algebra

1. Rooted

Can anyone solve this?
2. Solving equations

Write 3x^2 - 12x + 2 in the form 3(x-a)^2-b Hence solve the equation 3x^2-12x +2 =0
3. Dividing a square with arcs

over at https://brilliant.org/practice/joy-problem-solving-geometric-shortcuts/?chapter=introduction-to-joy&p=5 We find a problem involving dividing a square into two areas and comparing the areas. A geometrical solution there is convincing (the blue and white regions have equal areas), but...
4. I need guidance

Hi all, I want to know the difficulty level of the attached paper and the way to prepare for it. I completed graduation in Mathematics in 2015 and have a gap of more then 4 years because of jobs. Please help me in anyway if you can. Thanks a ton in advance. I'm attaching the...
5. prove that there is no rational number $x$ that satisfies $x^2=2$

I suck at proofs, I don't know why :( I want to improve my mathematics skills, because I like mathematics a lot and want to pursue a career in it. Please check the attached solution and let me know the changes/ way to solve it. Thanks a lot.
6. Help , question in a

I can't understand the last three line in a) ?
7. what algebraic manipulation was used here?

I have the equation (y-x*y/x)/y^2 = (y^2−x^2)/y^3 in my understanding the answer should be (y-x^2)/y^3. I just can't figure out what was done to get the first y squared. Edit: forgot to add ^ before powers
8. Help turning word problems into equations please...

Hello, my class has just started exploring rational equations. I have no problem solving the equations on their own but when I need to convert information into these equations I can confuse myself. If anyone can help me with turning these two problems into rational equations, I'd be really...
9. Help with fencing question... ASAP

This question from my assignment is giving me some trouble. I feel like I'm really close but my end results still end up screwed up. If anyone can help me solve this so I can hand it in tomorrow afternoon I'd definitely appreciate it :)! A farmer has 120m of fencing and plans to use it to...
10. algebra homomorphism

Can anyone offer some help? Thank you for your time. Let $\varphi :A\to B$ be an algebra homomorphism. (a) The inclusion $\varphi \left( Z(A) \right)\subseteq Z(B)$ does not always hold. To see why, give an example of when it does hold and another example of when it does not hold. (b) Come up...
11. Confusion about span in Linear Algebra

Hi there, this is my first post here. I am currently studying some control theory related stuff and it's basically linear algebra. However, I have some problems. I have given this exercise on which I already got an answer in Mathematics Stackoverflow: However, when checking other sources I...
12. Logarithmic algebra, why doesn't this method work?

Problem is as follows: Solve the equation 2^2x=5 The book tells me to solve it by changing both sides to an exponentiation with the base 10. Logically, I tried to the following (Method 1): (10^2)^2x=10^5 10^4x=10^5 \log10^4x=\log10^5 4x=5 x=5/4 However, somehow, that isn't correct. The actual...
13. Algebra Pythagorean Theorem

Hello all. I was wondering how to solve this particular problem. I am not certain I am setting it up correctly, and I think it's likely I don't have it quite right. Any help is deeply appreciated. (from textbook) "Use the Pythagorean Theorem to find the missing side length. Leave answer in...
14. College algebra pdf wanted

Does anyone here have a pdf copy of the book Paul Rider's College Algebra?
15. Direct Evaluation of Implications in Boolean Algebra

I used Latex to get the symbols: https://gofile.io/?c=T5RdqE In hindsight, using that template may not have been such a hot idea. I'd like to know some books or other materials that discuss such simplifications. Thanks.
16. Algebra what is the actual answer ?

$$(a-b)^2=a^2-b^2$$ Which values of a and b show that this is not true?
17. Nat 5 algebra problem

'100 people are on a plane. Some people have tickets for 70 POUNDS and some have tickets for 50 POUNDS. The total raised sum from the plane tickets was 6240 POUNDS. How many people bought 70 POUND seats and how many people bought 50 POUND seats?''
18. Sample Space Question (Algebra 2) [Probability]

Hey everyone, I needed help solving this problem for an assignment, I literally have no clue how to solve it. It's worth 10 points so it would mean a lot if someone could help. Thanks!
19. Algebra word problem

The formula for the length of the hypotenuse of a right-angled triangle, whose short sides are p, q is rÂ² = pÂ² + qÂ² 1. Make p the subject of this formula. 2. Evaluate the shortest side of a right-angled triangle, if the other two sides have lengths given by q = 9.3 and r = 11.4. State...
20. Solve for x

8(4x+2y-3)= This is an example of work that we did. Can anybody give me a hand because I have an Algebra exam today and I don't know where to begin? Can anybody help me? Please? Find x. Can you please answer as fast as possible, because the assignment is due today? Thanks.