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

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Question 1109881: I need help figuring out how to solve this problem
The weight of a can of soup is jointly proportional to its height and to the square of its diameter.
A can 7 inches high with a diameter of 2 inches weighs 11.1 ounces. What is the weight of a can that is 4 inches with a diameter of 4 inches.
The weight of the can is how many ounces?

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Question 1109878: I need help figuring out how to solve this problem.
The cost C of steel tubing is jointly proportional to its length L, in feet, and Diameter D, in inches. If a 9 foot tube with a 1 inch diameter cost $72, find the cost of a 9 ft tube with a diameter of 10 inches.

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Question 1110064: How do you solve this polynomial? (x^(2)y)(x^(2 )-y^(2))

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Question 1110098: Suppose that $9500 is placed in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Find the amount in the account at the end of year 1 and year 2

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Question 1110098: Suppose that $9500 is placed in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Find the amount in the account at the end of year 1 and year 2

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Question 1110127: Tammy simplified the problem as shown, (x^3+3x)-(x^2+6-4x)=x^3-x^2-x-6, Mr.Adkins told her she was wrong. Explain what she did wrong and give the correct simplification. (The numbers to the right of ^ are exponents)
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Question 1110452: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−3
Find a possible formula for P(x).
P(x)=

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Question 1110454: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−5. The y-intercept is y=−8.
Find a formula for P(x).
P(x)=

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Question 1110453: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=2 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,252).
Find a formula for P(x).
P(x)=

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Question 1110501: write each rational expression in lowest terms.
m^2-25/4m -20
(m+5)(m-5)/4(m-5)= m+5/4
What do I do now?

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Question 1110628: X11/12 , X5/12=

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Question 1110634: Given f(x)=4(x-3)^2 (x+2)^3 (5x-1), determine
The degree of the polynomial
The dominant term
The y-intercept

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Question 1110665: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3.
Find a possible formula for P(x).

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Question 1110774: The polynomial of degree 4, P(x), has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=−2. It goes through the point (5,112).
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Question 1110798: A tank in the shape of a rectangular prism has dimensions 2x,5x+3, and 3x+1 metres, a metal block is dropped into the tank and the tank is then filled with water. The volume of water is 22x3+18x2+3x cube metres. Determine the dimensions of the metal block in terms of x
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Question 1110854: This type of problem was not shown in our notes:
A polynomial function is described. Find all remaining zeros. Degree: 3 Zeros: -1,i.
Please help me, please and thank you.

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Question 1110856: Lewis and Paula both work at a fast food restaurant. When they both work together building sandwiches, they can make 70 sandwiches in one hour. Alone, Lewis can build 25 sandwiches in 45min. How many sandwiches does Paula build every hour working alone?
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Question 1111002: A rectangle is three times as long as it is wide. If its length and width are both decreased by 2 cm, its area is decreased by 36 cm^2. Find the dimensions of the original rectangle.
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Question 1111014: A piece of cardboard is 25 cm taller than it is wide. It is mounted on a wall so that there is a 5 cm border on all sides. If the area of the border alone is 1350 cm^2, what are the dimensions of the cardboard (not including the border)?
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Question 1111013: A rectangle is twice as long as it is wide. If both of its dimensions are increased by 4 m, its area is increased by 88 m^2. Find the dimensions of the original rectangle.
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Question 1111142: If a + b = 11, what are two possible values for c that satisfy the equation below:
(ax - 4)(bx + 7) = 30x^2 + cx - 28

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Question 1111142: If a + b = 11, what are two possible values for c that satisfy the equation below:
(ax - 4)(bx + 7) = 30x^2 + cx - 28

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Question 1111156: I really would appreciate your help understanding problems like the one below:
Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of shells. If she had enough shells for a border whose area is 128 square inches, determine the width of the border.

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Question 1111156: I really would appreciate your help understanding problems like the one below:
Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of shells. If she had enough shells for a border whose area is 128 square inches, determine the width of the border.

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Question 1111301: If a polynomial is divided by (x-2) and (x+1) leave the remainders 11and 1respectively, find the polynomial
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Question 1111313: the remainders when f(x)=x³+ax²+bx+c is divided by (x-1),(x+2) and (x-2) are respectively 2,-1 and 15, find the quotient and remainder when f(x) is divided by (x+1).
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Question 1111361: x^2+x+12
I went through with
x^2+x+12
x^2-3x+4x+12
x(x-3)+4(x+3)
Which shouldn't be correct, as the parentheses should be identical. I cannot find where I went wrong, either.

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Question 1111361: x^2+x+12
I went through with
x^2+x+12
x^2-3x+4x+12
x(x-3)+4(x+3)
Which shouldn't be correct, as the parentheses should be identical. I cannot find where I went wrong, either.

Click here to see answer by Boreal(15235) About Me 

Question 1111310: (1-x^4)/(1-x) + (1-x^3)/1+x
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Question 1111623: Trey can finish the floor of an apartment in 8 hr. Matt can refinish the floor in 6 hr. How long will it take them, working together, to refinish the floor? Write answer as a mixed number
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Question 1111690: find a fifth degree polynomial that has a zero of multiplicity 2 at x=2, a zero at x=5, and the factor x^2 + 2x + 4
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Question 1111773: Abby can process an order in 3 hours. Bill can process an order in 4 hours. Cliff can process an order in 6 hours. If they all work together how long would it take them (in minutes) to process 1 order?
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Question 1111915: Two cars race on a 4 mile oval track. The sum of their rates is 200 miles per hour. Find the rate of each if the faster car gains one lap in 40 minutes.

My work:
I know the rate of the slower car is 200-x and the rate of the other car is x. Then I know the time of slower car is 4/(200-x) and the time of the other car is 4/x. The distance for both is 4 miles. I'm not sure what to do with the "faster car gains one lap in 40 minutes". Thank you for your help!

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Question 1111967: The length of a rectangle is 1m more than double the width, and the area of the rectangle is 66m^2 . Find the dimensions of the rectangle.
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Question 1111983: Problem Page The area of a rectangle is 28m^2 , and the length of the rectangle is 1m more than twice the width. Find the dimensions of the rectangle.
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Question 1111995: 6 : 48 :: 56 :

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Question 1111990:
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Question 1112022: The area of a rectangle is 28m^2, and the length of the rectangle is 1m more than twice the width. Find the dimensions of the rectangle.
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Question 1112022: The area of a rectangle is 28m^2, and the length of the rectangle is 1m more than twice the width. Find the dimensions of the rectangle.
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Question 1112035: Perform the following operations. Put answers in standard form.
(x+4)^3

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Question 1112053: Problem Page The area of a rectangle is 65ft^2 and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.
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Question 1112053: Problem Page The area of a rectangle is 65ft^2 and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.
Click here to see answer by ikleyn(52750) About Me 
Question 1112053: Problem Page The area of a rectangle is 65ft^2 and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.
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Question 1112051: Perform the following operations. Put answers in standard form.
(16x^4-12x^3+16x^2+7)÷(2x-3).

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Question 1112061: The area of a carpet is 36x^2y-9xy square inches. If the width is 3xy inches, what is the length of the carpet?
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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, 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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