Questions on Algebra: Quadratic Equation answered by real tutors!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> Questions on Algebra: Quadratic Equation answered by real tutors!      Log On


   



Tutors Answer Your Questions about Quadratic Equations (FREE)


Question 206116: Can you please help me answer this question.
x/3=4/x + 1

Click here to see answer by stanbon(75887) About Me 

Question 206107: I really need some help for this problems because I have been confuse of this problems since the start and now the Examination is coming near and this is going to be added, I really will appreciate some help in this questions:
---find the value of k so that the equation +3x%5E2-7x%2Bk=0+ will have equal roots.
---find the value of k so that the equation +3x%5E2-%285%2Bk%29x-17=0+ will have one roots numerically equal but opposite in sign
--what should be the range of the value of k so that the equation +2x%5E2%2B3kx-9=0+ will have real and unequal roots.
---what should be the value of k so that the equation +x%5E2%2B%28k-2%29x%2B4=0+
will have equal roots?

Click here to see answer by Edwin McCravy(20055) About Me 

Question 206101: I really need some help for this problems because I have been confuse of this problems since the start and now the Examination is coming near and this is going to be added, I really will appreciate some help in this questions:
---find the value of k so that the equation +3x%5E2-7x%2Bk=0+ will have equal roots.
---find the value of k so that the equation +3x%5E2-%285%2Bk%29x-17=0+ will have one roots numerically equal but opposite in sign
--what should be the range of the value of k so that the equation +2x%5E2%2B3kx-9=0+ will have real and unequal roots.
---what should be the value of k so that the equation +x%5E2%2B%28k-2%29x%2B4=0+
will have equal roots?

Click here to see answer by Edwin McCravy(20055) About Me 

Question 206132: What are the inequalites that define the region in the first quadrant. How about 2nd, 3rd and 4th quadrants?

Click here to see answer by Targetweek(62) About Me 

Question 206100: 20. A punter can kick a football with an initial velocity of 48 feet per second. How many seconds will it take for the ball to return to the ground? (Hint: use the formula h= vt – 16t2.)
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 206105: 16. If 4/3x >-1, what is the set of all possible values of x?

Click here to see answer by Marth(57) About Me 

Question 206103: 18. What is the reciprocal of 2/x + 7/x+1.
Click here to see answer by Marth(57) About Me 

Question 206153: I need to determine a quadratic equation and solve the problem.
My word problems is as follows: The perimeter of a rectangle is 34cm, and the diagonal is 13cm. Determine the lengths of the sides of the rectangle.
I am setting up my problem as follows but not sure if it is correct:
2x + 2y = 34 (perimeter of the rectangle)
x^2 x y^2 = 13^2 or 169 (the diagonal portion of the rectangle)
I am then following through to make a quadratic equation where:
2x + 2x = 37 reduces to x = 17-7
Then I am taking (17-y)^2 + y^2 = 169 to come up with my final quadratic equation.
Am I on the right path?
Thanks - Lori

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

Question 206099: Find the value of k so that the equation +2x%5E2%2Bkx-15=0+ will have one root equal to 3.
Click here to see answer by jim_thompson5910(35256) About Me 

Question 206189: Hi, I really need help on this one problem... I need to solve for "x" by taking the square root, and there should be two answers. 2x%5E2+=+100
I just don't understand how to do it... if you could show me, I would be deeply grateful.

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

Question 206210: Can you please help me with this problem:
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and Train B is traveling at 48 miles per hour. Train A passes a station at 11:15PM.. If train B passes the same station at 11:30pm, at what time will train B catch up to train A? (write am, or pm in the answer)

Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 206219: 2x^2+20=-13x
Click here to see answer by anantha(86) About Me 

Question 206066: Hi, Im having problems trying to solve these rational equations. its a extraneous solution. Can you help please.
5/y-3 = y+7/2y-6 + 1

Click here to see answer by edjones(8007) About Me 

Question 206232: 2(x-4)^7/3-(x-4)^4/3-(x-4)^1/3
Click here to see answer by stanbon(75887) About Me 

Question 206229: Solve the formula for the indicated letter.
S=4Pir^2, for r^2;
P=2L + 2W, for w

