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

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

Question 1097525: The ages of John and Mary total 27 years. Mary's age plus twice John's age is 40. How old is each person?
j+m = 27
m+2j = 40
Now I'm stuck...
Click here to see answer by jim_thompson5910(35256)

Question 1097536: The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by 40x - 0.0002x^2, what is an expression for the profit?
Click here to see answer by Alan3354(69443)

Question 1097564: Form a polynomial whose zeros and degree are given.
Zeros: negative −2, 2, 4, 5; degree 4
Click here to see answer by math_helper(2461)

Question 1097630: find the quotient and remainder when 6X^3 + 3X^2 - 2X + 1 is divided by
(a) 3X^2 +2X + 1
(b) X^2 - 3X + 2
Click here to see answer by Jeetbhatt10th(11)

Question 1097630: find the quotient and remainder when 6X^3 + 3X^2 - 2X + 1 is divided by
(a) 3X^2 +2X + 1
(b) X^2 - 3X + 2
Click here to see answer by MathTherapy(10551)

Question 1097653: For each polynomial function, find all zeros and their multiplicities.
f(x)=5x�(x^2-16)(x+5)

Click here to see answer by josgarithmetic(39616)

Question 1097705: What are the leading coefficient, constant term and degree, if any, of the algebraic expression -7.
Click here to see answer by ikleyn(52775)

Question 1097735: 1. Find the polynomial with integer coefficients that satisfies the given conditions. Distribute the factors completely.

Q(x) has degree 3 and zeros −15, 6i and the leading coefficient is 10.
Click here to see answer by greenestamps(13198)

Question 1097736: 1. Find all the zeros and write P(x) in factored form:
𝑃(𝑥)=𝑥3−125
Click here to see answer by josgarithmetic(39616)

Question 1097946: An astronaut on the moon throws a baseball upward. The astronaut is 6 fee, 6 inches tall and the initial velocity of the ball is 30 feet per second. The height of the ball is approximated by the function
s(t)= -2.7t^2 + 30t + 6.5,
where t is the number of seconds after the ball was thrown.
(a) After how many seconds is the ball 12 feet above the moon�s surface?
(b) How many seconds after it was thrown will the ball return to the surface?
(c) The ball will never reach a height of 100 feet. How can this be determined analytically?
Click here to see answer by ikleyn(52775)

Question 1098025: I have the following polynomial function and I'm trying to find the y-intercept:
S(x) = 1/2(x-1)^3+4
I set x to zero and proceeded this way:
(0-1) = -1
(-1)^3 = -1
1/2(-1) = -1/2 (or -0.5)
-0.5 + 4 = 3.5
so y=3.5
Unfortunately, the answer my textbook gives for the y-intercept is -1. I have no idea where I'm going wrong. Also, I tried transforming the graph from the parent function y=x^3, so I moved it right one unit and up 4 units (I didn't get as far as compressing it vertically by a factor of 1/2) and I can't figure out how to get it to cross the y-axis at -1, let alone 3.5. I am so confused! I'd appreciate whatever help you can give me. Thanks!

Click here to see answer by ikleyn(52775)

Question 1098005: the lenght of a shipping box is two inches longer than the width and four times the height.
write a fuction v(w) that models the volume of the box, where w is the width, in inches.
Click here to see answer by ikleyn(52775)

Question 1098020: Find a polynomial of lowest degree with rational coefficients that has 3 and 4i as some of its zeros.
Click here to see answer by ikleyn(52775)

Question 1098071: This is factorization of polynomials, I just wanted to ask how this is factorized? Thank you.
(4+a)(4-a)-12-3a

Click here to see answer by Theo(13342)

Question 1098071: This is factorization of polynomials, I just wanted to ask how this is factorized? Thank you.
(4+a)(4-a)-12-3a

Click here to see answer by ikleyn(52775)

Question 1098071: This is factorization of polynomials, I just wanted to ask how this is factorized? Thank you.
(4+a)(4-a)-12-3a

Click here to see answer by MathTherapy(10551)

Question 1098188: Find a polynomial with smallest degree with rational coefficients that has roots (2 - i√ 3), (2 - i√ 3) and 1 of muntiplicity 2.
Click here to see answer by t0hierry(194)

Question 1098319: Determine the zeros, the degree, and the leading coefficient to graph this function.
f(x) = (x2+2x)(x-3)
Click here to see answer by greenestamps(13198)

Question 1098319: Determine the zeros, the degree, and the leading coefficient to graph this function.
f(x) = (x2+2x)(x-3)
Click here to see answer by ankor@dixie-net.com(22740)

Question 1098319: Determine the zeros, the degree, and the leading coefficient to graph this function.
f(x) = (x2+2x)(x-3)
Click here to see answer by KMST(5328)

Question 1098258: you are given a piece of cardboard that is 6 inches by 4 inches. You would like to cut equal-sized squares out of each of the 4 corners and fold the card board in such a way to make an open-top rectangular box.
(") means INCHES
Part A: Complete the table below.
Length of Square Cut Length of Box(") Width of Box(") Volume of Box (")
I (")
0.25
0.50
0.90
1.40
1.80
Part B:
1. What are the Possible values of I?
2. What is the dependent and independent variable?
3. Using I and V, find a cubic function of best fit.
4. To maximize the volume of the box, what should be the side length of the corner squares?

