that joint mixed up it told me to put at the back patio i'm gonna put this right here i ain't no games and they're all already know my name give me kids and there ain't nothing and a few moments later all right we in this joint they actually want to do it but i'm gonna take it to him because i want to make sure i take it to the right place 101 102 104 right here step back from the photo your nose man we gone stop number two get this money is what we about to do they said leave by the front door are you a real real man like you know we jump like top step back with the photo y'all know that smack we gone and we went around the corner to drop off order number three we are trying to get to all his sheets jump like top step back turn with the photo y'all know smack we gone now we are around the corner and stop number four y'all know we love running up these dope stuff like a time step back from the photo y'all know though smack we gone order number five guess what it's a great time to be alive drop the phone off and then we got to drive step back on the photo y'all know those yet again we gone and just that fast we are here to drop off order number six we are here in the mix and you hate you a drop like that step back from the photo y'all know we gone we gone we gone got it got it order number seven order number seven three of look we is not going to affect it i almost feel that last word y'all so well foot got caught on the uh just bush and that joint almost bust myself in front of the people house they creep like a mouse if you hate me i don't know what to say we want the money out of the cloud step back on the photo y'all know that we gone order number eight don't be good be great and guess what keep faith and grind until you shine keep on climbing to the top no never stop stop at the top step back on the photo y'all know that we gone order number nine we are here on the grind rain sleep or sunshine it ain't still not right now but it's raining but we are here doing our thing in this chain step back on the photo we gone order number 10 we back at it again with uh uh uh another another in my dj caliber step back on the photo smack we gone order uno uno we trying to get our pockets fat like sumo we're in stars bars like uno come on step back from the photo y'all know smack we gone order number 12 what's that smell money we get to this buddy baby we love get to this buddy jump like it's hot step back photo smack gone order number 13 it's raining but not pouring it ain't pouring outside it's raining a little bit baby we ain't complaining though we doing our thing in this change baby this house is beautiful step back get away with the photo smack we gone order one fold guess what we here to do we here to go y'all we know we here to go baby jump like it's hot step back on the photo smack let's go order number 15 we here to get cream cash rules everything around me cream get the money dollar dollar dollar dollar bills y'all step back on the photo let's go order number one six first they love you gonna switch i'll be seeing some of y'all in the comment section hey i'll be seeing y'all outside they love me switch so i'll tell everybody who's staying around to stick around step back on the photo smack let's go order number 17 my favorite number you know i'll spit that hot stuff like thunder step back with the photo y'all know let's go order one eight we got five more to go and then we skate baby we only got five more to go i had to come to the side door i had a dog bark no i'm on no five he about to give it to the customer right here here you go sorry you're welcome you have a good one order one nine if you want to stay rich stay on the ground baby you got to stay on the ground all the time i love step back on the photo order 20 comment below and let me know do y'all love getting to this money because i love getting to this money baby it's my favorite thing to do i know i'll take like a fluke it's smelling good in this you know they got the fabuloso in this one they're getting right step back let's order 21 can you do some 21 under order 21 saps if you want you can have it i'm leaving right here because i don't want them to hit the joint when they come out the screen and we're trying to get this green step back on the photo let's go and we are here to drop off the second to last we are here having a blast getting this can you're having a blast baby in this rain we doing our thing photo let's go last one we are here to get this job done baby this is our last one i'm glad we done we did have a little fun sounds everybody is someone step back to know the photo you are gonna know we go it just like that is game time well we're out there to shine that's all shine baby we're always on the grind and guess what thank you for giving me your time and you watching this video or listen to this video whatever you did but let's talk about acts so hard let's talk about the pros and the cons the things i like and the things i dislike we're going to go here and start off with the things i like the thing one thing i like is in certain areas you get to pick your own route so you get to decide on which one you want to pick so it's usually pop up in the phone is going to show you which different roster they have you get to pick which one that you want to pick in my in my area unfortunately we did not get to pick our own route today but they do have that in some area so you might want to check it out now number two you have a variety of pickup times i'm talking about from 6 a.m all the way to 8 p.m so if you whenever you want to do the route they have 6 6 30 7 7 30 8 8 30 all those times all the way until 8 p.m so that's the great thing they have going on with axle hire then we're going to go into number three number three you can take more than one route at one time so say for instance we there was another route going to that same area we were going to we actually could have got another route add on to the one we had we couldn't fit anything else in here but if we had the suv or if we had smoke we can go out there and get to this money no joke so that's a great thing i love about axle hires you can take more than one route and you can get the money out of the cloud now let's get into the dislikes dislike number one it takes way too long for you to actually be able to load everything go we literally waited over like we waited like just about an hour before we even got to the loading dock so we can get our stuff situated so we had to wait in line the line goes so it didn't take one person about each each person one two three so when somebody pulled out somebody is pulling when somebody else put out somebody else put in you do not get to pull in the warehouse you got to pull it outside so if it's raining snow whatever it is you still got to go outside and handle your business so i don't like that another thing that i had an issue with whether everything axle hire for i ain't really gonna blame them it was way too many apartments i'm talking about majority of the stuff we dropped off was apartments and they want you to do special instructions and all that stuff and also i don't like that they make you um you have to take the photo with their address facing you which i understand on the end but that takes me way more time and i don't like doing all that i'm gonna jump like it's hot step back in with the photo and i'm gone now let's get into what everybody wants to know everybody always noticed