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

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Question 214807: Solve the problem. Please show your work.
1. The population of a colony of bacteria is growing exponentially according to the function below, where t is the time in hours. How long will it take for the population of the colony to grow to 1,000?
B(t)=12*e^(0.2*t)
e=2.718
Click here to see answer by Theo(3504)

Question 214806: Solve the problem. Please show your work.
1. The population of a colony of bacteria is decaying exponentially according to the function below, where t is the time in minutes. How many minutes will it take for the population of the colony to drop to 50?
B(t)=2000*e^(-.03*t)
e=2.718

Click here to see answer by Theo(3504)

Question 214960: 15x(x-y)
________
5x^3y(x-y)
Click here to see answer by Alan3354(31519)

Question 214960: 15x(x-y)
________
5x^3y(x-y)
Click here to see answer by stanbon(57967)

Question 215091: I'm having trouble completing the square and finding the vertex of the following function:

Is making it into this the correct way to go about it??

Please help me!
Click here to see answer by jim_thompson5910(28715)

Question 215173: find and define all the intervals where the following function is increasing, decreasing, or constant. h(x)=-7
Click here to see answer by stanbon(57967)

Question 215450: i have no idea how to graph this function. help?
Click here to see answer by drj(1380)

Question 215221: The officejet h470 printer takes twice the time required by the hp officejet pro k5400 color printer to photocopy brochures for the New Bretton Arts annual arts fair. If working together, the two machines can complete the job in 45min, how long would it take each machine, working alone, to copy the brochures?
Click here to see answer by ankor@dixie-net.com(15746)

Question 215668: Simplify (3a + 12) / 3
Click here to see answer by m777dhoom777t(4)

Question 215675: Solve (x – 2) / (x – 4) = 2/(x – 4)
Click here to see answer by m777dhoom777t(4)

Question 215672: Determine the vertical asymptotes of g(x) = (21 – 7x) / (3x – 9)
Click here to see answer by jsmallt9(3296)

Question 215685: Multiply and simplify.
[ (5t^3)/(4t – 8) ] [ (6t - 12) / (10t) ]

Click here to see answer by stanbon(57967)

Question 215685: Multiply and simplify.
[ (5t^3)/(4t – 8) ] [ (6t - 12) / (10t) ]

Click here to see answer by jsmallt9(3296)

Question 215684: Write in simplified form. Be sure to list any restrictions on the domain.
g(t) = ( 25 – p^2) / (p^2 + 10p + 25)

Click here to see answer by stanbon(57967)

Question 215674: Add (x – 7) / (x^2 – 16) + (x – 1) / (16 – x^2)
Click here to see answer by jsmallt9(3296)

Question 215683: Write an equivalent expression using exponential notation. ^5√(n^4)
Click here to see answer by jsmallt9(3296)

Question 215680: Simplify √[ (a + 3)^2 ]
Click here to see answer by rfer(12730)

Question 215975: determine the vertical asymptotes of g(x) = (x2 – 4) / (2x2 -5x + 2)
Click here to see answer by jsmallt9(3296)

Question 216177: how do I solve this rational expression
9 / x+5 + x / x-3 = 5
my answer is x = 2 and x = 7/3
Click here to see answer by stanbon(57967)

Question 216187: Hi, I'm taking an online college algebra class but can't quite recall all the review concepts and am really stuck on this problem--
Factor the expression completely:
4x^4 + 1 + 3x²
Answer: (2x² + x + 1)(2x² - x - 1)
I can't figure out how to get the answer, it won't factor like a regular trinomial and doesn't come out right if I separate out the x², for instance.
And since I've been just trying to learn online so far (my textbook hasn't arrived yet), I really don't get how each set of terms has three factors instead of two. Hope my question makes sense, my math-speak probably isn't too great.
I would really appreciate any help you can give me. And feel free to dumb it down! Also if you know where I could find more problems similar to this for practice, that would be fantastic.
Thanks--
EL
Click here to see answer by stanbon(57967)

Question 216263: What is the answer for the following problem? the directions are graph each inequality on a coordinate plane. 2x-5y<-10
Click here to see answer by vleith(2825)

Question 216517: Solve
Click here to see answer by ichudov(499)

Question 216512: Divide and, if possible, simplify

Click here to see answer by ichudov(499)

Question 216521: Determine the domain of g(x) = √(x + 8)
Click here to see answer by stanbon(57967)

