Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

Tutors Answer Your Questions about Polynomials-and-rational-expressions (FREE)

Question 1029838: ****Corrected the complete question*****
Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rate of 4 mph, she reaches the station 5 minutes before the arrival of the train. Find the distance Gilda walks to the station.
David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations:
Using d = rt, the distance is the same, but the rate and time are different.
If Gilda misses the train, it means the time t needs 7 more minutes so d = 3(t + 7).
If she gets to the station 5 minutes early means the time t can be 5 minutes less so d = 4(t - 5).
3(t + 7) = 4(t - 5)
3t + 21 = 4t - 20
t = 41
d = rt, so d = 3(41) = 123
Find David's mistake in his calculations. Include the correct calculations and solutions.
Click here to see answer by Fombitz(32388)

Question 1029839: The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages?
Caitlin says the difference in their ages is 24 years. In two or more complete sentences, explain whether or not Caitlin is correct. In your explanation, include the equations and calculations necessary to support or contradict Caitlin's answer.
Click here to see answer by josmiceli(19441)

Question 1029878: Find the values of x for which f(x)=g(x).
f(x)= 9x^2-64
g(x)= 5x^2-32
Click here to see answer by Fombitz(32388)

Question 1029879: Write the following equations in standard form.
2i+(sqrt-1)+4
-4i^3+2i^2+i-3
Click here to see answer by Boreal(15235)

Question 1029931: x+3 over x^2-1 minus 2x over x-1 = 1
Click here to see answer by Boreal(15235)

Question 1029950: Find a polynomial function of lowest degree with rational coefficients with the given zero.
3i
Click here to see answer by robertb(5830)

Question 1029956: What value of M (The variable) makes this equation true?
(5x+5)(x+m)=5x^2+15x+10
This question is about polynomials. Thank you!
Click here to see answer by josgarithmetic(39613)

Question 1029983: [(4m)/(m^2+9m+20)]-[(16)/(m^2+7m+12)]
I have tried to do this problem at least 8 times. i don't know what i am doing wrong. I factor the denominator and then make sure i have the same denominator.
Click here to see answer by solver91311(24713)

Question 1029994: For a maths assignment, I am supposed to graph polynomials.
One of the rules of these graphs is P(x) = ax^2+bx+c where x = 1,2,3,4,5,6. Stuck and no ideas what to do
Click here to see answer by josgarithmetic(39613)

Question 1029993: f(x)=7x3−x2+2
That is the problem. The instructions say ' Use the rational zero theorem to list all possible rational zeros for the given function'. I have tried everything, I just can not figure out this problem!

Click here to see answer by Theo(13342)

Question 1030029: Solve each set of equations by substitution or elimination:
a) 2x-3y=18
2x+2y=28
b) 5x-2y=15
3x-2y=-21

Click here to see answer by stanbon(75887)

Question 1030033: Im having trouble doing a Pythagorean Theorem problem, I was wondering if you can help me better understand it.
https://gyazo.com/4eee19e7edbabefe3db5a5bdeedf2b06
Here is a picture of the triangle.
Click here to see answer by richard1234(7193)

Question 1030021: Use the one-to-one property to solve the equation for x.
e^(5x+1)=e^16
That equation is supposed to read this-
e to the power of 5 x plus 1 end exponent equals e to the power of 16
Just in case I did not write the equation correctly
Click here to see answer by josmiceli(19441)

Question 1030058: (x+1)^1/2-1/3(x+1)^3/2
looking for GCF of above expression...stuck
Click here to see answer by Fombitz(32388)

Question 1030056: Simplify:

root of 19a^2b^5
__________
root of 57a^5b^3

Click here to see answer by fractalier(6550)

Question 1030067: Add or Subtract
x^2/x^2+x-2 + 3/x-1 - 4/x+2
Click here to see answer by mananth(16946)

Question 1030052: simplify completely:
1-2x/3x-4
____________
x-32/3x-4
Click here to see answer by macston(5194)

Question 1030103: Simplify the expression: (2x-3y)^/(3y-2x)^2
I keep getting -1
What am I doing wrong?
Could you please show me the steps so I see my mistake? Thank so much in advance.
Click here to see answer by josgarithmetic(39613)

Question 1030102: Complete the synthetic division problem and enter the solution in polynomial form. For example, 2 3 0 would be written as 2x + 3 (you would not enter the remainder, 0).
-1|_2 9 7
It is synthetic division please help
Click here to see answer by josgarithmetic(39613)

Question 1030101: There are 4 pints of green paint in a gallon bucket. The paint is made from equal amounts of yellow paint and blue paint. To create a different shade of green, the mixture needs to be 80% yellow. How many pints of yellow paint need to be added to the bucket to make the mixture 80% yellow?
Brandon says to get that shade of green, 6 pints of yellow paint need to be added to the bucket. Bianca says that won't work. Who is correct and why?include the calculations to support the correct answer.
Click here to see answer by josmiceli(19441)

