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

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

Question 1119891: 16x^2+1≥−8x
Click here to see answer by Alan3354(69443)

Question 1119891: 16x^2+1≥−8x
Click here to see answer by rapture1965(18)

Question 1119891: 16x^2+1≥−8x
Click here to see answer by ikleyn(52776)

Question 1119901: How can I get the three possible dimensions of the rectangle if the perimeter of a rectangle is ?

Click here to see answer by Alan3354(69443)

Question 1119950: I am not sure if I went about solving this correctly, could anyone lead me in which way to go/ possibly reveal the final answer?
The profit of a company can be modelled by the polynomial function�, where�P�is the profit, in thousands of dollars, and�t�is the time, in years. When will the company make their maximum profit of $18 000?
Click here to see answer by math_helper(2461)

Question 1119949: How do I determine if the following polynomial functions have even or odd symmetry, or neither/ how do I justify my reasoning?
A) f(x)=-x^3 +3x
B) f(x)=x^4+x^2+x
C) f(x)=x^6-x^4-x^2
D) f(x)+1/3x^4-2/3x^2
Click here to see answer by Boreal(15235)

Question 1119948: How do I determine the function that would model this data/ what should the final answer be?
x: 1, 2, 3, 4, 5, 6
f(x): 0, 3, 16, 45, 96, 175
Any help would be so appreciated! Thank you!

Click here to see answer by solver91311(24713)

Question 1119947: Without graphing, answer the following questions for each of the functions below:
i. What are the end behaviours of this type of function (what quadrant does it begin and
end in?)
ii. What is the maximum and minimum number of�x-intercepts for this type of function?
iii. What is the maximum and minimum number of turns for this type of function?
iv. State if there are any restrictions on the domain and range on this type of function.
It may be easiest to format your answer by setting up a chart with the headings "End Behaviours, Maximum number of x-intercepts, Minimum number of x-intercepts, Maximum number of turns, Minimum number of turns, and Restrictions", then filling in your answers for the functions listed.
A) f(x)=7x^4+kx^3+8
B) f(x)=1/4x^3+4x2-x
C) f(x)=-x^10+kx^4+7
Any help would be amazing, thank you so much.
Click here to see answer by solver91311(24713)

Question 1119975: I am sorry I know this is a lengthy question but I am just not sure what the answers are.
f(x)=-x^10+kx^4+7
i. What are the end behaviours of this type of function (what quadrant does it begin and end in?)
ii. What is the maximum and minimum number of�x-intercepts for this type of function?
iii. What is the maximum and minimum number of turns for this type of function?
iv. State if there are any restrictions on the domain and range on this type of function.
Any help to any of these questions would be so helpful thank you so much in advance.

Click here to see answer by solver91311(24713)

Question 1119973: How would I go about solving this? My first attempt did not seem right! Any help with this would be amazing, and if anyone knew the final solution for me to work towards would be so amazing.
The profit of a company can be modelled by the polynomial function P(t)=-4t^3+10t^2+8t-6, where P is the profit, in thousands of dollars, and t is the time, in years. When will the company make their maximum profit of $18 000?
Any help is so appreciated! Thank you.

Click here to see answer by solver91311(24713)

Question 1119976: I am sorry I know this is a lengthy question but I am just not sure what the answers are.
f(x)=7x^4+kx^3+8
i. What are the end behaviours of this type of function (what quadrant does it begin and end in?)
ii. What is the maximum and minimum number of�x-intercepts for this type of function?
iii. What is the maximum and minimum number of turns for this type of function?
iv. State if there are any restrictions on the domain and range on this type of function.
Any help to any of these questions would be so helpful thank you so much in advance.

Click here to see answer by solver91311(24713)

Question 1119978: How would I go about solving this? My first attempt did not seem right! Any help with this would be amazing, and if anyone knew the final solution for me to work towards would be so amazing.

This is an algebraic question.
The profit of a company can be modelled by the polynomial function P(t)=-4t^3+10t^2+8t-6, where P is the profit, in thousands of dollars, and t is the time, in years. When will the company make their maximum profit of $18 000?
Any help is so appreciated! Thank you.
Click here to see answer by ikleyn(52776)

Question 1119974: I am sorry I know this is a lengthy question but I am just not sure what the answers are.
f(x)=1/4x^3+4x2-x
i. What are the end behaviours of this type of function (what quadrant does it begin and end in?)
ii. What is the maximum and minimum number of�x-intercepts for this type of function?
iii. What is the maximum and minimum number of turns for this type of function?
iv. State if there are any restrictions on the domain and range on this type of function.
Any help to any of these questions would be so helpful thank you so much in advance.