Click here to see answer by stanbon(75887) About Me 

Question 206213: This problem with linear functions is getting me confused, can you help me please? I appreciate it.
In 1991, the life expectancy of males in a certain country was 66.3 years. In 1995, it was 68.9 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991.
The linear function E(t) that fits the data is E(t)=___t + ____ (round to the nearest tenth)
Use the function to predict the life expectancy of males in 2008. E(17)=___
(round to the nearest tenth)

Click here to see answer by stanbon(75887) About Me 

Question 206212: Please help, I am having problems with this one, thanks
Media services charges $40 for a phone and $20/month for its economy plan. The equation C= 20t + 40 describes the total cost, C, of operating a media service phone for t months. the total cost for 4 months of service is $____.
If a customer has only $90 available, how many months of service can she receive? Would it be 3, 2 1/3, 2 1/2 or 2?

Click here to see answer by Theo(13342) About Me 
Question 206212: Please help, I am having problems with this one, thanks
Media services charges $40 for a phone and $20/month for its economy plan. The equation C= 20t + 40 describes the total cost, C, of operating a media service phone for t months. the total cost for 4 months of service is $____.
If a customer has only $90 available, how many months of service can she receive? Would it be 3, 2 1/3, 2 1/2 or 2?

Click here to see answer by nerdybill(7384) About Me 

Question 206251: Wondering if I am on the right track. I need to determine a quadratic equation to solve the problem and also solve the problem. My word question is as follows: The perimeter of a rectangle is 34 cm and the diagonal is 13 cm. Determine the lengths of the side of the rectangle.
I am setting up my equation as follows:
2x + 2y = 34
x^2 + y^2 = 169
I then determine (x) by the following equation:
2x + 2y = 34
2x = 34 - 2y
x = 17 - y
Then I am taking the following equation to come up with a quadratic equation:
(17-y)^2 + y^2 = 169
189 - 34y + y^2 + y^2 = 169
2y^2 - 34y = -20
2y^2 - 34y + 20 = 0
Then my final answer (?) after calculating the quadratic equation is:
x = 34 + or - 498 / 4
x = 133 and x = 116
My question is, am I doing this correctly or am I missing a step?
Your input would be greatly appreciated.
Lori

Click here to see answer by Targetweek(62) About Me 
Question 206251: Wondering if I am on the right track. I need to determine a quadratic equation to solve the problem and also solve the problem. My word question is as follows: The perimeter of a rectangle is 34 cm and the diagonal is 13 cm. Determine the lengths of the side of the rectangle.
I am setting up my equation as follows:
2x + 2y = 34
x^2 + y^2 = 169
I then determine (x) by the following equation:
2x + 2y = 34
2x = 34 - 2y
x = 17 - y
Then I am taking the following equation to come up with a quadratic equation:
(17-y)^2 + y^2 = 169
189 - 34y + y^2 + y^2 = 169
2y^2 - 34y = -20
2y^2 - 34y + 20 = 0
Then my final answer (?) after calculating the quadratic equation is:
x = 34 + or - 498 / 4
x = 133 and x = 116
My question is, am I doing this correctly or am I missing a step?
Your input would be greatly appreciated.
Lori

Click here to see answer by mickclns(59) About Me 

Question 206280: Can you help me with this problem,
The function H(x)= 2.75x +71.48 can be used to predict the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long.
Predict the height of a woman whose humerus is 36cm long. the predicted height of a woman whose humerus is 36cm long is _____cm

Click here to see answer by Theo(13342) About Me 
Question 206280: Can you help me with this problem,
The function H(x)= 2.75x +71.48 can be used to predict the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long.
Predict the height of a woman whose humerus is 36cm long. the predicted height of a woman whose humerus is 36cm long is _____cm

Click here to see answer by Targetweek(62) About Me 

Question 206301: (2x+5)(3x-4)=0
Click here to see answer by scott8148(6628) About Me 

Question 206302: (x+2)(x+6)=12
Click here to see answer by Edwin McCravy(20055) About Me 

Question 206322: The width of a rectangle is fixed at 14cm. what lengths will make the perimeter greater than 78cm? the length must be greater than _____cm.



I thankyou for your help.

Click here to see answer by rfer(16322) About Me 

Question 206320: I am having problems with this application, as simple as it may seem. thanks
On three consecutive passes, a football team gives 6 yards, loses 24 yards, and gains 49 yards. The total net yardage is _____yards.