how much did you get paid i'm going to tell you guys just give me a second hey hold on send me down send me down give me a second let me just say this for that route from the pickup location to actually from the pickup location to do the route and that's it we drove 40.29 miles i know it sounds terrible but just to get to the first drop-off location that was like 40 minutes probably like 30 miles all together i'm gonna say this every single drop-off that we had today was right by each other the furthest we had to drive was three minutes that's it everything i'm talking about is right there so as far as their route how you do the route is absolutely excellent the best i've ever seen everything was literally right there low key it was so it was so close together you could have rolled a bike and dropped them joints off and you had in the room i'm talking about right there super sweet most of them was one to two to three minutes that's it nothing else but all together we only made $56.89 saying that's the issue with the route if they paid more i'm gonna say this axle higher if you paid about 150 dollars for that route or i say 125 you paid 125 for that route you would probably want to be one of the best uh like the routes the best routes out here i'm just gonna say it on the truth if you pay like 150 for that route 125 125 150 you would probably be the best now we do got drop off drop off you could go crazy on drop off but the stops ain't close like that that joint had that how they brought it that was excellent i've never seen like it before dude i'm talking about right around the corner for each other so as far as route and go they do an excellent job with that the pay is a little on the low side i will definitely want to get paid more um it's similar to a i can't really say it's similar to amazon flex i can't really say that amazon flex probably would have paid us a little bit more for that route no no no no no no no i'm mistaken baking maybe not because for a three-hour block in my area it's probably like 72 dollars so that took us an hour and 55 minutes it was supposed to take us on from the on the thing it's saying it's supposed to take us two hours and 15 minutes so the pay is not off it's off a little bit but not that much so come up below and let me know what you guys think do you think the pay was way too low what do you think about the route would you do what you're not doing have you done axle higher come up below and let me know now if you guys would like me to show you how to sign up for axle higher you need to get this video to 1000 likes you guys have 24 hours and 24 hours if you get this video to 1000 likes i know y'all can do it baby i've seen y'all do amazing things before y'all do this is nothing if you get this video to 1000 likes i would do a video showing you guys how to sign up for axle higher and guess what it's time for us to retire i hope you guys enjoyed this video again if you're not subscribed make sure to subscribe and also give me a thumbs up and if you're a partner crew you already know what to do don't don't seize up don't seize up any comment section below i love going out to the sco i'll see you guys on next one be going be going be flowing you already know i'm the dk and i'm on my way


a blog in live for siliconangle.com at the Lexmark international booth at the official CES free show. I wanted to give you a quick glimpse of something that caught my eye and that is the new Lexmark pro series of printers. As you guys know, one of the common things among printers is that they've amortized the costs by charging a whole lot for the actual print cartridges. And one thing that Lexmark has decided to do in their pro series, which is available for $299 for a full multi-function printer, not particularly high price. One thing that they have done is they've substantially lowered the cost for a black ink.  It's a high-yield cartridge that produces 500 pages of standard output. So one thing that caught my eye here, I know it goes a little bit, it's a trend.  So I think this is an interesting trend and hopefully we see more of this.


Here at the ELC, we faced a major challenge when moving classes online. How can we keep classes student-focused and interactive? Our subjects aim to enhance the communication skills our students need to deliver key messages here at the university or beyond. No matter if we're teaching face-to-face or online, we need to make sure that we're giving our students sufficient time to practice and get feedback on delivering clear, appropriate, and persuasive messages. To keep our classes student-focused and interactive, we use a combination of asynchronous and synchronous modes, small group consultations, and we've kept all of our ELC services open. To make sure that our materials are easily accessible by all of our students, we make full use of the capabilities of the LMS. For example, the discussions, the blogs, and the peer and self-assessments. We also make use of our MOOCs and SPOCs to encourage blended and independent learning. Our online courses cover a range of topics, from job interview skills to grammar to the enjoyment of reading. We use Urwind for teachers to deliver content and for students to upload videos and receive feedback. We also use external platforms to encourage peer interaction, for example, Perusso. In our synchronous sessions, we make full use of different platforms, such as Microsoft Teams, Collaborate Ultra, and Zoom. And we make our classes as interactive as possible by using breakout rooms and third-party quiz tools. Teachers also use PolyU collaborative tools, such as Microsoft Whiteboard and OneDrive, fully involving students in practice activities. And out of scheduled class time, teachers make use of online synchronous tools to conduct small group consultations. These give students the opportunity to ask questions, clarify problems, and improve their language skills. Our Center for Independent Language Learning is open, giving students the space to take online classes, to meet fellow students face-to-face, and to use the latest technology. It's been a challenge, but we are confident that we have been able to provide our PolyU students with the English language enhancement opportunities they so clearly need.


Hi everyone, this is Jason Zach from Nathaniel School of Music. In this lesson, we are going to learn a few easy ways to help remember your chords by grouping them and combining them or comparing them with each other. And we are going to do it in a rather exhaustive way. We are going to do everything ranging from major, minor to the sevenths, major seven, minor seven, minor seven, flat five, diminished seven, so pretty even the augmented and the suspended. So do stay tuned till the very end. We are going to look at not how to form them, which you probably already know, or you can watch a lot of the other videos which I have done on our YouTube channel on how you can intervallically form each of these chords. But in this lesson, it's more how you can remember them and use them a lot better. By remembering just one simple thing, that each set of what I'm telling you, each set of chords or each set of data, which I'm gonna give you, are very related to each other. So if you find the relation or if you find what's similar between the two chords, then the naming and the usage and how you improvise and compose with this stuff will be a lot easier on the head. And you can get the