Questions on Algebra: Equations answered by real tutors!

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Question 862677: I have this math problem but can't find the steps
9a+6b=-9
-9+b=30

Click here to see answer by Fombitz(32388) About Me 

Question 862680: Translate the question into an equation. Do not solve. Let x be the unknown number.
81% of 83 is what number?

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Question 862726: y = 3x + 8
4x + 2y = 18

Click here to see answer by josgarithmetic(39617) About Me 

Question 862752:
Solve for the following systems of equations. If they cannot be solved, explain why.

5x-2y=-24
-4y=-48-10x

Click here to see answer by Lukas007(2) About Me 

Question 861873: 332/372 = x/12
How do I find x ?
Thanks,
Laurie

Click here to see answer by lenny460(1073) About Me 

Question 862854: (t-4)^2=/T+4)^2+32
Click here to see answer by Alan3354(69443) About Me 

Question 862952: 3x+6/ x^2+3x+2*x+1/2x+8
Click here to see answer by Alan3354(69443) About Me 

Question 862983: If y=
(4x−5) 6
, differentiate with respect to x.

Click here to see answer by ewatrrr(24785) About Me 

Question 863095: at a movie theater a couple buys one large popcorn and two drinks for $9.00 a group of teenagers buy two large popcorn and a drink for $20.50 find the cost of one large popcorn and the cost of one drink
Click here to see answer by richwmiller(17219) About Me 

Question 863119: What is the solution to the following system of equations?
2x + 3y = 6
x + y = 4
Explain how you got what you got if possible, thanks.

Click here to see answer by ewatrrr(24785) About Me 

Question 863165: 1)Find all values of k that ensure that the given equation has exactly one solution.
kx2 + 26x + k = 0
k = (smaller value)
k = (larger value)
2)What quantity of pure acid must be added to 300 mL of a 25% acid solution to produce a 70% acid solution?
3)Mary has $3.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and negative six more nickels than dimes, how many coins of each type does she have?
4)A coffee merchant sells a customer 2 lb of Hawaiian Kona at $5.50 per pound. The merchant's scale is accurate to within ±0.09 lb. By how much could the customer have been overcharged or undercharged because of possible inaccuracy in the scale? (Round your answer to the nearest whole cent.)
5)It is estimated that the annual cost of driving a certain new car is given by the formula
C = 0.38m + 2100
where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car and decides to budget between $6660 and $8180 for next year's driving costs. What is the corresponding range of miles that she can drive her new car?
6)

Click here to see answer by josgarithmetic(39617) About Me 

Question 863151: help pls f(x) = 2x + 7 and g(x) = 3x + c. Find c if (f \circ g)(x) = (g \circ f)(x) for all x.
Click here to see answer by josgarithmetic(39617) About Me 

Question 863270: Find 'n'
1+3+...+2n-1=10(4n+50)
Do I have to do something with (2n-1+2)(2n-1)
I have no idea. Please help.

Click here to see answer by metodi022(3) About Me 
Question 863270: Find 'n'
1+3+...+2n-1=10(4n+50)
Do I have to do something with (2n-1+2)(2n-1)
I have no idea. Please help.

Click here to see answer by lenny460(1073) About Me 

Question 863222: Hi i'm not to sure if this is in the right section but hope so. I'm currently having problems with the following question.
Given a parametric curve x = 2sint, y=sin(2t) where t takes all values in R (real numbers)
(a) Find an implicit equation of this curve by eliminating t,
(b) Sketch this parametric curve in the xy-plane.
I'm more confused about a , I don't expect anyone to do (b) perhaps just inform me if my thoughts are correct.
Do i set it so that 0 = arcsin(x/2) - (arcsin(y))/2 --> from setting t=t OR somewhere along the lines of x + y = 2sint + sin(2t) and it's somehow a circle.. Or am I just completely off.. Thanks to anyone who responds !!

Click here to see answer by Theo(13342) About Me 

Question 863271: Find 'n'
1+3+...+2n-1=10(4n+50)
Do I have to do something with (2n-1+2)(2n-1)
I have no idea. Please help.

Click here to see answer by rothauserc(4718) About Me 
Question 863271: Find 'n'
1+3+...+2n-1=10(4n+50)
Do I have to do something with (2n-1+2)(2n-1)
I have no idea. Please help.

Click here to see answer by Theo(13342) About Me 

Question 52722: -4x – 2 = -6 – 2x
Click here to see answer by lenny460(1073) About Me 

Question 863313: HI! how would i solve and equation like 487 / 6 * X +12-7=1628.3 find x?

Click here to see answer by richwmiller(17219) About Me 
Question 863313: HI! how would i solve and equation like 487 / 6 * X +12-7=1628.3 find x?