Click here to see answer by josgarithmetic(39616)

Question 1098425: find an nth degree polynomial function with real coefficients satisfying the given conditions n=3 f(-1)=20 3 and 2i are zeros
Click here to see answer by greenestamps(13198)

Question 1098533: If it take Karen 2 hours to wax SUV and Clarann 3 hours how long would it take them to wax it together.

Click here to see answer by Boreal(15235)

Question 1098543: Not sure which category to put this Algebra question in:
A golf ball is hit with an initial velocity of 150 feet per second at an inclination of 45 degrees to the horizontal. in physics, it is established that the height h of the golf ball is given by the function:
h(x) = -32x^2/150^2 + x
Where X is the horizontal distance that the golf ball has traveled.
Use a graphing utility to determine the distance that the ball
has traveled when the height of the ball is 80 feet? (round to one decimal place) the answer is 92.1,611.1 ft. I just can't figure out how to figure this part out. How to find the answer.What to do to get the correct answer.
Click here to see answer by Theo(13342)

Question 1098592: (4�-y)3
(2a+b-3c-d)
(�/2-y/3)3
Pls can you solve this..

Click here to see answer by Alan3354(69443)

Question 1098636: Find a polynomial P(x) with real coefficients having a degree 6, leading coefficient 3, and zeros 6,0 (multiplicity 3), and 2-4i.

Click here to see answer by greenestamps(13198)

Question 1098702: quadratic polynomial that have no zeroes as real numbers

Click here to see answer by Alan3354(69443)

Question 1098761: Find all numbers for which the rational expression is undefined.
8z^2/2z+1

Click here to see answer by Alan3354(69443)

Question 1098844: Hi,
I would appreciate if someone might help here.
Exercise instructions: Express following in form X + Y*2^(1/2); X and Y are rational numbers:
(7 + 5 * 2^(1/2))^(1/3)
The answer given is: 1 + 2^(1/2)
I have no idea how they got there.
Thanks
Click here to see answer by KMST(5328)

Question 1098880: 4/x +2/x^2 / 2+1/x
NEED HELP WHATS THE FIRST STEP TO SLOVE?
Click here to see answer by richwmiller(17219)

Question 1098880: 4/x +2/x^2 / 2+1/x
NEED HELP WHATS THE FIRST STEP TO SLOVE?
Click here to see answer by ikleyn(52775)

Question 1098880: 4/x +2/x^2 / 2+1/x
NEED HELP WHATS THE FIRST STEP TO SLOVE?
Click here to see answer by Alan3354(69443)

Question 1098886: A partial solution set is given for the polynomial equation. Find the complete solution set. (Enter your answers as a comma-separated list.)
x^3 + 5x^2 − 20x − 42 = 0; {−7}
Click here to see answer by josgarithmetic(39616)

Question 1098987: simplifying the following complex rational expression
(4/x)+(2/x^2)/(2+1/x)
NEED HELP WHAT IS THE FIRST STEP TO SOLVE???
IS IT TO MULTIPLY THE LCD x^2
Click here to see answer by Fombitz(32388)

Question 1098995: The question asks me to decompose the expression in factors.
2x(to the power of 2) - 6x + 8
Click here to see answer by ikleyn(52775)

Question 1098995: The question asks me to decompose the expression in factors.
2x(to the power of 2) - 6x + 8
Click here to see answer by josmiceli(19441)

Question 1098993: Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the form d(x) times Q(x)plus R(x).
P(x)equals x Superscript 4 Baseline minus 6 x squared minus 31
d(x)equals xplus3
P(x)=(x+3) (?)+ ?

Click here to see answer by Fombitz(32388)

Question 1099067: Find a polynomial with integer coefficients that satisfies the given conditions.
Q has degree 3 and zeros −4 and 1 + i

I do not know how to do this could you please help me.

Click here to see answer by Boreal(15235)

Question 1099077: Determine all integral values of "k" so that each trinomial can be factored
X^2 + kx - 9
Click here to see answer by josgarithmetic(39616)

Question 1099071: Form a polynomial whose zeros and degree are given.
Zeros: -6, multiplicity 1; -2 multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1.
Click here to see answer by Fombitz(32388)

Question 1099057: Dog Years. A dog's life span is typically much shorter than that of a human. Age equivalents for dogs and humans are listed in the table below.
Age of Dog, x (in years)
0.25
0.5
1
2
4
6
8
10
14
18
21
Human Age, h (x) (in years)
5
10
15
24
32
40
48
56
72
91
106
a) Use a graphing calculator to fit linear and cubic functions to the data. Which function has the better fit?
b) Using the function from part (a), estimate the equivalent human age for dogs that are 5, 10, and 15 years old.
Click here to see answer by Boreal(15235)

Question 1099167: P(x) = x4 − 6x3 + 38x2 − 80x + 200; 2 + 4i
Click here to see answer by josgarithmetic(39616)

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