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

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Question 1188647: Rewrite by using base e.
y = 8.9(9.8)^x
Click here to see answer by Edwin McCravy(20054)

Question 1188647: Rewrite by using base e.
y = 8.9(9.8)^x
Click here to see answer by mccravyedwin(405)

Question 1188645: add (5m²n+3mn-6mn²) to the difference of (7m²n-2mn²) and (-m²n+9mn²)
Click here to see answer by MathLover1(20849)

Question 1188648: f(x) = log 6(x + 4) and z(x) = 6 x + 1 .
Solve z -1(x) = 2. What point is on the graph of z -1(x) ?

Click here to see answer by greenestamps(13195)

Question 1188716: Divide(9x2-7x2+x)÷x2
Click here to see answer by MathLover1(20849)

Question 1188724: Show that 𝑥 − 𝑐 is not a factor of 𝑓(𝑥) for any real number. Let 𝑓(𝑥) = −𝑥^4 − 3𝑥^2 −2.

Click here to see answer by Solver92311(821)

Question 1188736: (4x² + 25x - 9) + (10x² - 5x - 9)
Click here to see answer by josgarithmetic(39613)

Question 1186976: Determine all the factors given polynomial function use rational theorem to determine possible roots.
1.f(x)=x³+6x²+11x+6
2.g(x)=x³-7x+6
3.h(x)=x³+x²-12x
4.p(x)9x3-7x+2
5.y=5x³+4x²-31+6
Click here to see answer by Boreal(15235)

Question 1188813: A sculpture uses ice cube for his masterpiece. The volume, V (in cubic centimeters) of a block of ice can be modeled by the V(t)=4t³-15t²-81t-5, where t represents the thickness of the block of ice cube in centimeters. How thick is the block of ice with a volume of 65cm³? Show solution.
Click here to see answer by Alan3354(69443)

Question 1188848: Ravi runs 6 miles in 45 minutes. At the same rate, how many minutes would he take to run 4 miles?
Click here to see answer by ikleyn(52748)

Question 1188883: 3x2 - 12x + 18
Click here to see answer by ikleyn(52748)

Question 1188884: 15x2 + 30x
Click here to see answer by ikleyn(52748)

Question 1188889: Greatest Common Factoring
Factor each polynomial.
15x2 + 30x

Click here to see answer by josgarithmetic(39613)

Question 1188888: Greatest Common Factoring
Factor each polynomial.
3x2 - 12x + 18
Click here to see answer by josgarithmetic(39613)

Question 1188886: Divide the polynomials using the long division.
x^3-4x^2+5x-10 by x-2
Click here to see answer by ikleyn(52748)

Question 1188992: To divide the function f(x) by (x^2-4x-12), we find that the quotient is Q(x) and the remainder is (x+6). If f(-2)=a and f(6)=b, what is the value of b/a?
Click here to see answer by ikleyn(52748)

Question 1189019: HOW CAN I DO THIS WITHOUT A CALCULATOR?
A giant redwood tree casts a shadow, as shown in the figure. (Hint: tan25.7 = 0.4817)
(A) If the shadow casted is 532 At long, and if the angle of elevation of the sun is 25.7°, then the height of the tree
approximately equals to 378 ft.
(B) If the angle of elevation of the sun is 48.5°, the height of the tree is 256 ft, then the shadow casted is approximately
312 ft.
(C) If the angle of elevation of the sun is 36.8°, the shadow casted is 312 ft then the height of the tree is approximately
432 ft.
(D) None of the above (A) (B) (C) is correct
Click here to see answer by ikleyn(52748)

Question 1189314: A function f(x) = x3 + 2x - 1 has a zero within (0.1). Find the interval that the zero exists.
(A) (0.1, 0.3) (B) (0.4, 0.5) (C) (0.6, 0.7) (D) (0.7. 0.9)
Click here to see answer by greenestamps(13195)

Question 1189317: Mia has a certain amount of money. If she buys 4 pens and 1 pencil, she will have $5 left over. If she buys 2 pens and 2 pencils, she will have $3 left over. If Edward arrives with the same amount of money as Mia, together they can buy 7 pens and 4 pencils and spend all their money. If a is the cost of one pen and b is the cost of one pencil, compute the ordered pair (a,b).
Click here to see answer by greenestamps(13195)

Question 1189470: A function 𝑓(𝑥) = 𝑥^3 + 2𝑥 − 1 has a zero within (0,1). Find the interval that
the zero exists.
(A) (0.1, 0.3) (B) (0.4, 0.5) (C) (0.6, 0.7) (D) (0.7, 0.9) (E) none of the
above.
Click here to see answer by Edwin McCravy(20054)