Click here to see answer by rothauserc(4718) About Me 

Question 861583: 2x + 5 = 3x + 8
Click here to see answer by cjc394123(2) About Me 

Question 863458: Translate this sentence into an equation.


66is the sum of 21 and Jose's score.
Use the variable j to represent Jose's score
I am having a problem can't get it

Click here to see answer by cjc394123(2) About Me 
Question 863458: Translate this sentence into an equation.


66is the sum of 21 and Jose's score.
Use the variable j to represent Jose's score
I am having a problem can't get it

Click here to see answer by Alan3354(69443) About Me 

Question 863480:
Click here to see answer by Alan3354(69443) About Me 

Question 863612: Differentiate with respect to x,if y =
4x 3 .sinx

Click here to see answer by Alan3354(69443) About Me 

Question 863611: If y=tan2x
Click here to see answer by Alan3354(69443) About Me 

Question 863623: Differentiate with respect to
x:f(x)=(ax 3 +bx)

Click here to see answer by Fombitz(32388) About Me 

Question 863617: Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for a,b,c
Click here to see answer by Fombitz(32388) About Me 

Question 863798: School A and School B sent groups of students to a trip. School A rented and filled 2 mini buses and 3 coaches with 170 students. School B rented and filled 3 mini-buses and 2 coaches with 135 students. Every mini-buses had the same number of students in it, as did the coaches.
A) Write down two equations to represent the above information.
B) find the number of students in each mini-bus and in each coach

Click here to see answer by richwmiller(17219) About Me 

Question 863836: A = πr2 + 2πrh for h
Click here to see answer by ewatrrr(24785) About Me 

Question 863922: A man goes to the bank and asks for x dollars and y cents. The banker by mistake gives him y dollars and x cents. After a nickel drops on the floor, the man looks at his money and realizes that he now has twice the amount he asked for. What was the amount he asked for?
I can only come up with the equation: 2 ( x +.01y) = y + .01x - .05 to reflect this.
I have tried to solve it and can't do it.
Would you please give me some guidance or explain what to do? Is my equation incorrect.
Thank you,
Deborah Aboud

Click here to see answer by richwmiller(17219) About Me 

Question 864063: find the product(5m-2n)^2

Click here to see answer by Fombitz(32388) About Me 

Question 864101: Differentiate with respect to
x:f(x)=(8x 3 +x 2 )

Click here to see answer by ewatrrr(24785) About Me 

Question 864115: The bicyclists were 300 miles apart at 3 p.m. and were headed toward each other. If they met at 9 p.m. and one was traveling 20 miles per hour faster than the other, what was the speed of each bicyclist? Can you include the rates and time of the problem please.
Click here to see answer by dkppathak(439) About Me 

Question 864112: Differentiate with respect to x :f(x) = cos x
Click here to see answer by ewatrrr(24785) About Me 

Question 864105: Differentiate with respect to x ;f(x) = tanx
Click here to see answer by ewatrrr(24785) About Me 

Question 864141: If A.x=
λx
,where A=
∣ ∣ ∣ ∣ 2 1 1 2 3 2 −2 1 2 ∣ ∣ ∣ ∣
,determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If
λ=2
,what is b

Click here to see answer by Fombitz(32388) About Me 

Question 864174: How to solve this equation ?
2(5x-3)^(1/3) -4 = 0

Click here to see answer by lwsshak3(11628) About Me 

Question 864207: What are the ordered pairs of -4x+2y=10
a.-3,-1
b.-1,2
c.2,8
d.4,11

Click here to see answer by ewatrrr(24785) About Me 

Question 864198: How do I find the constant rate of change in the given equation:
y=4x_6

Click here to see answer by Alan3354(69443) About Me 

Question 864313: Find the vertical asymptotes, if any, of the graph of the rational function.
g(x) =
A) x = 4, x = -4
B) x = 4
C) x = 4, x = -4, x = 0
D) no vertical asymptote

Click here to see answer by jim_thompson5910(35256) About Me 

Question 864430: Please help me solve these i need them today
145-5x=4x+10
2x+11=-16-7x
-15x-7x=10x+19
14-8x=34-15x
219-2x=34+19

Click here to see answer by Alan3354(69443) About Me 

Question 864566: What value of x will make the equation 3(x + 15) - 6x = -6(x - 3) true?
Click here to see answer by stanbon(75887) About Me 

Question 864615: 2(x+4)=16 what's the x equal

Click here to see answer by jim_thompson5910(35256) About Me 

Question 861006: I need to know k squared +3k-54 over k9
Click here to see answer by tommyt3rd(5050) About Me 

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, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580