Questions on Algebra: Rational Functions, analyzing and graphing answered by real tutors!

Tutors Answer Your Questions about Rational-functions (FREE)

Question 32806: How much water must be added to 180 grams of a solution that is 35% acetic acid to produce a solution that is 10% acetic acid?
Click here to see answer by stanbon(57332)

Question 32885: What if 0 and 3-2i are roots of a polynomial equation. What are the other roots of the equation?
Click here to see answer by stanbon(57332)

Question 32594: Can someone please show me how to simplify this rational expression?
3x^2 – 3y^2 / x^2 + 2y + 2x +yx

Click here to see answer by sarah_adam(201)

Question 32948: 4)A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet.
Answer:
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5)Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point?
Answer:
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6)The volume of a cube is given by V = s3. Find the length of a side of a cube if the Volume is 729 cm3.
Answer:
Show work in this space.

Click here to see answer by sarah_adam(201)

Question 32956: 1)Solve the following equations.
a)sqrt x - 1 = 3
Answer:
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b)sqrt x^ = 8 .
Answer:
Show work in this space.

c)3sqrt x^ = 4 .
Answer:
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2)Is sqrt x^ = x an identity (true for all values of x)?
Answer:
Explain your answer in this space.

3)For the equation x - sqrt x = 0 , perform the following:
a)Solve for all values of x that satisfies the equation.
Answer:
Show work in this space

b)Graph the functions y = x and y = sqrt x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Graph
c)How does the graph relate to part a?
Answer:

Click here to see answer by sarah_adam(201)

Question 32954: Its actually the subtraction of unlike rational denominators.
The example in my phschool mathbook has the following rational expression:
_4_ _ __1__
5x x^2
Note: The 5x is the denominator for 4, and x^2 is the denominator to 1
and the given answer to is:
__4x-5__
5x^2
but everytime I try to solve the problem itends up bieng:
__4x^2-5__
5x^2
What am I doing wrong?
Click here to see answer by checkley71(8403)

Question 32996: sketch the graph of each rational function.
y=4x^2-100
________
2x^2+x-15
Click here to see answer by xcentaur(357)

Question 32330: I need help with this problem
The inverse of y=6x^2-13x
I got Y=13+or-square root 145 all over 2
Click here to see answer by stanbon(57332)

Question 33114: Simplify the rational expression

(x-5/x^2+2x-3)-(x-1/x^2+6x+9
Click here to see answer by sarah_adam(201)

Question 33114: Simplify the rational expression

(x-5/x^2+2x-3)-(x-1/x^2+6x+9
Click here to see answer by longjonsilver(2297)

Question 33155: please help: I am trying to solve rational expressions.
a)x/2 + 2x/5 = 9

Click here to see answer by sarah_adam(201)

Question 33145: Hi, please help. I tried doing this myself and ended up with x/x-1 as th e answer. Please show me the correct working.
1+1/x / 1-1/x^2
That is 1 plus 1 over x over(divided by) 1 minus 1 over x squared.
Click here to see answer by mukhopadhyay(490)

Question 33318: please help.
solve the following equation.
1/8 - 1/12 = 1/t That is 1 over 8 minus 1 over 12 equals 1 over t
Click here to see answer by priya(51)

Question 33331: please help.
Solve the following equation.
2/x + 3 = 5/x
Click here to see answer by sarah_adam(201)

Question 33317: Please solve the following equation
(4x + 1)/3 - (3x -1)/ 2 =1
Over : means divided by, and the equation is equal to 1.
Click here to see answer by sarah_adam(201)

Question 33317: Please solve the following equation
(4x + 1)/3 - (3x -1)/ 2 =1
Over : means divided by, and the equation is equal to 1.
Click here to see answer by stanbon(57332)

Question 33315: Find each functional value if h(x)= 2x+1.
h(-5)
Click here to see answer by sarah_adam(201)

Question 33339: let y vary directly as x. If y-10 when x=4, what is x when y =7?
Click here to see answer by stanbon(57332)

Question 33400: s² 1 ———————— — —————— 13s²-13s 13s-13

Click here to see answer by AnlytcPhil(1276)

Question 33493: Solve the rational equation:
1/(5x+5)= 3/(x+1) - 7/5
that is 1 over 5x+5 equals 3 over x+1 minus 7 over 5...
I have tried this problem several different ways and i can't seem to find the right least common denominator. Please Help!!
Click here to see answer by stanbon(57332)

Question 31213: I really could use your help on this problem please!
(Radical Functions)
-2^3sqrt(216)-3
Click here to see answer by mszlmb(115)

Question 33518: I am trying to simplify the sum of 5x/(x^2-x-6) and 4/(x^2+4*x+4). Please help.
Click here to see answer by Cintchr(481)

Question 33518: I am trying to simplify the sum of 5x/(x^2-x-6) and 4/(x^2+4*x+4). Please help.
Click here to see answer by longjonsilver(2297)