Question 216513: Determine the vertical asymptotes of f(x) = (4x – 20) / (4x + 12)
Click here to see answer by stanbon(57967)

Question 216519: If g(x) = √(x^2 – 25), what is the value of g(-6), g(3), g(6) and g(13)?
Click here to see answer by tutor_paul(490)

Question 216530: Find a Quadratic equation with roots of (4+i) and (4-i)?
Click here to see answer by stanbon(57967)

Question 216530: Find a Quadratic equation with roots of (4+i) and (4-i)?
Click here to see answer by drj(1380)

Question 216529: Hi, I need some help with my American School Algebra 2 work. Given X^*3-4x^*2+2x+1=0
A. How many possible positive roots are there?
B. How many possible negative roots are there?
C. What are the possible rational roots?
D. Using synthetic substitution, which of the possible rational roots is actually a root of the equation?
E. Find the irrational roots of the equation(hint:ust the quadratic formula to solve the depressed equation.
Click here to see answer by Alan3354(31519)

Question 217259: Please help me solve this rational equation, this is a sample problem and I have the answer we are suppose to study this but I'm not sure how they got certain numbers.
5/2x = 17/18 - 1/3x I know that x cancels out o
this is as far as I got then started getting confused.
18x x 5/2x = 18x (17/18 - 1/3x
18x x 5/2x = 18x x 17/18 - 18x x 1/3x
45 = 17x - 6
45+ 6 = 17x - 6 + 6
51=17x
51/17=17x/17 3=x I got lost starting at 45= 17x - 6 I don't know how they got the 45 and 17 so therefore I got confused through out the rest. Thank you for any help you can give me.
Click here to see answer by checkley77(12569)

Question 217017: x+3/x-3 = x-5/x+5
Click here to see answer by shymeerab(21)

Question 217402: Simplify. √(25t^2)
Click here to see answer by checkley77(12569)

Question 217450: x^2+x+1
is it able to be simplified
Click here to see answer by Theo(3504)

Question 217451: x^2+4x+16
is this able to be simplified
Click here to see answer by Theo(3504)

Question 217478: Determine whether y varies directly as x. If so, find the constant of variation.
y + 4x =0

Click here to see answer by vleith(2825)

Question 217490: how many solutions are there to the line y=-2x+5
Click here to see answer by RAY100(1637)

Question 217920: help me solve this problem..
What values of x are excluded from the domain of
f(x)=(2x-1)/3
Click here to see answer by rfer(12730)

Question 217952: f(h(x))= when f(x) = 2x-1 and h = x+4
I took (2x-1)(x+4) and that gave me 2x^+8x-x-4 which i 2x^+7x-4 but my options for an answer are 2x+3, 2x+7, 7, and 2x^+7x-8 - i dont get any of them and i have been working on this for 2 hours. Can anyone please help me - thank you.
Click here to see answer by scott8148(6628)

Question 217951: f(h(x))= when f(x) = 2x-1 and h = x+4
I took (2x-1)(x+4) and that gave me 2x^+8x-x-4 which i 2x^+7x-4 but my options for an answer are 2x+3, 2x+7, 7, and 2x^+7x-8 - i dont get any of them and i have been working on this for 2 hours. Can anyone please help me - thank you.
Click here to see answer by scott8148(6628)

Question 218173: use long division to express the following rational function in the form quotient + remainder/divisor : 6x^4+5x^2+3x+3/2x^2+1
Click here to see answer by jsmallt9(3296)

Question 218254: the volume of a sphere is a function of the radius of the sphere.
write a function for the volume of a ball.evalutae the function for a volleyball of radius 10.5cm
Click here to see answer by solver91311(17077)

Question 218381: We are working on rational expressions. I can not seem to get the jist of building rational expressions to higher terms. Example, I know that if x +3 was mulitiplied by x^2 + 3^2 the result would be x^3 + 27. That's easy enough, but I have problems writing that in correctly factored form. Any hints on how I can get better at this? Example/Question: How would I correctly write 12/x +3 = ?/ x^3 + 27? Thanks for your assistance, tips and suggestions.
Click here to see answer by vleith(2825)

Question 218415: the worksheet says write the eqation of the line in slope-intercept form,y=mx+b
through(-2,-1) and perpendicular to a line with a slope of -2. i realy dont understand this can you help me
Click here to see answer by britt_xoxo(2)

Question 218486: I need to solve 3/x-4 = x/x-2 for x.
Click here to see answer by chibisan(131)

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, 8056..8100