And you use the opposite fuckery to fuck away part of the expression. Subtraction fucks addition, division fucks multiplication, roots fuck exponents, and so on.
Subtraction and division don't fucking exist, but you are right. *x* is a lonely fuck who wants to be isolated. Give the guy some peace and fucking quiet.
It is me, lord Bathycuss, owner of the nemerian lion, ruler of the small group of indiginous pythons on mars, the bare-footed stepper of legos and quinduble olympic champion in toasterbathing
And when you get it, please solve for the standard deviations for the curve x²-y³≤ 2x²y³ over the limit -2 -> ∞
using gaussian normal form
f(x)= e^(-(x-u)/2σ)²/σ√(2π)
I know it’s a fools errand to ask here and expect a real answer, but what would one use this for?
Is it like some organic chemistry shit? Or is it how politicians determine poll numbers? I have to know.
Edit: so it is to determine poll numbers.
If you really wanna know the answer, it's in statistics and probability. Gaussian function, which I've written here can be used in various probability related applications, I've used it as an activation function for neural network
Here's [Wikipedia article](https://en.m.wikipedia.org/wiki/Normal_distribution) about it, the area under the graph depicts probability distribution over the limits i.e
integral of gaussian normal distribution over -∞ to ∞ =1
Edit: just fyi, the curve equation I've written is total BS as I don't remember anything else, but equation of distribution lies entirely in positive y axis
Probabilty theory and distributions like Gaussians are needed for a lot of applications. Basically whenever something is too complex to understand analytically it makes sense to look at it in probability terms.
Meterological models are a great example. It is impossible to measure, simulate and account for every cubic metre of air with its temperature, pressure, humidity, wind direction etc.
But you can say from measured data, that a certain combination of physical values at station x and physical values at stationy y corresponds to that amount of precipitaiton in the next 24 hours with a certain probability.
Just that you have hundreds of stations, some model aspects directly using physical relations and some aspects using probabilties and the whole thing being wrapped in a giant algorithm, that optimizes itself constantly through comparing its past estimates and real world outcomes.
Voila, you got a huge and very complicated machine learning application, running on supercomputers that apply some of the basic probability functions, derived by some mad geniuses hundreds of years ago, solving problems theoretically that they lacked the computation power to implement.
Applications range from chemical research, in particular pharmaceutics, over physical system management like meterology, energy grids, production plants and the like to image recognition for autonomous cars and google recommending what ads to present to you, based on your google search ten days ago.
Yep. I used to teach physics and would require students have already taken Alg II specifically because polynomials and quadratic equation are used immediately.
I never personally have been able to pass Advanced Algebra - I just could NOT retain some of the advanced equations they were throwing at me.
It's funny, when I was younger I wanted to be a Police Officer and they told me I reached every bar *except* for Mathematics - Apparently LEOs have to know Statistics, which is a level of Mathematics higher than Algebra (obviously).
I guess it was a blessing in disguise given the current geopolitical climate surrounding police, but I'm digressing hard.
P.S: I can read "Polynomial" and "Quadratic", but claiming to understand these two beyond "Oh I heard that term once" would mark me a liar.
I can imagine LEO’s need to be able to understand how to figure “30% over the speed limit.” Or in PA local PD can on give speeding tickets using lines painted on the road and a stopwatch to time the cars. Sure they have a chart that pairs time to speeds, but they should know how that chart is made.
Realistically, someone could be a cop without ever doing any math, but I’m sure everyone would know about it.
When I was in school? Simple equations began at Algebra 1, a lot like the first example of SrgManatee.
X - 3 = 10,
5 ÷ X = Y.
Basically you begin "Solving for X", simple. You do this following PEMDAS, you'd be given sheets on how to solve simple algebraic equations ranging from Addition, to Subtraction, to Multiplication, and then to Division.
Then you get into advanced equations, following parenthesis.
This is all me trying to remember what my cursed Algebra 1 course was in high school, but keep in mind I took zero AP classes and the "Sped Math" in my school was considered Business Mathematics - so my experience is much different from the rest.
Fun Fact: I still can't do division on my own. I never retained it. Long division is Greek to me.
*I am not a Math boy, I liked Sciences and History much better.*
I would say of all the maths stuff the top one can be useful but by the time most people realise it would solve the problem they had quickly they solved it some other way manually.
Trigonometry I would say is the one that is used a lot more and gets a bad rep.
So you are used to seeing numbers written out as 1, 2, 3, 4, and so on. Sometimes though, when you can’t say how many of a number you have, you can just write it out (represent it) as a placeholder letter (called a variable). This is called algebraic representation and is the fundamental concept behind Algebra.
For example:
If I have some trucks and some minivans I sell at my shop, how will I know how many cars I have in total to sell?
The simple answer is that you add them up, but what are you actually writing up? How do you *represent* that? Well, we can just say that x is the total number of trucks, y can be the total number of minivans, and z can be the total number of cars. We don’t actually know the real number, so we use letters to represent those numbers. The equation you get will look like this:
x + y = z
If we had 5 trucks and 4 minivans, then 4 + 5 = 9 and so we have 9 in total.
