# rational

1. ### Square root equation

Hello, I'm back in school after 26 years and in need of some help. I don't know how to say this problem, much less solve it. Since I don't know how to say it and I don't know how to type this from my keyboard, I haven't had much luck with searched. Any help would be appreciated.
2. ### Rational inequality word problem

Hi, I hope someone can help. I'm trying to understand in what cases it is okay for me to remove the denominator from a rational inequality without having to flip the inequality sign. I thought it was okay in the event that I knew that the denominator was positive. However the following word...
3. ### Solving inequalities question #2

Hi, I hope someone can help. I know that I just posted a question a few minutes ago, but I think this post might be more specific to my confusion. So I've been trying to understand why removing the denominator within a rational inequality is fundamentally "bad". I understand that you have to...
4. ### Solving inequalities

Hi, I hope someone can help. So I have solved the following inequality in a very specific way: I'm wondering whether there is a way to remove the denominator from a rational inequality while still providing the same solutions (i.e. -1 < x <3 or x >= 7)? All I know is that it is "bad" to...
5. ### IROC rational function

Hi, I hope someone can help. I'm trying to find two points on f(x) = (x+2)/(x-1) where the IROC is -3. I created the difference quotient for the equation and now I just have to solve for x in order to figure out these two points where the IROC is -3. REALLY what I need guidance on is the...
6. ### Rational Functions word problem

Hi, I hope someone can help. I'm currently trying to answer homework question 7a: I can't seem to be getting the correct answer - which according to my textbook is 0.01. Here are my calculations: https://www.wolframalpha.com/input/?...59)))%2F(61-59) Sincerely, Olivia
7. ### Rational function word problem

Hi, I hope someone can help. I'm trying to answer 12b. The solution is: "The function appears to approach 9kg/m^2 as time increases." I'm wondering whether there is a way to identify this behaviour (as noted in the solution) without graphing it? I understand that y = 9 must be the...
8. ### Rational Expressions and Equations

Can you check my work, and if I'm wrong, please show me how to do it. Word Problem: PART I When Mario works by himself, it only takes him 24 minutes. When Sarah works by herself, it takes her 40 minutes. How much time would it take if Mark and Sarah work together. My work: t= time...
9. ### When will sqrt(a)+sqrt(b) = rational number

Hi All, I've been struggling with this one today. I know how to prove that sqrt(2) is irrational but this is a variation. Let a and b be positive integers such that sqrt(a) and sqrt(b) are irrational numbers. When will sqrt(a)+sqrt(b) = a rational number I do not think that this will ever be...
10. ### Simplifying Rational Indices

Hi, I'm new to rational indices and I'm getting a bit confused on how to simplify them. Simplify: 3√a^2b / √ab^3 So I did the reciprocal... 3√a^2b/1 x 1/√ab^3 3√a^2b/√ab^3 = (a^2b)^1/3 / (ab^3)^1/2 So then I used the index laws to simplify and got a^2/3b^-1/3 however the text book answer says...
11. ### Rational Root Theorem

Hi I am confused on how to use the rational root theorem to help factorise the following problem: 2x^3-7x^2+16x-15 If you could explain how to use this theorem to factorise that would be helpful :) Thanks!
12. ### Rational Zeroes Theorem and Synthetic Division

Help! Really struggling with these two questions. I have started them, but get stuck. Help would be greatly appreciated. Question 1) A slice 1 unit thickness is removed from one side of a cube. Use the rational zeroes theorem and synthetic division to find the original dimensions of the cube...
13. ### Solving a rational function

Hi Everyone, I am trying to do the problems in an archived math midterm (#2) found here: Math 120 Exam Archive, Dr. Jonah Ostroff, Math 120 A Winter 2015 Question 1 breaks down to this problem (converting minutes to seconds): Suppose a function f(x) such that: f(0) = 480 f(3) = 306 f(15) =...
14. ### Can someone explain Rational, Irrational and Imaginary zeros to me?

Every time I search for the definition online, they always have really complex words that makes it even more confusing, I was wondering if someone can tell me the definitions but make it simpler. Thanks. Also this would be irrational right? -2 plus or minus square root of 5? How do you know...
15. ### Proof by contradiction question

Hey, can someone please help me with this question? "Let q be a rational number and r an irrational number. Using a proof by contradiction, show that 3q^2 + 5r is irrational." I know that I should start with considering 3q^2 + 5r as a rational number and define 2 integers a and b. q = a/b but...
16. ### Finding formula from rational function graph

The only x intercept is at the origin and the graph also goes through the point (6, -0.5). The vertical asymptotes are at x= -6 and x= 5 while the x axis is its horizontal asymptote. So being that its only x intercept is at the origin and it looks like an odd function, I figured it to be x3...
17. ### comparing and ordering rational numbers

Word problem: My answer is every 432. A quality control inspector in an egg factory checks every forty-eighth egg For cracks and fifty-fourth egg for weight. What is the number of the first Egg each day that the inspector checks for both qualities?
18. ### Rational Functions

Hi everyone I need some assistance solving this problem. I'm not sure how to find the x and y intercepts as well as finding the horizontal and vertical asymptotes for this problem. For this problem i think it has slant asymptote, but i'm not sure on how to do the long division???(Crying) help!!!
19. ### Find the domain of each rational function. Do not graph the function.

Hi, I need help on two problems. 23. f(x)=2x^2+7x-2/x^2-25 --> the answer for that one is : (- negative infinity, -5)U(5,5)U(5, positive infinity) My question is why is the answer (5,5) included in there. 25. f(x)= x-1/x^3-x --> the answer is (negative...
20. ### prove that the set of all intervals with rational end points is countable

can anyone help with this question. this si my work. i know it is incomplete clearly, rationals are coutable let S be the set of all the intervals with rational end points. then S is subset of QxQ let h be a mapping such that h:NxN->S. here S is coutable since h is bijective. where do i...