data out a lot quicker on your fingers because your mind already knows this stuff. It can interconnect two pieces together. Before we get started, it'll be awesome if you could consider hitting that subscribe button and hitting the bell icon for regular notifications Also, my handwritten notes for this lesson as well as all the lessons we've been doing on YouTube and that we are gonna continue to do on YouTube. The supplementary notes, the backing tracks, the MIDI files will all be on our Patreon page for just $5 a month. Do consider heading over there. Let's get cracking. So I'm gonna start with suspensions or suspended chords. You would have come across them pretty often because they tend to resolve to their major and they can so easily also resolve to their minor. Okay, I've done a lot of videos on suspended chords. Do check, we leave a couple in the description. So do check them out. So suspended chords have an interesting property that first of all, there are two kinds of suspensions. There's sus4, which has a perfect fourth in them. That's C, F, G, one, perfect four, perfect five. Now the interesting thing here is when you invert this chord, when you invert C sus4, you're gonna get F sus2. So C sus4 when inverted becomes F sus2. So it's a good way to package your suspended chords a sus4 is another sus2 and they are separated by a perfect fourth apart. If you can remember that. So then if you take D flat sus4, for example, what is D flat or C sharp's fourth, right? If you're a guitar player, it's usually the next string same fret. That's how you get your perfect fourths. But on the keyboard, you'll have to just remember it. So the circle of fifths can be a very good helpful tool. So D flat or C sharp's perfect fourth would be F sharp. So C sharp or D flat sus4 equals to, or is very similar to F sharp or G flat sus2. I repeat, C sharp or D flat sus4 equals to F sharp sus2 or F sharp or G flat sus2. Sus2 incidentally is where you have a root, a major second and a perfect fourth. So let's do, build that again from the context of C. Let's start with a sus4, so C sus4 equals F sus2. What if we started with C sus2? C sus2, now when you invert this chord, you're gonna probably think to yourself, okay, maybe I should now shove the C on top. You get a very interesting sound called the quartal chord, which I'm gonna cover very soon. So if I move this downward, if I take this G here and move this bottom, I'll get a G sus4. So C sus2, if you have to invert a sus2 chord, you would do the perfect fifth sus4. So what is C's perfect fifth? The answer would be G. C D E F G, so G sus4 happens to be C sus2. C sus2, it's pretty easy to remember, while C sus4 is equal to F sus2. Sus4 to two, when you convert, it'll have to be a perfect fourth movement, while sus2 to sus4 will have to be a perfect fifth movement. So C sus2 is G sus4. And coming to the third position, so all three note structures or all three note chords or triads or any three note harmonic structure will have three shapes. Now, this retains the quality of the chord if it's a major chord. For instance, C major, you invert it, you still get C major, but that's the first inversion. You invert that, you still get C major. It's a second inversion. Now the value or the use case for these inversions is more to do with how you're accentuating the bass. So if you play C major with like this, it's still a good old C major, but when you reinforce the bass, it becomes a C slash E kind of sound, right? So this changes the context. It makes the chord a lot more unstable. Even C over G is unstable. It wants to resolve to the fifth usually or C over E, C slash E. This is a slash chord. We'll want to resolve to the F and that's how slash chords come into being because you need to make the bass dominate the sound. You're trying to change the listener's ear from the traditional triad. C major is just C that it's driven by C. It's a stable sound, but when you change it with another note in the bass, it becomes a slash chord. Okay, coming back to suspension. So the argument here is you have three shapes for every three note chord and four shapes for every four note chord, which I'm going to come to shortly in the lecture. So if you come back to the case of C sus four, you have C sus four. When you invert the guy, you're going to get sus two, which is F sus two. Now, when you further invert it, you're going to start with G and you get this open, perfect fourth kind of voicing, which again is very easy to play on the guitar because perfect fourths are very close to each other. Okay, so you get this open sound. So you could say that this is some variant of G seven sus four, but we have another name for this in the quartal department. We call this as a G quartal chord or you can just say G capital Q. So what is a quartal chord? It's a root, perfect four and a minor seventh or a dominant seventh interval. It is not, that's also a quartal chord, but we give that as a quartal plus because it has a major seventh up top. And then there's another one called sharp four Q, where the four is sharpened, but I'm not going to deal with that. We've done quartal chords in other videos. So this would be G seven sus four. People tend to call it that. However, you can also call this as G quartal. So a G quartal chord would be one four seven flat in terms of intervals. So in conclusion, a suspended chord can give you three chords if you know how to invert it and if you know what the inversions will become. So C sus four, C F G in order will when you invert it, it'll become F G C in order. So that's a sus two, F sus two. When you further invert that to the G starting, it'll be G C F, that's a C quartal. And each of these flavors, each of these chords tend to sound very different than each other, but yet they have the same notes. You kind of get three different chords for the price of one set of three notes, you know? So C sus four, F sus two and G Q or G quartal. So that's about the suspended chord and its inversions, if you will. We don't study inversions of suspended chords and these other chords I'm gonna show you. We probably should. Another nice chord which when inverted, you should definitely figure this out because it'll help you learn that chord. It'll make your life easy for that chord. That is called as the augmented chord. So an augmented chord is built. Let me take this in the case of E augmented. So root, major third and augmented fifth. You could also argue that it's a major third between the root and the third and another major third between the third and the augmented fifth. What is augmented fifth again? It's the perfect fifth going up a step. That would have made it E major. That's now E augmented, okay? So this is an augmented chord. So what happens when you invert E augmented? When you invert E augmented, it becomes another augmented chord. Namely G sharp augmented. And if you invert G sharp augmented with C, what do you get? You get C augmented. So C augmented is the same as E augmented is the same as G sharp augmented or A flat augmented. So you may ask yourself, how many augmented chords should I learn in life? Well, if everything is a trio, then you just have to learn four. You have to learn four trios and probably practice them with maybe a simple drill, maybe using triplets. Come back. And maybe what I like to do is I like to arpeggiate in the right hand and block in the left hand. Block means play together. Descend. So