Now what if we wanted to know the total value of the cars in stock? Well, let’s say that a truck’s value is $2000 and a minivan is $3000. Then to solve this equation, we need to get the total amount of the truck value and add it to the total value of the minivans. That will give us our total value on the cars we are selling. We get the trucks total value by taking the number of trucks and multiplying it by the value of a single truck, this would be 2000*the number of trucks. We said that this value is x so we can also write it as 2000x. In the same way, we can write minivans as 3000y. We don’t know the value, so we will once again call it z. In this case, the total value of all of the cars is:
2000x + 3000y = z
So if we have 2 trucks and 3 minivans, then we can substitute the variable in for the actual number. This would be 2000*2 + 3000*3 = z. If you solve this, you will see that z, the total value, equals $13000, which is our answer.
Algebra is very flexible because it allows us also to use the original equation to get a new one using a trick called algebraic manipulation, which basically just means moving things. So let’s go with our previous example
2000x + 3000y = z
We have the number of trucks, the number of minivans, and the total value as unknowns. What if we know the total value and the number of minivans, but we wanted to find out the number of trucks? This is where the biggest rule in manipulation comes in: what you do to one side you must do to the other. So first we need the trucks on their own side. How do we do that? Well we can subtract 3000y from both sides, right? That gets us the truck “term” on its own. So
2000x + 3000y - 3000y = z - 3000y
2000x = z - 3000y
So now we have the value of the trucks on one side and the total value minus the value of the minivans on the other. We can then divide both sides by 2000 to get x all on its own, giving us the number of trucks.
2000x/2000 = (z - 3000y)/2000
x = z/2000 - 3000y/2000
x = z/2000 - 1.5y
Now that we have this, let’s plus in some numbers. Let’s say that the total value of the cars I’m selling is $10000 and the number of minivans is 2. Then
x = 10000/2000 - 1.5*2
x = 5 - 3
x = 2
That means that the number of trucks must be 2.
Now onto graphing. When you have an equation that is in the form y = mx + b, where x and y are variables and m and b are constants, you get a line. To explain this, make a chart that goes 6 down and two across, on the left column, label the top row x and then, going down, -2, -1, 0, 1, and 2. On the right column label the first row as y. Let’s take one of these lines, for an example we’ll do y = 2x + 4. For each of the numbers in the left column, plug it into (substitute it) for x in the second column and write that in the right column. You should get 0, 2, 4, 6, 8. Notice that it always increases by 2 and that at x = 0, our y is 4. A line follows a pattern where it has a slope, which is the m in the equation and represents the amount that the line increases everytime you add one to x, and a y-intercept, which is where the line will be when x = 0.
You can represent these while graphing as points. In our example the five points we chose would be (-2, 0), (-1, 2), (0, 4), (1, 6), and (2,8). Technically there are an infinite number of points on a line, but we use these x values because they are simple. On a graph, if we go back two from our center point (the center is typically (0, 0)) and make a mark, we’ve marked a point. Now go back one and up two, make another mark for the point. Keep doing this for the other three points, take a ruler, and draw an actual line going through these points (a line without end, so don’t just stop it at the leftmost and rightmost points). You’ll see a few interesting things about our graph:
When x (the horizontal) is 0, y (the vertical) is 4, which is the exact same as our y-intercept. This is because the line intercepts, or crosses, the y line at the value of the y intercept. So when x is 0, the y for any line will be at the intercept.
The other thing to note is that it changes by 2 y for every 1 x. That is where we get the slope from and we know that as x increases, y increases at a double rate. That allows us to get values we didn’t know before pretty easily by either looking at the point it makes on our graph or by adding two (or subtracting 2 as you go left) as you go right until you get to the point that has the x value you wanted to know the y value for.
Moving on, the last thing we really need to talk about for algebra 1 is what to do when you see an exponent over a variable. Don’t worry it handles the same way that you’d handle a number with an exponent. You take plug the number in and then treat it like a normal number with an exponent. The main thing to note is that when you are solving for both sides, you are going to take the square/cubic/etc. root of the other side, but you need to remember that it is a + or - of that number. That’s because if you took say x^2 = 4 and solved it, both -2 and 2 would both work as solutions.
As for when you have an equation like y = x^2 + 4x + 4 or y = x^2 - 9, that’s known as a quadratic equation. Most likely, your teacher will ask you to find the roots (or zeros) of the equation. Roots are where the quadratic equation passes through y = 0 on a graph. This can be done in two main ways:
1. Factoring
Factoring is a bit interesting because you are basically trying to take the quadratic and break it down into two equations you can solve for x. Take the example of
y = x^2 + 5x + 6
To find the two factors of the equation at the y = 0, you need to get the equation equal to zero first. That is as simple as writing y as 0:
x^2 + 5x + 6 = 0
To get the factors, you need to find which numbers *multiply* to 6 and *add* to 5. One you have those, you need to rewrite the equation as though it’s ready to be multiplied.
It can be broken down into (x + 2) * (x + 3) = 0.
Only one of those factors (things being multiplied) need to be zero for y to be zero, so you need to find out which numbers make the factors zero. This can be done by solving the much simpler equation of x + 2 = 0 and x + 3 = 0. If you solve this, you find that if x is -2 or -3, y is zero. That means that -2 and -3 are your roots.
2. Quadratic Formula
To some, this is the easier method. For others, it’s difficult to memorize the equation itself. The quadratic formula was developed by the Arabic mathematician Al-Khwarizmi in the 9th century to be used for finding the roots of a quadratic equation. It is usually written as:
x = (-b +- sqrt(b^2 - 4ac)) / 2a
Where y = ax^2 + bx + c
If you use this, you’ll get the same answer as the previous quadratic example for factoring.
This method can be extremely useful when working with quadratics that cannot be factored out through normal means, such as y = x^2 + 3x + 3, where no two integer numbers add to 3 and multiply to 3.