Click here to see answer by Boreal(15235)

Question 1120017: Could someone please walk me through how to do this. It is a question from my test prep of advanced functions.
How do I determine the equation of the function that would model this data?
x 1,2,3,4,5,6
f(x) 0,3,16,45,96,175
Any help would be so appreciated!!!
Click here to see answer by solver91311(24713)

Question 1120039: Give the polynomial function that has the given zeros. Show all work.
5, -7

Click here to see answer by josgarithmetic(39616)

Question 1120072: factor completely.
3mn-24m+12n+3
Click here to see answer by josgarithmetic(39616)

Question 1120112: solve the equation by the method of factoring: 4x^3+6x^2=70x
Click here to see answer by greenestamps(13198)

Question 1120113: factor completely: 10mn-40m^3+15n-20m^2n
Click here to see answer by solver91311(24713)

Question 1120230: Hi, I'm confused by a question here:
"x+y+z , classify this expression as either a monomial, binomial, or trinomial".
I'm not sure if it's a bionomial or trinomial expression.
Thanks!
Click here to see answer by ikleyn(52776)

Question 1120261: In polynomial p(x) = 3(x^2 + 10x + 5) - 5(x-k) , k is a constant. If p(x) is divisible by x, what is the value of k?

Click here to see answer by ikleyn(52776)

Question 1120268: A ship has a ratio of 4 officers for every 9 seamen. The crew of the ship totals 182 people. How many officers and how many seamen are on this ship

Click here to see answer by Boreal(15235)

Question 1120274: Please R=6%,T=8year,A=19125 how do you solve p and I
Click here to see answer by Theo(13342)

Question 1120395: Use the method of undetermined coef cients to nd the sum of 1 +2+3+��+(n−1)+n,n∈N
Click here to see answer by ikleyn(52776)

Question 1120414: Can someone please help me with this problem?

A six-sided figure has sides with lengths 3x, 8, 4x, 5, 5x plus 1, and 4.
3x
8
4x
5
5x+1
4

Find a polynomial for the perimeter of the figure.
The perimeter of the shaded region is?
Click here to see answer by ikleyn(52776)

Question 1120426: Eliana wants to make a diorama or an art contest contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open frontan open box front.
What is a strategy you Could try in order to solve the problem?
Based on the based on the given figure, are there any constraints on the values of x?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1120529: F(x) = square roots of (x+5) + 2, find the domain of f-1
Click here to see answer by Boreal(15235)

Question 1120713: Eliana wants to make a diorama or an art contest contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open frontan open box front.
Describe how you could identify which points on a graph of v(x)=(12-2x)(8-2x)x correspond to a volume of 36 in.
Click here to see answer by stanbon(75887)

Question 1120712: Eliana wants to make a diorama or an art contest contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open frontan open box front.
without graphing v(x)=(12-2x)(8-2x)x, describe the end behavior of the graph of the graph of the function y=v(x). Explain .
Click here to see answer by stanbon(75887)

Question 1120804: If 3x-6y =9z whichbof the following expressions is equivalent to x^2-4xy+4y^2

Click here to see answer by ikleyn(52776)

Question 1120884: Let C(t)=4t over t^+4 be the function that describes the concentration of a certain medication in the bloodstream over time t.
Click here to see answer by josgarithmetic(39616)

Question 1120960: A chemical company makes two brands of antifreeze. The first brand is
35%
pure antifreeze, and the second brand is
85%
pure antifreeze. In order to obtain
50
gallons of a mixture that contains
65%
pure antifreeze, how many gallons of each brand of antifreeze must be used?

Click here to see answer by greenestamps(13198)

Question 1121045: Mr. aquino wants to paint the ceiling of a room that has a length of (c^2 + 2cd + d^2) meters and a width of (c + d) meters. if one can of paint will cover (c + d) ^2 square meter, what is the minimum number of cans of paint needed? express your answer as a polynomial.
Click here to see answer by solver91311(24713)

Question 1121116: Find the polynomial function with the following roots: -1 of multiplicity 2; and 3. Show your work.
Click here to see answer by josmiceli(19441)

Question 1121125: Hello, I need help with factoring binomials. I was given problems such as x^7 + y^7 and w^12 - z^12, but I don't know how to solve these. I know how to solve simpler problems such as x^3 - 125, but when I get problems with higher exponents I get confused. Can someone explain the process of solving them? Thank you in advance to anyone who is willing to help.
Click here to see answer by ikleyn(52776)

Question 1121128: Let f(x) = x + 7 and g(x) = x − 4. Find f(x) ⋅ g(x)
Click here to see answer by greenestamps(13198)

Question 1120936: If a^3+12ab^2=679 and 9a^2b+12b^3=978, find (a-2b)^2.
Click here to see answer by greenestamps(13198)

Question 1121216: If (2006-a)(2004-a)=2005, find (2006-a)^2+(2004-a)^2
Click here to see answer by ikleyn(52776)

Question 1121217: Express the following product as a reduced fraction:
1(1-1/2)(1-1/3)(1-1/4).......(1-1/2000)
Click here to see answer by ikleyn(52776)

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