that's a good augmented practice because again, you're getting three for the price of one. So just remember, all augmented chords are inversions of each other. And before I move on to the other chord, the circle of fifths will be pretty helpful because if you look at, if you visualize, for example, C, E and G sharp in the circle of fifths, if you map them out geometrically, first of all, draw the circle well, use a proper circle creating device or maybe a tablet with a good app, giving a neat circle, you'll realize that there is a C, then there is an E. So C, G, D, A, E, that's four o'clock from C. So you draw four o'clock and then you go to the G sharp, which is the other side and then it joins back to C. So what do you get? You get an equilateral triangle. So if you think about it, any equilateral triangle in the circle of fifths, assuming you draw it correctly, will be an augmented shape. And these augmented chords, you don't have to just play them as augmented chords. You can even play them as major chords separated by the augmented chord interval. So this is what the film composers tend to do pretty often. So for example, you have just remember that C, E and G sharp are your pillars, those are your roots. So I can now say I'll play a C major, then go to E and play an E major, then go to A flat and play an A flat major. So it gives you a very interesting sound, a very movie-themed like sound. And see the distance or the gaps are an augmented gap. So. Now you may be thinking, what if I do this for minor chords with that augmented connection? Works pretty well. It's almost an instant way to create something very movie-themed like. Separate them by an augmented. And the next one I'm gonna talk about, the next chord which I would like you to learn the inversions of will again be very movie-themed like. That is called the diminished seventh chord. So the augmented chord is separated by major thirds, the diminished seventh chord or rather the diminished chord, first let's begin with that will be, let's, I'm taking C as the base, minor third and another minor third. So two minor thirds. Now to finish the puzzle, you can add a third minor third and you create a diminished seventh chord. Now diminished seventh chords are exactly like augmented chords. In fact, we call diminished seventh chords and augmented chords as the family being symmetric chords. Symmetric meaning when you flip them around, they pretty much behave the same. So diminished seventh, which is C diminished seventh, how do we form it again? C, E flat, F sharp, A, all minor thirds. Now when you invert C diminished seventh, you're gonna get the next roots diminished seventh, namely E flat diminished seventh. When you invert that, you're gonna get F sharp diminished seventh. When you invert that, you'll get an A diminished seventh. And now if you look at the circle of fifths, the equilateral triangle works for augmented chords for these intervals, for the diminished seventh or the minor third movement, C to E flat to F sharp to A, they're all minor thirds apart.  You'll basically get four corners. So because a diminished seventh has four. So if you visualize the circle of fifths, maybe maintain a page in your book and or maybe use the same page and have different colors for each of the squares or diamond shapes. You'll just need three diamonds basically or three squares and you have conquered the diminished seventh voicing. And the diminished seventh is a very important chord in music. We use it a lot to connect from point to point. So if you take C diminished seventh, very similar to all those four, they all have the same texture, the same flavor. So you don't, so how many diminished seventh chords do you have to actually remember? Well, three groups or three families of four augmented four families of three because the augmented chord has three notes. So diminished seventh, there we go. Now the diminished seventh chord has a lot of uses. One, which is where I want this lesson to drift towards. So we've covered suspended chords, inverted. I've showed you augmented chords when inverted. Diminished chords also when inverted. Remember you'll have four diminished seventh chords for the price of one. Now there's more you can do with diminished seventh chords. So check this out. So if I play C diminished seventh or E flat diminished seventh or F sharp diminished seventh or A diminished seventh, they're all inversions of each other. So I'm just gonna pick maybe A diminished seventh. I could have picked any of the other three. Now you can ask yourself, can this form a dominant seventh chord with some other root than any of these notes right now? So all you have to do is ask yourself, okay, there is a diminished shape in here. There's a diminished shape in here, isn't it? So what is a dominant seventh chord? It's a root and then a diminished chord. So forming, let's say in this case, F seventh.  Okay, so A diminished with an F bass, bang. You've already got a dominant seventh chord. And here's what's cool. Remember you come back to the diminished seventh flavor. You play the whole four note structure. Now you find what will make the diminished seventh dominant. That'll be F and you've got yourself an F seventh flat nine chord instantly. And here's what's really cool. You can go up a tritone. And this is what we call as tritone substitution or tritone movement in music. You just take a tritone from F. What is a tritone? Perfect five minus one. So F to C is a perfect five, minus one is B. And now you keep your right hand shape the same and just play B. You've got yourself A, B, A, B. You've got yourself a B seventh flat nine now. So that one diminished seventh chord is now giving you many dominant seventh chords. Separated a tritone apart, right? So I can take an F dominant seventh and you get a lot of options really. You can even get an A flat dominant seventh. All you have to do is pretty much ask yourself in this shape, what note in the bass would form a major third with respect to A? So A is here. What note in the bass would form a major third? The answer is F. But then you can also ask yourself what note will form a major third with respect to C? Because C is also part of this symmetric chord, isn't it? Just for hearing clarity, I'm going to invert it because I can. I'll do a C diminished seventh. Now what note in the bass will form a major third with respect to C diminished seventh? The answer would be A flat. And what's this called A flat, A flat seven flat nine. A flat dominant seven flat nine. Now I want to re-invert it here. And now you ask yourself, what note will form a major third with respect to D sharp or E flat? The answer would be B, isn't it?  Now you ask yourself, what chord will make it a dominant seventh? Well, what note will form a major third with respect to the F sharp? So I get all these dominant seventh chords. I'm getting an F seventh, right? Then I'm getting an A flat seventh. And I'm getting a B seventh.  And there's something even more weirdly cool about what just happened.  