Question 1030051: simplify completely:
2/b^2-5/ab-3/a^2
__________________
2/b^2+7/ab+3/a^2

Click here to see answer by robertb(5830)

Question 1030150: Simplify:
(root of 5x - 2 root of y)(root of 5x + 2 root of y)
Click here to see answer by josmiceli(19441)

Question 1030148:
square root of 91ab^4
_______
square root of 7ab

Click here to see answer by Theo(13342)

Question 1030142: Suppose f is a polynomial such that f(0) = 47, f(1) = 32, f(2) = -13, and f(3)=16. What is the sum of the coefficients of f?
Click here to see answer by richard1234(7193)

Question 1030197: A square pool has a 6-foot wide walk around it. If the sides of the pool have length x, find a polynomial that gives the area of the pool and sidewalk.
Click here to see answer by ikleyn(52752)

Question 1030202: Solve the partial fraction decomposition of the rational expression:
(3x^2+49) / (x(x+7)^2) = (A/x) + (B/(x+7)) + (C/(x+7)^2)
Thank you for your help!!
Click here to see answer by stanbon(75887)

Question 1030215: find cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 5, -2, -24 respectively.
Click here to see answer by josgarithmetic(39613)

Question 1030189: Solve each inequality by using the graphical method. State the solution set in interval notation.

Click here to see answer by Edwin McCravy(20054)

Question 1030143: Find t if the expansion of the product of x^3 - 4x^2 + 2x - 5 and x^2 + tx - 7 has no x^2 term.

Click here to see answer by robertb(5830)

Question 1030196: In a sample of 300 students what is the probability of seeing 32% of the students choosing sports when it is known that on an average 25% of the students go for the sports. It is assumed that selecting the sports is an independent event.
0.99
0
0.001 or 0.002
Not enough information is given
I have used Poisson distribution =POISSON.DIST(96,75,FALSE) which gave me 0.002. Is this correct?
Click here to see answer by robertb(5830)

Question 1030147: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, $f(1) = -5, and f(2) = 12, then what are the $x$-intercepts of the graph of f?

Click here to see answer by robertb(5830)

Question 1030145: There is a polynomial which, when multiplied by x^2 + 2x + 3, gives 2x^5 + 3x^4 + 8x^3 + 8x^2 + 18x + 9. What is that polynomial?
(Give your answer as a polynomial in which the terms appear in order of decreasing degree. In other words, "x^5 + x + 2" is a valid answer, but "2+x^5+x" is not.)

Click here to see answer by robertb(5830)

Question 1030128: Use a vertical format to find the product. Use FOIL.

4z+1
Click here to see answer by Fombitz(32388)

Question 1030546: Factor -12c^2 - 60cd - 75d^2
Click here to see answer by stanbon(75887)

Question 1030552: write a quadratic trinomial that cannot be factored over the integers
Click here to see answer by stanbon(75887)

Question 1030608: Please help me solve this I am really bad at algebra, and I don't understand how I can calculate this.
One of the most exciting plays in basketball is the dunk shot. The amount of time T that passes from the moment a player leaves the ground, goes up, makes the shot, and arrives back on the ground is called the hang time. A function relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is given by: V(T) = 48T^2
a) A Basketball Player has a hang time of about 0.828 sec.
What is the Basketball Player�s vertical leap? (T = hang time)
b) The record for the greatest vertical leap in the NBA is held by Darryl Griffith of the Utah Jazz. It was 48 in.
What was Darryl Griffith's hang time? (V is the vertical leap)
Click here to see answer by Boreal(15235)

Question 1030687: Find the polynomial function of degree 3 that satisfies the following conditions: Zeros of -3, 1, and 4; f(2) = 30
Click here to see answer by Fombitz(32388)

Question 1030792: Can someone please help me how do your write the exponent of powers on the computer to this problem what is the degree of this polynomial 2x to the third +x to the second +3x-4 I know that it is the 3rd degree but I don't know how to write the power sign on the keyboard
Click here to see answer by rothauserc(4718)

Question 1030826: 1+1/(1+1/(1+1/(1+1/1)))
Click here to see answer by josgarithmetic(39613)

Question 1030814: Mary and Richard leave Edmonton to go to Jasper, a distance of 400 km. Mary drives at an average speed of 15 km/h faster than Richard. If Mary arrives in Jasper 40 minutes before Richard, find Richard's average speed, to the nearest km/h.
Click here to see answer by mananth(16946)

Question 1030938: 2t^3 + 20t^2 - 48t
I need help factoring this completely. Please and thank you.
Click here to see answer by ikleyn(52752)

Question 1030939: a+3 a-2
___ + ____
a-5 a+4 Perform the indicated operations. Help please and thank you.
Click here to see answer by rothauserc(4718)

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, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105