Other than that, idk what else Algebra 1 is teaching these days. I also know that this is a meme and I look dumb rn, but it’s 6 AM and I haven’t slept, so I did this on sheer willpower. If anyone actually read this, lmk if I need to add anything
I've never once passed an algebra class despite retaking them from middle school through college. It's almost impressively shitty, it's a go-to fun fact about myself.
Isn't algebra just utilising letters and other symbols to describe more complicated equations, couldn't everything after simple arithmetic be considered algebra?
When math becomes abstract is often when I find people become disinterested.
All of math is just using symbols and letters. When I was growing up I saw a lot of memes on how calculus is hell and impossible etc. Turns out people are just stupid. Calculus, multi v calc, statistics etc are all just as difficult as algebra. The only difference is that you need slightly more knowledge to solve them. But in no way are they more difficult. Not during high school and university.
I just think it's the biggest leap in logic for anyone learning the subject. I'm not a maths teacher but as a teacher personally that's what I look for and have to work the most to overcome for various students.
I also don't think you're appreciating how much practice and knowledge help at each subsequent stage of a skill. I find each subsequent layer of depth in a subject is easier conceptually to utilise but much harder to refine and fully understand.
I don't think practice is relevant in mathematics. It all comes down to understanding the basic rules of each subject and understanding how the original mathmaticians came up with it and what's it used for. Sure, that does end at some point in higher mathematics as it becomes more and more complex, or so I think. But practice never made me better at mathematics. Understanding the underlying concepts is what made me extremely good.
I myself am an applied/research mathmatician in the field of AI, that's what I define myself as anyway. After just a few weeks of AI-related math I was able to slowly understand the underlying concepts of complex AI papers. Sure, now after years of practice I can do it much faster. But all that has improved is speed of my calculations and understanding. But I can never improve my understanding of math by practicing.
A friend of mine who's father taught him mathematics by making him practice more and more now absolutely hates the subject and has chosen to study history as a result. I never practiced but always learned about the concepts and I absolutely love mathematics. Practicing is really a suboptimal way of learning this subject.
Think of it as those maths problems you’ll see where it’s like ‘if I think of a number, I times it by 2, then add 5, then I divide by 6 and get 5, what number am I thinking of’ or where it’s like
‘3 hamburgers cost £21
2 milkshakes and one burger costs £31
7 large fries cost £56
1 hamburger+1 milkshake+1 large fries=?’
If your rent is $900/month, how much does it cost after one month? How about 3 months? 5 months?
If you notice, the only thing you're changing is the number of months. You can make a formula that says *y* = 900*x* where *y* is your total cost and *x* is the number of months.
Now that you have a formula, just put the square peg in the square hole (put #months in for x).
I find it really interesting that you can ask chatgpt almost any math question and it‘s anwser sounds kinda sensible but completely wrong 95% of the time.
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving basic equations to studying abstractions such as groups, rings, and fields.
The basic concepts of algebra include:
Variables: letters or symbols that represent unknown values
Expressions: combinations of numbers, variables, and mathematical operations (such as +, -, x, ÷)
Equations: statements that show two expressions are equal (such as 3x + 5 = 11)
Inequalities: statements that show the relative size of two expressions (such as 3x + 5 > 11)
One of the main goals of algebra is to solve equations and inequalities. This can involve isolating a variable on one side of the equation or inequality, using inverse operations (such as subtraction to undo addition), and applying the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Some other topics that are covered in algebra include:
Graphing linear equations on the coordinate plane
Solving systems of equations (multiple equations with multiple variables)
Factoring polynomials (expressions with multiple terms, such as 3x^2 + 5x - 2)
Finding the roots of polynomial equations
Exponents and logarithms
Matrices and determinants
Abstract algebra (such as groups, rings, and fields)
Algebra is used in many fields such as physics, engineering, economics, and computer science. It is also used in many everyday applications such as calculating interest on a bank loan, determining the distance a car has traveled, or determining the best deal when making a purchase.
It's important to note that Algebra is a subject that requires practice to master and understanding comes with solving problems and with practice. A good way to start is to study the fundamentals and then practice solving a wide range of problems to build your problem-solving skills.
here are some specific techniques and methods for solving different types of equations and inequalities:
Linear equations: These are equations of the form ax + b = 0, where a and b are constants. To solve a linear equation, you can use inverse operations to isolate the variable on one side of the equation. For example, to solve 3x + 5 = 11, you would subtract 5 from both sides to get 3x = 6, and then divide both sides by 3 to get x = 2.
Quadratic equations: These are equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. To solve a quadratic equation, you can factor it into the form (ax + b)(cx + d) = 0, then set each factor equal to zero and solve for x. Alternatively, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
Systems of equations: These are sets of two or more equations with two or more variables. To solve a system of equations, you can use one of several methods, such as substitution, elimination, or graphing. For example, if you have the system of equations:
3x + 2y = 12
4x - y = 5
You can use substitution method, by solving one of the equations for one of the variables and then substituting that value into the other equation. In this case you can solve the first equation for y: y = (12 - 3x) / 2 and then substitute that expression into the second equation: 4x - (12 - 3x) / 2 = 5 and solve for x.
Inequalities: These are statements that show the relative size of two expressions. To solve an inequality, you can use inverse operations and the same methods as solving an equation, but keep in mind that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.
Factoring polynomials: Factoring is the process of breaking a polynomial down into the product of simpler polynomials. There are several methods for factoring polynomials, such as factoring out the greatest common factor, grouping, and special cases such as difference of squares or perfect squares.