And you're forming another diminished seventh chord in the left hand. So the diminished seventh chords are probably sitting on top of everything music has to offer. Things like the diminished seventh chord, forming diminished scales, symmetric scales like the whole tone scale, the circle of fives. These are concepts which go way beyond scales. They've started scales. So you might want to look into some of these more symmetric concepts as you move forward because even if you're a beginner or even if you're new to the piano, it'll make your life easy. This is not just for piano, by the way. This is more of a general music theory kind of tutorial. So as long as you know how chords are linked with each other, how similar chords are, you'll make your life a lot more easier. You'll not have to deal with 12 versions of every chord and then shapes, voicings. You'd rather group them and package them together and the circle of fives is a great friend. The diminished seventh is a very good chord. You have to study that. We'll leave you a video in the description with some exhaustive study on the diminished seventh chord and how you can compare it with the next chord that I'm going to teach you in this lecture, the minor seventh flat five, also known as the half diminished chord. So on that note, let's now move on to the last bit of this lesson to hopefully have covered every single chord, mainstream chord out there. Let's look at the sixth chords and the seventh chords in more detail. What if I told you that every major sixth chord is a minor seventh chord? That's a weird thing to say. I'm going to prove that. And what if I told you that every minor sixth chord is a minor seventh flat five chord? Very important to know this for a lot of harmonic movement possibilities. So if you take, let's say, f major sixth, what's a major sixth chord? F major with a major sixth, namely, D on top. Very different than a major seventh, which is there. It's a major seventh on top. F major plus D, major sixth. Now the major sixth note, you just tell yourself this one thing. The major sixth note from my root is also the relative minor. Now this is where the terms and get a bit confusing. You have to understand that to form a relative minor from any major, you just go up a sixth. And what is the sixth? Major sixth. So you have minor formed with major sixth. Major sixth is the interval between the root and the relative minor's root. Example, F, whose relative minor is D. So if you take F major, take D minor. They have the same notes and the same key signature when we notate them. So you need to understand when you play an F major sixth, the major sixth is nothing but the relative minor interval. So D, if you now start this chord from D, inverted rather, and start the chord from D, I'm just gonna move the D from the top bottom. This is impossible to do. So I'm just gonna rewire my fingers. That's F major sixth and D minor seventh. You find F major sixth is a very grand, kind of positive, vibrant, bright kind of sound while D minor seventh is a more calm, melancholic, pensive sound because the intervals got restructured around the new root, which is D, which is pretty much why you feel a minor scale different than a major. Not because the scale sounds sad. It's because the intervals are sad or the intervals are different. And when are the intervals of anything going to change? When you alter the root, the bass, the lowest frequency that you're hearing at the current moment. So if you take F major sixth, you just have to remember the major sixth is its minor seventh, so minor seventh chord. So F major sixth is D minor seventh F major sixth is D minor seventh. Let's do this with a couple more options. Maybe E flat major sixth. E flat is a three flat scale. What is its relative minor? C. So E flat major sixth is C minor seventh. Similarly, C major sixth is A minor seventh. It's good to practice this exercise. Similarly, things like D flat major sixth, which I'm playing right now. B flat becomes the B flat minor seventh. E major sixth C sharp becomes the C sharp minor seventh. It's a good way to gang up those two chords, which are very common in music usage, right? Then we have the minor sixth chord. So if you take F minor sixth, a chord I really love to use, you can check out a playlist in the description. We leave you with that. It's called my favorite chords. Basically, all the chords that I use in my own compositions on a almost day-to-day basis, the stuff which I really love to work with, some of them are very mysterious and very interesting, especially when you first listen to it. You might even think those chords are wrong. Those are the chords which I tend to enjoy. So do check out my favorite chords playlist. So let's take F minor sixth. All you need to do is ask yourself the same question. F minor sixth, when you invert it, you invert it to its relative minor, which is D. But now when you play the inverted chord, it doesn't form a minor seventh. It forms a minor seventh flat five, which is also known as a half-diminished chord. We write it with a D and a Phi. The Greek symbol Phi is used to denote this chord because it's a rather weird, long name, minor seven flat five. Well, in theory, it's quite easy to understand. It's a minor seventh flat five with a minor chord, minor base, minor third. So in other words, F minor sixth is equal to D minor seventh flat five. So it gives you how many also a lot of harmonic movement. For example, I'm combining both those chords, F minor sixth, and then D minor seventh flat five because I wanted that tune. Na na na na na na na. Gives you how many a lot of motion and inspires the melody for sure. All right, guys, so in this particular lesson, we've figured out five ways to gang up or to package your chords a bit better and use them hopefully a lot more efficiently as musicians. We looked at the suspended chords and their inversions. Sus four is also, or sus two is also A, quartal. Then we said augmented chords are carbon copies of each other. Diminished seventh chords are carbon copies of each other. And diminished seventh chords, you can use that to make other chords better for your brain by adding the root which forms a dominant seventh with respect to that. And then last but not least, we looked at the sixth and seventh correlations. A major sixth happens to be A minor seventh and a minor sixth happens to be A minor seventh flat five. You can use tools like the circle of fifths with some visually appealing geometric shapes. You can make a neat set of notes for yourself. You can study my notes. Don't just look at it, try to write it yourself.  No magic of any sort will happen. You have to use this stuff, practice it, stare at it every day. Yes, but stare at it and use it. Only when you use it, compose, do exercises with this content will it start appealing to you number one because the sound has to get into your system. You have to enjoy the sound and I feel once you enjoy the sound, you'll use it more and you'll remember it better. So I hope you found the lesson useful. If you did, it'll be nice. If you can leave us a comment, hit the like button. If you liked the lesson and also if you haven't already, do consider hitting the subscribe button. Turn on that bell for regular notifications and the Patreon channel will give you access to my handwritten notes, midi files, backing tracks and many more content for all of our YouTube videos. And lastly, if you'd like to do a course at Nathaniel School of Music, probably cover the basics of guitar, learn how to sing with different styles of singing, learn the piano, learn, do live classes and not just these YouTube videos, you can consider filling up a form in our description or heading over to nathanielschool.com and one of our course advisors will reach you shortly. Thanks a ton for watching the video. Cheers.


