Checking Algebra Homework Solutions

AI Thread Summary
The discussion focuses on verifying algebra homework solutions, particularly for the equation 5/8x + 1/16x = 9/16 + x, where the user arrives at x = -9/5. There is also a query regarding the function f(x) = 2x^2 - 2x, with correct evaluations for f(-1) and f(2), but confusion about f(0). The domain of g(x) = 3/(5 - 3x) is discussed, with the correct conclusion that x cannot equal 5/3. Clarifications on notation and steps taken in solving the problems are encouraged for better understanding.
1babelove
Messages
4
Reaction score
0

Homework Statement


5/8x + 1/16x= 9/16 + x


Homework Equations





The Attempt at a Solution


10x+ x = 9+16
11x=9+16x
-5x=9
x= - 9/5
x =- 1.8

Is this correct. I am trying to make sure I am in the right direction


Also is f(x) = 2x^2-2x
f(0) = I got )
f(-1) I got 4
f(2) Igot 4

Is this correct also..

I need to make sure that this one is correct also

What is the domain of g(x) = 3/5-3x
I got that x is not equal to 5/3.

I hope I got all these right...
 
Physics news on Phys.org
I think you have a typo for f(0), what did you get? I agree with your answer for f(-1) and f(2). If part 1 has the x upstairs in the fractions like,
(5*x)/8 + (1*x)/16 = 9/16 + x
then I agree with your answer. But not if it is downstairs like,
5/(8*x) +1/(16*x) = 9/16 +x

I'm not sure I agree with your domain of g(x). What is your reasoning for 5/3?
 
Because I can not see g(x) = 3/5-3x answers being either a.not equal to 3, b. equal to 0. or c x greater than or equal to 5/3..My head is spinning numbers maybe I am wrong

and for f(0) = 2x^2 -2x when you mutiply be zero the answer is 0..right?
 
The problem with the domain question is that we were not sure if you meant
g(x) = \frac{3}{5 - 3x}
or
g(x) = \frac{3}{5} - 3x.

It looks like you meant the former. (That is why it's helpful to learn LaTex. :wink:) Anyway, you're right -- the domain is
x \neq \frac{5}{3}.


01
 
I have a some more problems that I want checked will you be willing to look at them, please.
 
Just post them in a new thread. Also, if you're seriously unsure whether your answer is correct or not, point out which steps you weren't sure about when you were solving the question.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
Back
Top