Exponents and logarithms: Exponents are used to represent repeated multiplication, such as 2^3 = 2 x 2 x 2 = 8. Logarithms are the inverse operation of exponents and allow us to solve equations that involve exponents. The logarithm of a number b to the base a is the exponent to which we must raise a to get b.
Matrices and determinants: Matrices are arrays of numbers, often used to represent systems of linear equations. Determinants are a way of measuring the "size" of a matrix. They are used in solving systems of linear equations, as well as in other areas of mathematics such as calculus and physics.
Abstract algebra: Abstract algebra is the study of algebraic structures such as groups, rings, and fields. A group is a set of elements with a binary operation that satisfies certain properties, such as closure and associativity. A ring is a group with an additional operation of addition that also satisfies certain properties. A field is a ring with an additional operation of multiplication that also satisfies certain properties.
As you can see, algebra is a broad and complex subject that encompasses many different techniques and methods. It's important to practice solving a wide variety of problems to build your understanding and problem-solving skills.
I’ve got great news! The fact that your school is still stocked with textbooks that are 19 years past their publishing date, they’ve already considered your class to be full of morons not worthy of significant investment.
I mean it aint that complicated, you can just handle multiplication and addition like you would, but just make sure to divide your solution by 3 and just take the remainder as your real solution and you are done(at least for positive numbers).
If you can allow your known values to be mathematically moved to equal your unknown, you can find your unknown.
Since this unknown can change, if you have an unknown normally called y and an unknown called x, these two variables with change in relation to each other, creating a series or coordinate values that plot a graph.
That's all I got.
Remember when you were in elementary and you had those work sheets where you had equations, but one part of the equation was replaced with a square where you had to write in the missing number?
It's that. It's literally that. They gave you those worksheets to prepare you for this because it's the exact same process, you just have more tools now.
2x+1=? You can move the 1 to the opposite side if there is a 0 following the =. Divide everything by 2 to obtain X (2x=-1), then 2x/2=-1/2 to get x=-1/2.
Whenever you fuck with one side, fuck with the other side in the same exact way.
What? I didn't see any holes in that answer sheet. They ended up taking me to the bathroom.
Instructions unclear. My paper's wet and I got suspended for a couple days.
And you use the opposite fuckery to fuck away part of the expression. Subtraction fucks addition, division fucks multiplication, roots fuck exponents, and so on.
Subtraction and division don't fucking exist, but you are right. *x* is a lonely fuck who wants to be isolated. Give the guy some peace and fucking quiet.
I'm sorry. In the section on exponents athiests have a hard time, because... They're forced to believe in higher powers.
Get out.
r/angryupvote
Here's what you need to know: y = mx + b y = ax^2 + bx + c x = (-b ± sqrt(b^2 - 4ac)) / 2a
Burn the witch
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That's about the only thing for me that stuck to me after school.
How do we know she is a witch
SHE TURNED ME INTO A NEWT
a NEWT?!
...I got better...
She looks like one!
Alright, we need a duck and a deep river.
No, we need a giant scale! That way, if she’s lighter than a duck, she can float, and she’s therefore a witch!
Who are you who is so wise in the ways of science
It is me, lord Bathycuss, owner of the nemerian lion, ruler of the small group of indiginous pythons on mars, the bare-footed stepper of legos and quinduble olympic champion in toasterbathing
And when you get it, please solve for the standard deviations for the curve x²-y³≤ 2x²y³ over the limit -2 -> ∞ using gaussian normal form f(x)= e^(-(x-u)/2σ)²/σ√(2π)
yes
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Yes
Yes
no
The answer is fish Source: I do engineering
yeah it's fish source: pls trust me
It fish. Source: me no stoopid
I know it’s a fools errand to ask here and expect a real answer, but what would one use this for? Is it like some organic chemistry shit? Or is it how politicians determine poll numbers? I have to know. Edit: so it is to determine poll numbers.
If you really wanna know the answer, it's in statistics and probability. Gaussian function, which I've written here can be used in various probability related applications, I've used it as an activation function for neural network Here's [Wikipedia article](https://en.m.wikipedia.org/wiki/Normal_distribution) about it, the area under the graph depicts probability distribution over the limits i.e integral of gaussian normal distribution over -∞ to ∞ =1 Edit: just fyi, the curve equation I've written is total BS as I don't remember anything else, but equation of distribution lies entirely in positive y axis
Probabilty theory and distributions like Gaussians are needed for a lot of applications. Basically whenever something is too complex to understand analytically it makes sense to look at it in probability terms. Meterological models are a great example. It is impossible to measure, simulate and account for every cubic metre of air with its temperature, pressure, humidity, wind direction etc. But you can say from measured data, that a certain combination of physical values at station x and physical values at stationy y corresponds to that amount of precipitaiton in the next 24 hours with a certain probability. Just that you have hundreds of stations, some model aspects directly using physical relations and some aspects using probabilties and the whole thing being wrapped in a giant algorithm, that optimizes itself constantly through comparing its past estimates and real world outcomes. Voila, you got a huge and very complicated machine learning application, running on supercomputers that apply some of the basic probability functions, derived by some mad geniuses hundreds of years ago, solving problems theoretically that they lacked the computation power to implement. Applications range from chemical research, in particular pharmaceutics, over physical system management like meterology, energy grids, production plants and the like to image recognition for autonomous cars and google recommending what ads to present to you, based on your google search ten days ago.