This is stock number 90144A. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used light-duty truck headquarters. Remember, we are the guys with the trucks on 41. Today, we are checking out this super clean 2012 Ram 1500 Crew cab short box. This truck has the 5.7 liter V8 Hemi motor. From this HD video, you will be able to tell that for the age and miles on this truck It is an excellent condition. Deep Cherry Red Metallic is the color and I'd like to point out we shoot all of our videos in 1080p 60 frames per second So if you have HD capabilities on your computer tablet or smartphone device, turn them on right now because it is the best and most accurate way to check out this vehicle without actually being here in person. This vehicle has the 20-inch factory alloy rims with the chrome covers, and it has Goodyear Wrangler SRA 27560R20 tires on this truck. These tires are brand new. We put these on during our safety inspection You can still see the little mark right there from when they were made No dents or dings on that front fender. The hood is an excellent condition on this truck I didn't see any major dents or dings on that You do get the chrome trimmed grille. I didn't see any dents on the front bumper It does come with factory fog lights. The headlight lenses are nice and clear Passengers side fender is an excellent condition as well. No dents on that and the passenger side rim No scuffs or scrapes. As you go down this side of the truck You can see just how clean that body is, how reflective and mirror-like that paint is We take these HD videos So if you are far away or even if you're close by and just cannot make the trip down You can still see the truck here the truck and of confidence in the vehicle that you're looking at before you even get here I think somebody's gonna be really happy with the condition of this truck Has over a hundred thousand miles on it, but for those miles and the year Really really nice shape. The body is in excellent shape. Didn't see any Corrosion or anything on the lower rockers. This back rim is in nice shape as well Looks like it is brand new brakes in the back here and these back tires are brand new as well It does have the plastic wheel well liner And as we come around to the back of the vehicle You'll notice it has the dual rear exhaust full towing package, which includes the receiver hitch four pin and seven pin wiring chrome tipped exhaust The tailgate is an excellent condition as well. It does have a locking tailgate a drop-in Pendeliner bedliner That's in really nice shape as well Comes with bed rail covers That tailgate shuts nice and solidly And as you go down this side of the truck just as clean as that passenger side I Didn't see any Corrosion or anything on the box no dents on the box Passenger side rear rim is an excellent shape as well for full disclosure and that tire is brand new too and Finally down this side of the truck Just as clean as that passenger side No dents or dings on the doors. It does have the heated power mirrors Inside the bighorn package gives you the gray cloth interior. There are no rips. There are no tears in the seats They are in really nice conditions smells very clean in this truck does come with a power driver's seat and lumbar We have weather tech floor mats in the front here to keep your carpeting nice and clean power windows power locks and power mirrors Does have the auto headlamps and as we hop inside the truck here You can see that this truck indeed does have a hundred and four thousand 117 miles instrument cluster is nice and clean has a leather wrapped steering wheel cruise controls on the right Information center controls on the left does have radio controls on the back of the steering wheel has the automatic transmission with the manual tap shift has AM FM and Serious satellite radio capabilities on it Just checking here. This is a six speed automatic transmission Turned out a four-wheel drive with the four-wheel drive auto feature and four-wheel drive lock and low features If your climate control down here stability control in a tow-haul mode also has a hundred fifteen volt hundred fifty watt plug-in You can see that that weather tech floor mat covers the entire hump there and the passenger side as well No rips or tears on the passenger seat does come with side curtain airbags headliner is nice and clean comes with the power sliding rear window right there and Very clean throughout this vehicle Take a quick look at the back seats and then we will check out under the hood Back seats are just as clean as the front seats. No rips No tears back here on any of the seats does have the latch child safety system for your car seats Very nice and clean these seats do fold up for extra storage and speaking to that extra storage That is where it's at and I believe on each side There is in-floor storage with two removable bins for easy cleaning You can put ice and drinks in here and basically have two Mini coolers wherever you go We'll take a quick look under the hood. I would personally like to thank you for checking out the video today Hopefully from this HD video you will have been able to tell just how clean this truck is Inside and out all the way around under the hood. We had the 5.7 liter v8 legendary Hemi motor Anger Bay is very clean runs very smooth This truck has been fully safety and inspected by our service shop has a fresh oil and filter change All the fluids have been checked and topped off And this ram is 100 ready to go To see more pictures of this ram 1500 or one of our other 450 New and used cars trucks sdvs mini vans wranglers halftones recorder tons one tons. You name it We got to go to our website. www.summitauto.com full pictures and descriptions of every single vehicle on our lot Videos of every single used vehicle that we have all at summit auto.com If you want to check out just our used inventory, you can go to trucks on 41.com That's trucks on 41.com And if you'd like to make this one yours, give us a call right now<PHONE_NUMBER> You will not be disappointed once again that number is<PHONE_NUMBER> And if you'd like to check out more hd videos, you can go to youtube.com slash summit auto Remember to like subscribe and share on this video and all the videos that you see there In fact in a second you will see a link to subscribe to our youtube channel on your left The link to more halftone truck videos like this one on your right If you have not been to our website on the bottom link to this vehicle on our website Click those check us out and we really look forward to help you with this super clean 2012 ram 1500 crew cab short box Thanks again


Welcome to Greg and Ellie Uncensored, our little free game show before we go totally live and uncensored on Rumble at APM Eastern, 5pm Pacific and 1am UK. How are you? I'm good. Yep, I'm good. Been doing some lovely reading today. I did a little, her mum, this lady's, I've been reading for this lady's mum for a long time and she asked for her daughter to see if her daughter could have a chat with me just to see what could be done.  