Click here to see answer by rfer(16322) About Me 

Question 206316: Problem:
Soybean meal is 14% protein, cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 13% protein? How many pounds of the cornmeal should be in the mixture? ____pounds.
How many pounds of the soybean meal should be in the mixture? ____pounds.
Thanks

Click here to see answer by mickclns(59) About Me 

Question 206311: I do not know how to figure this out, can you help?
The equation y= -1777x+27,153 can be used to predict the number y of gun deaths in the United States X years after 2000, that is, X=0 corresponds to 2000, x=3 corresponds to 2003, X=4 corresponds to 2004, and so on. The predicted gun deaths in 2004 will be ____. The predicted gun deaths in 2008 will be _____. The predicted number of gun deaths will be 11,160 in the year _____.

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

Question 206356: please help!
Translate the following into a quadratic equation, and solve it:
The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions?

Click here to see answer by rfer(16322) About Me 

Question 206447: what is the equation of a parabola graph?
The parabola opens downward. The vertex is (0,2). It also has points (-2,-2) and (2,-2)

Click here to see answer by stanbon(75887) About Me 
Question 206447: what is the equation of a parabola graph?
The parabola opens downward. The vertex is (0,2). It also has points (-2,-2) and (2,-2)

Click here to see answer by mickclns(59) About Me 

Question 206241: Good day! please help me with this problem... i'm kind of slow in math.
A survey shows that 60000 people will buy a certain type of sandwich in a period of one week if the cost is 40. Suppose that for every 2.50 added to the price, 2000 fewer people will buy the sandwich
a.) What price will give the greatest revenue for the week?
b.) What is the approximate maximum possible profit for the week if the food supplier spreads approximately 1.5 million pesos to ensure a supply of the sandwiches for one week?

Click here to see answer by RAY100(1637) About Me 

Question 206435: I am trying to figure out a word problem (I don't know why but I just can't get how to set up any word problems). Anyway, I need to determine a quadratic equation to solve the problem and then solve the problem. My word problem is as follows:
A river has a current of 5mph. It takes Al half an hour longer to paddle upstreat 1.2 miles than to paddly downstram the same distance. What is Al's rate is still water?
In attempt to set up the problem I am doing the following:
P = Paddle
(p+5)(p-5)
The trip upstream takes 1/2 hour longer
(1.5)/(p-5) + (1.5)/(p+5) = 0
Am I on the right track? Any suggestions on how to set up word problems - I have such difficulty no matter what the problem is.
Thanks - Lori

Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 206423: How do you compute the "intercepts' of a quadratic function? What is the number of intercepts that a quadratic function have? Please explain
Click here to see answer by jim_thompson5910(35256) About Me 

Question 206501: I was trying to figure this problem out, I got confused with it, can you help me.
collect like terms
18u +4v-3u-9v

Click here to see answer by rfer(16322) About Me 

Question 206491: 3x2(squared)+48=24X
Click here to see answer by mickclns(59) About Me 

Question 206469: Sketch the graph of a quadratic function for which the related quadratic equation has only one solution. Then, sketch one that has two solutions. Explain how you know by looking at the graph the number of solutions there are.
Click here to see answer by stanbon(75887) About Me 

Question 205849: A plane reaches 1200 Km 1 hr earlier, if the speed of the plane is increased by 60km/hr from its initial speed. what is the initial speed of the plane?
Click here to see answer by AndrewRyan(3) About Me 

Question 206575: URGENT QUESTION NEEDED BY TOMORROW. hey there.. thankyou soom much..:) great help. the question is
solve.
2x-3y+1=0
x^2 -y^2=7
thank you so much

Click here to see answer by nerdybill(7384) About Me 

Question 206577: What is the basic method for graphing a linear equation>
Click here to see answer by stanbon(75887) About Me 

Question 206592: I know rate times time equals distance, but I'm still confused. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Click here to see answer by Theo(13342) About Me 

Question 206599: apply the quadratic formula to find the roots of the given functionand then graph the function g(x) = x^2 -x -12
Click here to see answer by Marth(57) About Me 

Question 206607: When solving a quadratic equation, if it can be solved by factoring, does this mean it has to be solved this way. I find using the formula method much easier, but I'm unsure if this method works for all quadratics?
Thanks!

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

Question 206593: A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.

Click here to see answer by ankor@dixie-net.com(22740) About Me 
Question 206593: A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.

Click here to see answer by Marth(57) 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