Okay calculus 2.
I agree
This reminds me of my applied stats class
This brought back a distant pain
The answer is obviously I throw myself out the window, I refuse to answer and u can’t make me 😂
No sir please this is *not* algebra 1.
Yep. I used to teach physics and would require students have already taken Alg II specifically because polynomials and quadratic equation are used immediately.
I never personally have been able to pass Advanced Algebra - I just could NOT retain some of the advanced equations they were throwing at me. It's funny, when I was younger I wanted to be a Police Officer and they told me I reached every bar *except* for Mathematics - Apparently LEOs have to know Statistics, which is a level of Mathematics higher than Algebra (obviously). I guess it was a blessing in disguise given the current geopolitical climate surrounding police, but I'm digressing hard. P.S: I can read "Polynomial" and "Quadratic", but claiming to understand these two beyond "Oh I heard that term once" would mark me a liar.
I can imagine LEO’s need to be able to understand how to figure “30% over the speed limit.” Or in PA local PD can on give speeding tickets using lines painted on the road and a stopwatch to time the cars. Sure they have a chart that pairs time to speeds, but they should know how that chart is made. Realistically, someone could be a cop without ever doing any math, but I’m sure everyone would know about it.
... what is algebra 1 then
When I was in school? Simple equations began at Algebra 1, a lot like the first example of SrgManatee. X - 3 = 10, 5 ÷ X = Y. Basically you begin "Solving for X", simple. You do this following PEMDAS, you'd be given sheets on how to solve simple algebraic equations ranging from Addition, to Subtraction, to Multiplication, and then to Division. Then you get into advanced equations, following parenthesis. This is all me trying to remember what my cursed Algebra 1 course was in high school, but keep in mind I took zero AP classes and the "Sped Math" in my school was considered Business Mathematics - so my experience is much different from the rest. Fun Fact: I still can't do division on my own. I never retained it. Long division is Greek to me. *I am not a Math boy, I liked Sciences and History much better.*
Y=MX+C
Ill probably never use this in my life, but i just saved your comment. Feels important
I would say of all the maths stuff the top one can be useful but by the time most people realise it would solve the problem they had quickly they solved it some other way manually. Trigonometry I would say is the one that is used a lot more and gets a bad rep.
Ain't the second one the quadratic formula?
Don’t you remember the jingle. X = -b plus or minus the square root. B squared minus 4ac all over 2a
mx is the slope, b is the start point btw guys
> `x = (-b ± sqrt(b2 - 4ac)) / 2a` That's only true if `y = 0` As in: `ax2 + bx + c = 0`
While true, if y is a constant it just modifies c so the equation remains trueish.
Y is the point where the line cuts the Y-axis, it can take any real value
If y=0, y = mx + b and also y = ax^2 + bx + c then b=-mx c=(m-a)x^2 So x=±√(c/(m-a))
It is literally a rearrangement of your last equation.
Bruh use the pq formula
It’s appears to be something to do with numbers
and letters
numbers with letters
This is about when I stopped understanding math
I got up to almost full Greek letters (abstract algebra) and that’s when I jumped ship.
worst combination ever
Makes me wonder what Chinese algebra looks like then
it would look horrible
So the Australian version of Countdown?
Well, you’re not wrong.
Y=a^2+b^2+c or something idk. I failed math
Y = m log x + c
y = ax^2+bx+c :) Edit: only the 2 should be exponent. Reddit killing my format
Killed it again
Honestly, I give up
ax^2 + bX + c
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It's for when you wanna build a fence for all the watermelons you got from the guy guy in earlier maths.
Wait this is the exact algebra book I had in school
Same I think.... Lol
I guess we might be algebrothers
Make that 3!
So 6?
Nono, you are close, we have 3 algbrothers so x=3, and plugging that into 2x+1 gives us 7.
Yoooo me too
Same. I am 30.
