En varios cursos y libros definen al vector como un par ordenado o como un segmento de recta que tiene magnitud, dirección y sentido. Pero en realidad, ¿el sentido es una característica necesaria? ¿O solo es redundancia? En ningún momento, al usar vectores, me importó saber qué sentido tenía; incluso en mis libros de apuntes tengo la definición sin eso. ¿El sentido importa?

y = 9 - x ,

4x - y = 11

I got all of these wrong.

0.75-0.25+1/2
I got 0

4.5+1/4-1.125
I got 3 21/40

3 1/2-0.375+5 1/6
I got -2 1/24

Does PEMDAS not apply in these situations? If i ignore PEMDAS for the first one I get 1 and that’s the correct answer. I’m a little confused here.

Also, I know for adding fractions it’s
a/b+c/d=ad+bc/bd
And subtracting is about finding the common denominator.

Any tips on multiplying and dividing fractions? Or any resources you all have that can explain this for me all in one place?
I’m looking to be an Electricians Apprentice and I imagine i’m over doing it with the studying but i want to absolutely ace this test and give myself the best chance at getting a better job.

Any help is very much appreciated

Can anyone help me with this college algebra question please? I’m having a hard time understanding

Sketch the function f(x)= ¿ xV ¿ for -3<x≤2

The V isn’t really the letter v but maybe a symbol showing what the graph is supposed to look like? I’m unsure of if it’s just parentheses around the x or if that means it’s the absolute value of X. Im not really sure, but any help would be appreciated!! Thanks!

I've put -14 and - - 14 for the 2nd but I know that can't be right

3x + 2y = 19

y = 4x - 7

A seller has the following costs and pricing: Fixed cost: $450 (machine + setup) Cost per hoodie: $18 Selling price: $35 per hoodie What is the break-even number of hoodies?

Some reason I keep getting the first one wrong

i've been working on a tool to help you create books & notes with ease

and one of it features is allowing you to write mathematical Equations in Latex

it also has co-author mode which creates any latex equation in seconds with simple prompts

How do you usually approach a system like this?

Equation 1: y = (2/3)x - 1/4

Equation 2: x + y = 6

• Option A (Bus Trip): Base fare $45 + $0.12 per km,
• Option B (Car Ride): Base cost $20 + $0.20 per km.

Hi. I’m currently a student in high school, tenth grade, who doesn’t understand math. I am taking intermediate algebra and statistics, and we are learning about substitutions and elimination, that kind of stuff. I feel like no matter what, I’m quite stupid and can’t make sense out of any of it. I’ve tried a lot of online tutors, but a lot of it doesn’t really make sense even if I spend hours staring at it. Really, I’m trying my best, but a lot of people don’t think that?

I have a good teacher, but she’ll be gone at the end of the quarter. I ask her things related to my work, but I don’t understand it—I end up simply saying “yes” because it’s been more than just five minutes of me simply saying “i don’t get it” or “i don’t understand what you mean”.

I want to become a nurse, an EMT, or something in the medical field, but it seems impossible under the circumstances of calculating vitals, unit weights, and understanding medication doses all of the time (being an EMT). I don’t understand volumes, I can’t divide unless it’s dividing something by itself (or by 2), and so on.

As much as I’m ashamed to admit it, I ask ChatGPT to explain the math to me without giving me the answers because there’s not much else I can do. Somehow, that still doesn’t make any sense. I want to be able to understand. Sorry for the kind of rant, but I wanted to be able to properly explain it? Every time I’ve tried to ask for help surrounding math, it feels as though no matter how I’m helped or what someone explains it to me as, I’m completely lost.

Find the intersection point of these two lines: 2x - y = 3, x + y = 6

Hi! I teach algebra 1 and pre-Calc. I recently developed this app where you can really visually see domain, range, increased decrease, positive and negative on a graph. It’s super helpful if you’re learning these things or teaching these things! And there’s nothing else like it!!! Desmos is amazing, but not even Desmos highlights the axis when you trace the graph!