Question 30958: Please help me! I have to find the remaing roots (zeros) but I'm confused. The problem is f(x)=x^3+2x^2-3x+20. One root is there and it is -4. I have to find two more roots (zeros). I tried to work it out using synthetic division:
4/ 1 , 2 , -3 , 20
____4 , 24 , 84
= 1 , 6 , 21 , 104
The problem is really confusing when I type it out but I hope you can help me...
Click here to see answer by venugopalramana(3286)

Question 33559: Simplify the expression...

sqrt -(x^2-10x+25)
that's the square root of x^2 minus 10x plus 25. with the a negitive symbol on the outside of the square root sign. I think i need to factor this but i dont think i did it right... please help
Click here to see answer by priya(51)

Question 33628: I need help!
This is a discussion board it needs to at least 3 paragraphs please.

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear.
Click here to see answer by Nate(3500)

Question 33656: Sam must have an average of 70 or more in his summer course to
obtain a grade of C. His first three test grades were 75, 63, and 68. Write an inequality representing the score that Sam must get on the last test to get a C grade.
Click here to see answer by benni1013(197)

Question 33654: Translate the following statement into an inequality. Let x represent the number in each case.
2 times a number, increased by 28, is less than or equal to 6 times that number.
Click here to see answer by longjonsilver(2297)

Question 33768: I need to solve the equation square root of x+56=x and i ned to check for extraneous solutions
Click here to see answer by venugopalramana(3286)

Question 34046: 3/x+2/y / 2/x - 3/y = ?
Click here to see answer by ichudov(499)

Question 33923: Rationalize the denominator and simplify.
√5+1
------
2+√2
Click here to see answer by xcentaur(357)

Question 34124: hi, i am having a lot of difficulty with rationals and here is one question i cannot get.
³√-8m¹²
thanks!!
Click here to see answer by sarah_adam(201)

Question 34134: using the foil method find the product.(x+3)(x2-2x+6)
then i got x3+-6x2+-36x+18 as my answer but my book got x3+x2+18
can u show me how they got that answer or what i did wrong
Click here to see answer by longjonsilver(2297)

Question 34140: using the foil method (3+2s-s2)(s-1)
i got it down to (3s-3)(2s2-2s)(-s3+s2)
but i got confused and can't get the final answer.can u help me with the rest?
Click here to see answer by longjonsilver(2297)

Question 34186: Consider the rational function f(x)=2x/x-1. Give:
The domain
The Vertical Asymtote
The Horizontal Azymptote
The Graph.
Please help me with this problem. I don't even know where to start. Thank you.
Click here to see answer by venugopalramana(3286)

Question 34335: rationalize the denominator, then simplify, if possible
sqrt (x)-2/sqrt (x)-5
Click here to see answer by venugopalramana(3286)

Question 34334: use rational exponents to simplify the espression below if rational exponents appear after simplifying, write the answer in radical notation.
(the 8th root of 2a)^6
sorry i cant really figure out a way to write that more clearly...
Click here to see answer by longjonsilver(2297)

Question 34333: multiply and simplify the expression below. assume all variables and radicands are possitive.
the fourth root of 4x^2y^3z^3 * the fourth root of 8x^4yz^6
I get the multiplying part but im having a hard time figuring out what the perfect fourth root is.
Click here to see answer by longjonsilver(2297)

Question 34348: I am having difficulty with inverses of functions:
What is the inverse of the following function:

Heres what I did:

When it is checked however, it does not work:

This check works, but...

This doesn't, I found the graph of the inverse of the function, but I need the equation. Please help!
Thank you,
Sally Mat
Click here to see answer by Earlsdon(6287)

Question 34332: divide, and if possible, simplify.

please help!
Click here to see answer by mbarugel(146)

Question 34471: Hi my name is Eddie and I am a 11th grade student. I am have trouble with Graphing Radical Functions. I have a online text book that shows the problems
http://www.phsuccessnet.com/altcontent/products/0-13-037881-X/Ch07/07-08/PH_Alg2_ch07-08_Ex.pdf
I need help on problems 2,6,10, and 18. Any help would be helpful. Thank you.
Click here to see answer by venugopalramana(3286)

Question 34601: Consider the rational function f (x) =2x/x-1 . Give:
(i) The domain.
(ii) The Vertical Asymptote.
(iii) The Horizontal Asymptote.
(iv) The graph.
Please help me to solve this problem. I am no good with rational functions. Thank you.
Click here to see answer by stanbon(57332)

Question 34622: x-sqrt(x)=0
Click here to see answer by checkley71(8403)

Question 34747: What does the symbol "i" represent?
Is "12.5555…" a rational or irrational number? Explain.
Is "2.1273685…" a rational or irrational number? Explain.
Is "548/799" a rational or irrational number? Explain.
Simplify "(5 + 3i)(5 - 3i)". Is the result real, complex, or both? Explain.
Click here to see answer by venugopalramana(3286)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055