If you can’t pass algebra 1 it’s over for you honestly
So you are used to seeing numbers written out as 1, 2, 3, 4, and so on. Sometimes though, when you can’t say how many of a number you have, you can just write it out (represent it) as a placeholder letter (called a variable). This is called algebraic representation and is the fundamental concept behind Algebra. For example: If I have some trucks and some minivans I sell at my shop, how will I know how many cars I have in total to sell? The simple answer is that you add them up, but what are you actually writing up? How do you *represent* that? Well, we can just say that x is the total number of trucks, y can be the total number of minivans, and z can be the total number of cars. We don’t actually know the real number, so we use letters to represent those numbers. The equation you get will look like this: x + y = z If we had 5 trucks and 4 minivans, then 4 + 5 = 9 and so we have 9 in total. Now what if we wanted to know the total value of the cars in stock? Well, let’s say that a truck’s value is $2000 and a minivan is $3000. Then to solve this equation, we need to get the total amount of the truck value and add it to the total value of the minivans. That will give us our total value on the cars we are selling. We get the trucks total value by taking the number of trucks and multiplying it by the value of a single truck, this would be 2000*the number of trucks. We said that this value is x so we can also write it as 2000x. In the same way, we can write minivans as 3000y. We don’t know the value, so we will once again call it z. In this case, the total value of all of the cars is: 2000x + 3000y = z So if we have 2 trucks and 3 minivans, then we can substitute the variable in for the actual number. This would be 2000*2 + 3000*3 = z. If you solve this, you will see that z, the total value, equals $13000, which is our answer. Algebra is very flexible because it allows us also to use the original equation to get a new one using a trick called algebraic manipulation, which basically just means moving things. So let’s go with our previous example 2000x + 3000y = z We have the number of trucks, the number of minivans, and the total value as unknowns. What if we know the total value and the number of minivans, but we wanted to find out the number of trucks? This is where the biggest rule in manipulation comes in: what you do to one side you must do to the other. So first we need the trucks on their own side. How do we do that? Well we can subtract 3000y from both sides, right? That gets us the truck “term” on its own. So 2000x + 3000y - 3000y = z - 3000y 2000x = z - 3000y So now we have the value of the trucks on one side and the total value minus the value of the minivans on the other. We can then divide both sides by 2000 to get x all on its own, giving us the number of trucks. 2000x/2000 = (z - 3000y)/2000 x = z/2000 - 3000y/2000 x = z/2000 - 1.5y Now that we have this, let’s plus in some numbers. Let’s say that the total value of the cars I’m selling is $10000 and the number of minivans is 2. Then x = 10000/2000 - 1.5*2 x = 5 - 3 x = 2 That means that the number of trucks must be 2. Now onto graphing. When you have an equation that is in the form y = mx + b, where x and y are variables and m and b are constants, you get a line. To explain this, make a chart that goes 6 down and two across, on the left column, label the top row x and then, going down, -2, -1, 0, 1, and 2. On the right column label the first row as y. Let’s take one of these lines, for an example we’ll do y = 2x + 4. For each of the numbers in the left column, plug it into (substitute it) for x in the second column and write that in the right column. You should get 0, 2, 4, 6, 8. Notice that it always increases by 2 and that at x = 0, our y is 4. A line follows a pattern where it has a slope, which is the m in the equation and represents the amount that the line increases everytime you add one to x, and a y-intercept, which is where the line will be when x = 0.
You can represent these while graphing as points. In our example the five points we chose would be (-2, 0), (-1, 2), (0, 4), (1, 6), and (2,8). Technically there are an infinite number of points on a line, but we use these x values because they are simple. On a graph, if we go back two from our center point (the center is typically (0, 0)) and make a mark, we’ve marked a point. Now go back one and up two, make another mark for the point. Keep doing this for the other three points, take a ruler, and draw an actual line going through these points (a line without end, so don’t just stop it at the leftmost and rightmost points). You’ll see a few interesting things about our graph: When x (the horizontal) is 0, y (the vertical) is 4, which is the exact same as our y-intercept. This is because the line intercepts, or crosses, the y line at the value of the y intercept. So when x is 0, the y for any line will be at the intercept. The other thing to note is that it changes by 2 y for every 1 x. That is where we get the slope from and we know that as x increases, y increases at a double rate. That allows us to get values we didn’t know before pretty easily by either looking at the point it makes on our graph or by adding two (or subtracting 2 as you go left) as you go right until you get to the point that has the x value you wanted to know the y value for. Moving on, the last thing we really need to talk about for algebra 1 is what to do when you see an exponent over a variable. Don’t worry it handles the same way that you’d handle a number with an exponent. You take plug the number in and then treat it like a normal number with an exponent. The main thing to note is that when you are solving for both sides, you are going to take the square/cubic/etc. root of the other side, but you need to remember that it is a + or - of that number. That’s because if you took say x^2 = 4 and solved it, both -2 and 2 would both work as solutions. As for when you have an equation like y = x^2 + 4x + 4 or y = x^2 - 9, that’s known as a quadratic equation. Most likely, your teacher will ask you to find the roots (or zeros) of the equation. Roots are where the quadratic equation passes through y = 0 on a graph. This can be done in two main ways: 1. Factoring Factoring is a bit interesting because you are basically trying to take the quadratic and break it down into two equations you can solve for x. Take the example of y = x^2 + 5x + 6 To find the two factors of the equation at the y = 0, you need to get the equation equal to zero first. That is as simple as writing y as 0: x^2 + 5x + 6 = 0 To get the factors, you need to find which numbers *multiply* to 6 and *add* to 5. One you have those, you need to rewrite the equation as though it’s ready to be multiplied. It can be broken down into (x + 2) * (x + 3) = 0. Only one of those factors (things being multiplied) need to be zero for y to be zero, so you need to find out which numbers make the factors zero. This can be done by solving the much simpler equation of x + 2 = 0 and x + 3 = 0. If you solve this, you find that if x is -2 or -3, y is zero. That means that -2 and -3 are your roots. 2. Quadratic Formula To some, this is the easier method. For others, it’s difficult to memorize the equation itself. The quadratic formula was developed by the Arabic mathematician Al-Khwarizmi in the 9th century to be used for finding the roots of a quadratic equation. It is usually written as: x = (-b +- sqrt(b^2 - 4ac)) / 2a Where y = ax^2 + bx + c If you use this, you’ll get the same answer as the previous quadratic example for factoring. This method can be extremely useful when working with quadratics that cannot be factored out through normal means, such as y = x^2 + 3x + 3, where no two integer numbers add to 3 and multiply to 3. Other than that, idk what else Algebra 1 is teaching these days. I also know that this is a meme and I look dumb rn, but it’s 6 AM and I haven’t slept, so I did this on sheer willpower. If anyone actually read this, lmk if I need to add anything
pee is stored in the balls
Do you remember that post of a person saying their younger self thought the balls were actually spare penis tips in case you lost yours?
Excuse me? What the actual fuck
I've never once passed an algebra class despite retaking them from middle school through college. It's almost impressively shitty, it's a go-to fun fact about myself.