Question 1189469: A function is given. What is the minimum value of the function?
𝑓(𝑥)=3𝑥^2 −11𝑥+𝐶, 5≤𝑥≤10, 𝐶 is a constant
(A)𝑓(5) (B) 𝑓(10) (C) 𝑓(11/3) (D) 𝑓(11/6) (E) none of the above.
Click here to see answer by ikleyn(52748)

Question 1189675: Determine whether each algebraic expression is a polynomial or not.
1. 𝑥^3−2𝑥^2+𝑥+1/3
2. (𝑥+1)/5
3. −𝑥^2+2𝑥+√3
4. 𝑥^2−1/𝑥^2
5. 𝑥^4−3𝑥^2+2𝑥+1/4
6. 𝑥^10−𝑦^10
7. √2𝑥+ 4
8. 1/𝑥^2 +2/𝑥+3
9. 3/(2𝑎^3 )−8𝑎^2+3
10. 3/4 𝑦^2−1/8 𝑦^2+1/3

Click here to see answer by Edwin McCravy(20054)

Question 1189727:
Click here to see answer by ikleyn(52748)

Question 1189728: Find a polynomial f(x) with real coefficients that satisfies the given conditions: degree 5; zeros 2 of multiplicity 3, i, and -i.
Click here to see answer by Boreal(15235)

Question 1189985: A baseball team plays in a stadium that
holds 55,000 spectators. With the ticket price at $10, the
average attendance at recent games has been 27,000. A mar-
ket survey indicates that for every dollar the ticket price is
lowered, attendance increases by 3000.
(a) Find a function that models the revenue in terms of ticket
price.
Click here to see answer by Solver92311(821)

Question 1190092: Please verify that I have properly completed the below using the given values of x, and evaluated the polynomial functions:
PROBLEM 1:
F(x) = x^2 + 7x -2
F(3)
F(3) = (3)^2 + 7(3) -2
= 9 + 21 -2 = 28
PROBLEM 2:
F(x) = 5x^2 - 11x +5
F(-1)= 5(-1)^2 - 11(-1) +5
= 5 + 11 + 5 = 26
Have I correctly evaluated the 2 given polynomials below by synthetic substitution:
Problem 1:
3x^2 - 5x -5
F(-6)
F(-6) = 133
Problem 2:
7x^2 -9x +2
F(-2)
F(-2) = 12
Thank you

Click here to see answer by Boreal(15235)

Question 1190148: Have I correctly determined if the first polynomial is a factor of the second polynomial below and stated why it is?
Problem 1:
x + 1; x^3 + x^2 -4x - 4
YES it is - F(-1) because = 0

Problem 2:
x + 3; 2x^3 -11x^2 + 12x - 4
NO it is NOT Because F(-3) = -193
Thank you

Click here to see answer by math_tutor2020(3816)

Question 1190358: Having trouble factoring x^3-5x^2-14x-60 given than x-3 is a factor.
Click here to see answer by Alan3354(69443)

Question 1190371: factor 2x^3+9x+7-6=0
Click here to see answer by MathLover1(20849)

Question 1190371: factor 2x^3+9x+7-6=0
Click here to see answer by greenestamps(13195)

Question 1190368: How do I factor x^3-4x^2+x+6 to find out the solutions?
I was given that x=-2 is one of the solutions.
The factoring is what is giving me trouble.
Click here to see answer by MathLover1(20849)

Question 1190576: 2a⁴b^6-3a²b²-20
Click here to see answer by Alan3354(69443)

Question 1190616: Write a polynomial function in standard form with real coefficient who zeros include -3, -1, and 3-2i
Click here to see answer by Alan3354(69443)

Question 1190669: find the product of polynomial
3𝑦^3 (−6𝑦^2−4𝑦+6)

Click here to see answer by Alan3354(69443)

Question 1190770: 2ce+4df-de-2cf
Click here to see answer by Alan3354(69443)

Question 1190770: 2ce+4df-de-2cf
Click here to see answer by ikleyn(52748)

Question 1190769: When a polynomial is divided by C +3 the quotient is 3C - 3 and the remainder is 5. Find the polynomial

Click here to see answer by ikleyn(52748)

Question 1191032: Determine if the following are equivalence relations:
1. S=ℝ
define
(a,b)∈R if a=b+1

Click here to see answer by ikleyn(52748)

Question 1191222: add 5 x ^ 2 -7 x + 3 and 7x^2 -x-2
Click here to see answer by josgarithmetic(39613)

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