So yeah, it was, so I gave her some insights as to kind of where her life's going to be, you know, like in the future. Like, she liked, I said, what did you like to do when you were growing up? You know, what was your thing? And she said dressing up in different kind of costumes and things like that. And I said, so how would you think about maybe doing acting and maybe, you know, a theater and things. And so she went, oh my God, yeah, I'd love to do that. So she went from thinking, I've got no hope, nothing. And then in an instant, she then opened up and got all of that. So yeah. You know, when, while you were describing that, I'm watching this path that's opening up, that never existed before. And I could visually see what you were explaining. Yes. Yeah. And that's called timeline weaving. Yeah. Yeah. I teach a class on it, timeline weaving. Because as a reader, that's what you do. You pick the best pathway possible and make that really strong. And you make that person feel empowered. You make that person feel as if they can conquer anything, they can do it. I believe in you, spirit believes in you, go for it. And that does an amazing, it has an amazing boost in it because it's the truth. You can, you can feel the team, their team, you can feel them get excited for them. Yeah. And that, that truth vibration is such a high vibration. Yeah. So that was lovely. Little 11 year old, bless her. High kind spirit. Thank you for joining us. Hello. Hi, you two love birds. I've not been around much to watch videos. This new place I moved into appears to be the house of obstacles. Oh no. Well, you're there for a reason, you know, and you're definitely there to anchor the energy for that area. So, hi Rosie. I love when soulmates such as yourselves mirror each other. Thank you. Kind spirit. I just got a message for you. This will be okay. It is just, it's like, the house feels as if it's got to, it's got to be part of your life. So I feel that you need to throw a party or have a dinner party or do something like that to make the spirits happy. You know, it's like a, imagine that the house as an inner child.  We're going to do fun things together. We're going to do this. I know you think I'm crazy, but house and energy. Yeah. But have you been, you've been busy? Well, actually I drew some cards for her. And initially, initially I, you're going to have some, you got, you got some challenges going on initially. But like Ali said, I see, you know, you got the, the Empress and, and the 10 of cups.  So it's, it's just temporary. These things that are happening right now are just minor compared to what you're going to experience in that home for the rest of your life or for as long as you can hold on to it. So yeah, it'll be okay. It will. And if you just, if it is haunted and there are spirits that want to go to move on, then create a white light, ask, ask your guides to bring in golden light, shine it in the middle of each room one at a time and then spin it like a, like a tornado, spin it and create a vortex and then ask them to step in. And some of them you have to say, you know, it is, you know, there's only love and light waiting for you. There is no, there's no bad. There you go. Hi to Lydia. Thank you for joining us. Yeah. The house was built in 1910. That's old for a house here in the United States. Yeah. Yeah. Hi to Michelle and Sarah Ann. Thank you for joining us. Yeah. Oh, that's a good idea. You could leave some things out for them if they're elementals. Good idea, Sarah.  Honestly, the spirit, the spirit children, they love it. That's what we do with, when we do paranormal investigations, we bring little cars and toys and we put talcum powder. This is going to sound, we put talcum powder down, we place the car on top of the talcum powder and then we leave it and then later on you can see if it's moved because the talcum powder will be moved. So have you ever came back and there was like all sorts of little car wheels? Not to that degree. No, not to that degree. Because that would have been me. I was a spirit.  Look, we got a toy to play with. Yeah. Yeah. No, no, not to that degree. Okay. Yeah, it would be good. I'd like it. Yeah, that's a great idea though. I like that too. So how are you guys doing? Magical maiden? Hello? Michelle, if you want to ask a direct question, I'm happy to roll the dice for you if you want. So you can ask a direct question if you want. I'm not afraid, seriously. I'm strong spiritually. I find it a great new experience. And, you know, obviously, I'm sure you've already done this, but if you haven't, do so. Smudge. And what I do when I smudge, I say something along the lines, reword it any way you want. But I sell any and all negative entities. You're not welcome here. I demand that you leave immediately. Only those of the highest vibration of truth, love, and light are welcome here. And I just repeat that and they go around from each room to each room. And I try to do it about once a month or so. It's difficult to answer that one without doing an actual reading. But if you've got an actual question, you know, just to kind of do a reading on because because this is a yes or no. Will she have it? Yes. Yeah. I'm sorry. I will come on. And I do come on sometimes and just do three weeks. I promise you I do. At the beginning of Astrology meetings, I tend to do that now. So that's every two. Well, Sunday, every Sunday. So yeah. So kind spirit says I smudge the heck out of it with Sage and Palo Santo. That's exactly what I say, Greg. Very good. Yeah. That's all you need to say. Stuff like that. Just keep repeating it. Because I, you know, I'm glad that you say only those of highest, highest vibration of truth, love, and light are welcome here or something along that line because you don't want to ban everybody. You want the good spirits to feel welcome. Like I wouldn't get my sister ever wanted to visit or, you know, galactics from my star family. Yeah, you're always welcome to come here. So that's why I always include that. Yeah, definitely. What about the dog's kind spirit? If the dogs come with you. So Michelle Hornby, are you asking, sorry, are you asking whether or not you're going to have a relationship or whether your relationship right now is a yes or no? I'm so sorry. It's so difficult to, oh, yeah. Is the spirit of the man that died here still around? Okay, I'll answer that one in a minute. So Michelle, going to, are you going to be in a relationship soon? Shall I ask that? I already got an answer for that spirit as well. 16. 16. 16 is 7. Now, that means that it's a gamble energy, which means that you might not be ready fully. You might think you are, but you're not quite ready. So that could be that you've got some past emotional stuff that you're needing to get through. You're needing to address that, some pain. Are you happy enough to be sending the right signals out? That sounds crazy, doesn't it? Because it's like you want to be in a relationship who are usually unhappy, but if you are too unhappy, it can push other people away because there's an energy of I'm in need, I'm in need, I'm in need, I'm in need, and it then becomes intimidating energy. So it could mean maybe that it may not be that, but there's something that you might be doing. Does that mean that it's something that you might need to work through? And so it's not a no, it's a maybe, but kind of thing. Kind spirit says my question would be is the spirit of the person, the man that died here still around. I smell cigarette smoke in one place and looking at I drew some cards here and I'm getting, yeah, he is still there. I got the Hierophant, the Ace of Swords, and the Six of Pentacles. And what I'm getting on this is that there may have been somebody that was there before you. I don't know. He wants, there's an attachment going on and he wants to be sure that everything's fine. And what I'm getting with the Six of Pentacles is that that's all he's doing. He's basically hanging out, checking you guys out, make sure everything's fine before he goes and crosses over to the other side. He may not be aware that he can also cross over to the other side. But just if you do try communicating with him, tell him it's okay, follow the light, and that you'll be taking great care of his house, his house is in good hands. Yeah. I wonder if he was part of building that house, I wonder, what do you feel about that, Greg? I don't know. There's somebody that died there, but to own, to be part of the builders back in 1910, I doubt it. I don't know how the spirit is. But you know, who knows, maybe that was a house that was in his family, maybe his father built it or something. Exactly. There's something to do with history. Yeah. There's an energy of fast. Yeah. And a concern for, you know, is the house in good hands. Yeah. Yeah. Oh, so kinds of it's here with me because she rescues cats and dogs. That's what she does, kind of spirit. And the people before her were drunk. So I live here alone. I promise the spirits and the house that it will take you. Perfect. You're doing everything perfectly. Yeah. Oh, he did build the house. Wow. Okay. So that's, yeah, that's what it is. He just wants to be sure that the house is going into good hands, which you sound like you are the hands that it needs to go into. So he might not be hanging out much longer, unless you say, hey, it's okay, you know. He might go and then come back because if he's earthbound, it means he's in limbo, which is not a nice place to be. If you've got undone business, you kind of stay in the limbo. But when you are satisfied and happy, you can then go to the light. And the other times is, if somebody's highly religious, and they're told that if you've sinned at all, you're going to go to hell, they're not going to walk into the light freely. So this is why you need to say to them, hey, there's only love waiting for you over that side. There is no hell. Sometimes, when we're going through all the pain that we might have caused another person, we can create our own kind of like lessons that we're having to go over and learn and understand.  