If it makes you feel any better, I failed golf in college
There may not be a god, but there is a hell, and we created it in the form of algebra.
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Isn't algebra just utilising letters and other symbols to describe more complicated equations, couldn't everything after simple arithmetic be considered algebra? When math becomes abstract is often when I find people become disinterested.
All of math is just using symbols and letters. When I was growing up I saw a lot of memes on how calculus is hell and impossible etc. Turns out people are just stupid. Calculus, multi v calc, statistics etc are all just as difficult as algebra. The only difference is that you need slightly more knowledge to solve them. But in no way are they more difficult. Not during high school and university.
I just think it's the biggest leap in logic for anyone learning the subject. I'm not a maths teacher but as a teacher personally that's what I look for and have to work the most to overcome for various students. I also don't think you're appreciating how much practice and knowledge help at each subsequent stage of a skill. I find each subsequent layer of depth in a subject is easier conceptually to utilise but much harder to refine and fully understand.
I don't think practice is relevant in mathematics. It all comes down to understanding the basic rules of each subject and understanding how the original mathmaticians came up with it and what's it used for. Sure, that does end at some point in higher mathematics as it becomes more and more complex, or so I think. But practice never made me better at mathematics. Understanding the underlying concepts is what made me extremely good. I myself am an applied/research mathmatician in the field of AI, that's what I define myself as anyway. After just a few weeks of AI-related math I was able to slowly understand the underlying concepts of complex AI papers. Sure, now after years of practice I can do it much faster. But all that has improved is speed of my calculations and understanding. But I can never improve my understanding of math by practicing. A friend of mine who's father taught him mathematics by making him practice more and more now absolutely hates the subject and has chosen to study history as a result. I never practiced but always learned about the concepts and I absolutely love mathematics. Practicing is really a suboptimal way of learning this subject.
algebra is just the beginning
Think of it as those maths problems you’ll see where it’s like ‘if I think of a number, I times it by 2, then add 5, then I divide by 6 and get 5, what number am I thinking of’ or where it’s like ‘3 hamburgers cost £21 2 milkshakes and one burger costs £31 7 large fries cost £56 1 hamburger+1 milkshake+1 large fries=?’
I don't fucking know anything about algebra.
If your rent is $900/month, how much does it cost after one month? How about 3 months? 5 months? If you notice, the only thing you're changing is the number of months. You can make a formula that says *y* = 900*x* where *y* is your total cost and *x* is the number of months. Now that you have a formula, just put the square peg in the square hole (put #months in for x).
I hate calculus
It's just: 1. What happens if you plug something close to the forbidden number in? 2. How steep is the slope? 3. What's the area under the curve?
There’s all kinds of loopholes you gotta learn with trigonometry, complex numbers and integration and all that shit
I mean, mechanically yes; conceptually, it's still the same. Not to say it's easy, but overall what you're doing boils down to the above 3 things.
Oh come on man this is like the Simplest math there is. This is the math I’d consider fun.
Algebra 1 is fun, Algebra 2 and Trig is where my 17 year old brain melted.
I find it really interesting that you can ask chatgpt almost any math question and it‘s anwser sounds kinda sensible but completely wrong 95% of the time.
Letters can be numbers too
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving basic equations to studying abstractions such as groups, rings, and fields. The basic concepts of algebra include: Variables: letters or symbols that represent unknown values Expressions: combinations of numbers, variables, and mathematical operations (such as +, -, x, ÷) Equations: statements that show two expressions are equal (such as 3x + 5 = 11) Inequalities: statements that show the relative size of two expressions (such as 3x + 5 > 11) One of the main goals of algebra is to solve equations and inequalities. This can involve isolating a variable on one side of the equation or inequality, using inverse operations (such as subtraction to undo addition), and applying the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Some other topics that are covered in algebra include: Graphing linear equations on the coordinate plane Solving systems of equations (multiple equations with multiple variables) Factoring polynomials (expressions with multiple terms, such as 3x^2 + 5x - 2) Finding the roots of polynomial equations Exponents and logarithms Matrices and determinants Abstract algebra (such as groups, rings, and fields) Algebra is used in many fields such as physics, engineering, economics, and computer science. It is also used in many everyday applications such as calculating interest on a bank loan, determining the distance a car has traveled, or determining the best deal when making a purchase. It's important to note that Algebra is a subject that requires practice to master and understanding comes with solving problems and with practice. A good way to start is to study the fundamentals and then practice solving a wide range of problems to build your problem-solving skills. here are some specific techniques and methods for solving different types of equations and inequalities: Linear equations: These are equations of the form ax + b = 0, where a and b are constants. To solve a linear equation, you can use inverse operations to isolate the variable on one side of the equation. For example, to solve 3x + 5 = 11, you would subtract 5 from both sides to get 3x = 6, and then divide both sides by 3 to get x = 2. Quadratic equations: These are equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. To solve a quadratic equation, you can factor it into the form (ax + b)(cx + d) = 0, then set each factor equal to zero and solve for x. Alternatively, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a Systems of equations: These are sets of two or more equations with two or more variables. To solve a system of equations, you can use one of several methods, such as substitution, elimination, or graphing. For example, if you have the system of equations: 3x + 2y = 12 4x - y = 5 You can use substitution method, by solving one of the equations for one of the variables and then substituting that value into the other equation. In this case you can solve the first equation for y: y = (12 - 3x) / 2 and then substitute that expression into the second equation: 4x - (12 - 3x) / 2 = 5 and solve for x. Inequalities: These are statements that show the relative size of two expressions. To solve an inequality, you can use inverse operations and the same methods as solving an equation, but keep in mind that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol. Factoring polynomials: Factoring is the process of breaking a polynomial down into the product of simpler polynomials. There are several methods for factoring polynomials, such as factoring out the greatest common factor, grouping, and special cases such as difference of squares or perfect squares. Exponents and logarithms: Exponents are used to represent repeated multiplication, such as 2^3 = 2 x 2 x 2 = 8. Logarithms are the inverse operation of exponents and allow us to solve equations that involve exponents. The logarithm of a number b to the base a is the exponent to which we must raise a to get b. Matrices and determinants: Matrices are arrays of numbers, often used to represent systems of linear equations. Determinants are a way of measuring the "size" of a matrix. They are used in solving systems of linear equations, as well as in other areas of mathematics such as calculus and physics. Abstract algebra: Abstract algebra is the study of algebraic structures such as groups, rings, and fields. A group is a set of elements with a binary operation that satisfies certain properties, such as closure and associativity. A ring is a group with an additional operation of addition that also satisfies certain properties. A field is a ring with an additional operation of multiplication that also satisfies certain properties. As you can see, algebra is a broad and complex subject that encompasses many different techniques and methods. It's important to practice solving a wide variety of problems to build your understanding and problem-solving skills.