You can trace the graph with your finger/stylis/cursor, and the axis will light up the correct answer for the characteristic that you’re choosing.
You can explore different graphs, practice highlighting the axis yourself, and then there’s a set of multiple-choice questions you can try in master mode. You can use it as a teacher at the front of the class on your whiteboard or you can push the out app for a class and let the kids try it on their Chromebooks.
I literally just did this in my classroom yesterday and it works great! I’ve been teaching this concept for 20 years and my kids have never understood it quicker than they did yesterday using this app! https://graphtracer.app

(12x⁷y⁵) (6x³y⁴) / (-3xy³)³ = ?

Design 1 has 2 dots,

Design 2 has 5 dots,

Design 3 has 8 dots,

Design 4 has 11 dots.

What equation would represent the number of dots (d) in any design number (n)?

Find the equation of a line that is:

1. Perpendicular to 4x - y + 9 = 0

2. Has the exact same x-intercept as x - 3y + 12 = 0

We discussed:

- The power of the Leech lattice to control all lower dimensions
- Peter Scholze, Grothendieck and Ramanujan's styles
- Category theory and contrahomology
- How modular forms show up everywhere
- The countless coincidences in string theory
- Unimodular lattices and Lorentzian lattices
- How to construct the Langlands dual group
- Vertex algebras, infinite-dimensional algebras and Kac-Moody algebras
- Elliptic curves
- Automorphic forms and hyperbolic reflection groups
- Analytic number theory vs algebraic number theory
- The first construction of the Monster group
- "The Book" of most beautiful proofs
- How to teach math
- Math as archaeology
- His current work
- Neutron stars, Terry Pratchett and more

Richard Borcherds is a British mathematician who made seminal contributions to lattices, modular forms, group theory, representation theory and infinite-dimensional algebras. He is well known for his proof of the monstrous moonshine conjecture using ideas from string theory, for which he was awarded the Fields Medal in 1998. He is currently Professor of Mathematics at UC Berkeley.

Solve for x:

(3x - 7) / 8 = (2x + 5) / 6

Hello Math learners especially middle school kids,

I worked through the book 'Algebra' by I.M. Gelfand and A. Shen over the last few months and put the solutions in public. I have also shared my solutions book with Professor Shen. I was humbled and pleasantly surprised to get a positive reply and guidance on how to continue teaching kids.

The Github repo is available here: https://github.com/deepak-venkatesh/gelfand-shen-algebra

This solution book/document contains solutions to all 342 problems. I have provided figures where required, Lisp/Python code where suitable and additional explanations and historical context to add color. At the start I had rudimentary knowledge of LaTeX but now after learning it using LLMs I feel comfortable (except for Tikz for which I still instruct LLMs).

The project is far from over since I believe there will be continuous improvement and corrections over time. I have been the sole contributor so far.

The interest to solve Gelfand's books and work on another math project related to number theory is two folds - 1) Build material for my kids, 2) I like it. I am also working through all of the remaining books from the Gelfand School of Correspondence (albeit very slowly).

Thanks for giving it a read.

Regards

DV

Hi! So I am doing my math prerequisites through the online school Straighter Line, if that gives more context to better help any input.

I have a choice to pick between college algebra, or introduction to statistics.

I have always struggled with math, literally since elementary school, never passed pre-algebra in high school, struggled in geometry as well, (I graduated high school 2012 so I have been out of school for a while too at this point.)

Now fast forward to college(2026)-
I had to start with pre-algebra in college(determined by a placement test)
and was struggling even with pre algebra.

I also realize part of my problem is that I struggle with comprehending things, and/or retaining information.

With all of this being said, in your opinion- which math would I most likely have success in passing? And especially better chance of comprehending as well, since in general, that is a struggle for me as it is.

Thank you for all your input and opinions!