So yeah. Good point.  Well, he must have lived a long life if he helped build that house. Yeah. Wow. I mean, I don't know how long the drunks were there living in that house. But yeah, it's fascinating just to look at this. Hi, Marsha. Or is Allie was saying Marcia? No, I would say Marsha. Okay. Maybe not. Is there anyone spirit world? Is there? And I think it should be another. Is there another spirit world around me? I don't get the question. Maybe asking if there's spirit around, around her. Yeah. Here's a question you could do on the dice. Recently, I lost my good friend. Is he happier now? 10 is always the perfect number. It's completion. He did everything he was supposed to do down here. Even if you don't, if you don't think so, it doesn't matter if you don't think so. If you think he was gonna do this and gonna do that, he might have only been here on a mission to just do this, this and that. And then, of course, they go. So, yeah. The answer is absolutely. He feels complete. Or she feels complete, you know. Can I just say that? I'll talk to him again tonight. I found out he was a heavy smoker. And you get one question you can probably tackle right now too. From Linda Wenger. That was just brought a question to my mind. Is the spirit of the man who died across the hall from me still hanging around? Do you want to do it? You want to do this one? No, you do it. You do. You got your dice out. Short, quick questions with dice. Six, seven, eight. Eight means yes. Continual. He will be there quite often. I don't think he's earthbound. I don't think he's stuck. I think he just chooses to come there. Mainly when you're jumping in the shower. Do you know what? He had in my head. I hope he's not a stalker. Honestly, that's what came into my head as you said that. No, they don't. They don't. They're not allowed. No. Really? No. Because if I predecease you, I'm gonna be stalking you in the bathroom. No, you're not. Hell, yeah. Well, not if you're taking a dump. I'll give you that practice. If you're going in the shower, yeah.  Yeah, so yes, no answer is impossible. Yeah, because we've only got a little bit of time. We've got four minutes left. Yeah, he was in his late 80s. The house was built in 1910. That means he died around 1980s, 1990 or so, I would say probably around 1990. And then since 1990, that's 33 years. Interesting master number. It's been 33 years since he's been in that home. Or he's always been. You see, time doesn't exist the way it exists here. Everything is in the now.  Yeah. Thanks, Greg. I had not thought about the shower before. I'll give him a show. Michelle, I'm kind of more of future predictions than medium. I can dab into mediumship, but you're needing a medium, I think, to find out about people in the spirit world. If you tell me who, I can talk to you about them, but to bring them through. It's my grandfather watching over me. Is he one of my guides? I've got a big fat yes for that. I didn't even need to ask. So, yes, absolutely. And he's loving it. Very proud of you. There is a female. That's all I'm getting for you, Michelle. There is a female, elderly female. So, orange juice. I'm drinking apple juice today. Yeah. Isn't it funny? He put all of his love into his house. He was a local policeman, and I can tell he was very organized. Do you know what? If he then had to watch drunks in his beloved house, you can understand why he doesn't want to go until he knows it's in good hands. Wonder if he tipped off any of his police friends from the spirit side. You know, those guys who are driving drunk or something. Yeah. Yeah, yeah. Will my job interview go well? Yes, perfect question. I can do that, Michelle. Okay. That's going to have to be it because it's 7.59 right now. I know, love. That's 9, 10, 11. 11 is that it's all in the hands of the angels. So, that means angelic intervention is happening. So, it's a very, very good numbers. So, I always say with my job interview, it might not be the one that you're thinking of. It may be, you know, maybe one after that, but they've got it in hand to give you the perfect job. And if this next one isn't good enough for you, just because you think it is, they're not going to let you have it, it will only be the perfect. It's 8 o'clock. We got to go, folks. There's a link above. If you're watching on Facebook and link below in the more info section. If you're watching on YouTube, see us over there on Rumble. Completely live and uncensored. Love you all. See you later.


We're going to talk about finding the equations of lines today. So we already have the equation y equal mx plus b where m is the slope and b is the y-intercept. So we are going to look at a very simple equation first. We want to write the equation of line that satisfies negative 4 of slope in containing 0, 2, and it says, what is the special point, special about 0, 2? 0, 2 is the y-intercept. So that tells us that b is equal to 2. We know that already. And we know what the slope is. As long as we know the slope and we know the y-intercept, we can write the equation of the line, which is exactly what we did here, y is equal to negative 4x plus b, which is 2. So let's try again. Slope is positive 3 halves. It contains a point 0 negative 3. This is the y-intercept. So we just have to say 3 halves times x minus 3 because it's a negative 3b. All right. This time it's a little bit harder. We don't have the y-intercept. This is not the y-intercept. So we have to use a plug and chug. So now we know m, 1 is our x, y is our negative 5. So if we plug back in for y equal mx plus b, everything we know, y is negative 5, equal to m, which is 2, times x, which is 1, plus b, which we're trying to find. So negative 5 is equal to 2 plus b. And if I subtract 2 from both sides, then b is negative 7. So now I know b and I know m. And I can put both of those together to make the equation 2x minus 7. What happens if I don't know slope? Well, I might have to find the slope. So if I have this problem here, 6, 5, and 2, negative 7, I need to find the slope. So we're going to do our slope formula. Negative 7 minus 5, y2 minus y1, over 2 minus 6, x2 minus x1. This is negative 12 on top. 2 minus 6 would be negative 4. So negative 12 divided by negative 4 would be positive 3. I know that slope is 3. I'm going to use the point 6, 5. So x is 6, y is 5, and b is what I don't know. So we plug in chug. So y is 5, equal m, which is 3, times x, which is 6, plus b. Y equal mx plus b. So 5 is equal to 18 plus b. And if we subtract 18 from both sides, we should get a negative 13. And that would give us y equal slope, which is 3, times x, plus b, which in this case is negative 13. If I choose the other point, I would have y is equal to negative 7, equal m, 3, times x, which is 2, remember this is my x, this is my y, plus b. So negative 7 is equal to 6 plus b. And if I subtract 6, I get negative 13. So I have y equal slope of 3 times x, plus my b, which is negative 13. Same equation. So does it matter which point we choose? No.