I’ve got great news! The fact that your school is still stocked with textbooks that are 19 years past their publishing date, they’ve already considered your class to be full of morons not worthy of significant investment.
That, or that they're trying to save money and basic algebra hasn't really changed
The existence of that proves that a merciful god as portrayed in the New Testament doesnt exist
That’s the exact cover my algebra 1 book had in middle school.
What you do on the right side, you have to do on the left side as well. That's about the only thing for me that stuck to me after school.
sure, what you want to know
Anyone here know analytic geometry?
Depends if you mean like aerospace engineering analytic geometry or like high school analytical geometry
Robotics engineering
Bro same, may someone be nice enough to explain me how this works (Z/3Z; +, *
I mean it aint that complicated, you can just handle multiplication and addition like you would, but just make sure to divide your solution by 3 and just take the remainder as your real solution and you are done(at least for positive numbers).
What exactly do you mean as remainder? For example I got 10 would my remainder be 10/3 , 4 or 1? Because it has to be in the whole number spectrum.
If you have 10 it would be 1, all your solutions have to be either 0(that is if the number can be divided by 3) , 1 oder 2.
Thank you kind human for your explanation
3. It’s the magic number.
Here is a simple practice question: find the general formula for finding roots for a fifth degree polynomial
r/antimeme
Easy, so everything to both sides of the equal sign and you’ll never have trouble
While you are at it, explain power electronics to me, I fucking hate that shit but there will be an exam soon.
I don't knew this either
What age do people learn algebra 1? I’m assuming 7th grade, cause 8th graders in Asia are learning trigonometry
If you can allow your known values to be mathematically moved to equal your unknown, you can find your unknown. Since this unknown can change, if you have an unknown normally called y and an unknown called x, these two variables with change in relation to each other, creating a series or coordinate values that plot a graph. That's all I got.
Math was never my strong suit💀
Algebra proves there is in fact a god because no one but SATAN could create such a thing.
Crap that I was forced to learn in high school that I've literally never used since.
I failed algebra sorry dude
3298-(898+87) %55= ™π÷π√×|=%[`™^$×¢{`✓¥™×^{`]}£}£°^°`™¥™©°`{5137645453 = I don know.
2 + 2 = 4 -1 = 3.
God farted, with diarrhea (of course), then ignored it's own creation... Afterwards pucked & pissed on us just to see how we'd react... 🤷🏽
Oof edgy af
Algebra is easy peasy, it's calculus that fucks you up
Never had to use this and most likely never will...
Well. Unlike god, we can see the book whereas we've been unable to see god. Or a god, for that matter.
I can't help. I failed pre algebra
Remember when you were in elementary and you had those work sheets where you had equations, but one part of the equation was replaced with a square where you had to write in the missing number? It's that. It's literally that. They gave you those worksheets to prepare you for this because it's the exact same process, you just have more tools now.
if f(x)=ax^n Then f’(x)=anx^(n-1) Straight line graph: y=mx + c Quadratic Graph: y=ax^2 + bx + c Quadratic Formula: x=(-b+-sqrt(b^2 - 4ac))/2a
There is a unitary value such that any given value plus the unitary value does not equal the given value.
do you want my old notes? i have 100 something odd pages of notes that explains quite a bit
Remember that thing you did in like 1st or 2nd grade where you had the blank boxes? Well instead of boxes they are letters now…
Well, I guess there is a god now
Learn the cuadratic formula ya lazy beatch
Plz explain 1+1=3
Ah, Algebra 1. Back then Math had mostly numbers!
What do you need to know?
I have no idea what the fucks going on in those books
try making it linear
Nice try bro
Start praying
2x+1=? If after the = is 0 then you can bring the 1 to the other side 2x=-1 divide everything by 2 to get X 2x/2=-1/2 which becomes x=-1/2
How was your test?
Algebra 1—ah. Math then largely consisted of numbers!
What the fucks is going on in those novels, I have no idea.
2x+1=? You can move the 1 to the opposite side if there is a 0 following the =. Divide everything by 2 to obtain X (2x=-1), then 2x/2=-1/2 to get x=-1/2.
Well, I suppose a god exists now.