Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 633202: A small leak will fill an empty boat in 5 hours. The boat's bilge pump will empty a full boat in 3 hours. If the boat were half full and leaking, how long would it take the pump to empty the boat?
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Question 633297: write a quadratic equation in standard form having the given solutions 4i,-4i
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Question 633321: I think this is using the pythagorean theorem and I get really confused...
A mason wants to be sure he has a right angle corner of a building's foundation. He marks a point 3 ft from the corner along one wall and another point 4ft from the corner along the other wall. If the corner is a right angle, what should the distance be between the two marked points??
I did the a^2 + b^2 = c^2 formula and plugged in 3^2 + b^2 = 4^2 and got an -7 as an answer. I know a negative # can't be it so that's where I need assistance. Thanks in advance.

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

Question 633337: Please shed some light on finding the solution.
If Emily hits a golf ball from the upper deck of a driving range (twelve feet above the ground) with an initial velocitynof 117 feet per second, after how many seconds should the ball land (assume her ball does not encounter any obstacles)? Round to the nearest tenth.

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Question 633223: Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by c(x)=0.2x²-1.3x+8.181, where c(x) is in hundreds of dollars.
The shop should build_____bicycles.

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Question 633339: Please shed some light on finding the solution.
If Emily hits a golf ball from the upper deck of a driving range (twelve feet above the ground) with an initial velocity of 117 feet per second, after how many seconds should the ball land (assume her ball does not encounter any obstacles)? Round to the nearest tenth.

Click here to see answer by jsmallt9(3758) About Me 

Question 633226: 4x^2-4sq.root3x+3=0
sq.root2x^2-3x+sq.root2=0

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Question 633253: there were studied the effects on the rats fed on a diet that contains 10 % of protein. The protein was consisting in of yeast and cornflour. changing the percentage P of yeast in the miscellany of the above mentioned protein, it was estimated that the weight gained (in grams) of a rat in a period of time, it was f (p), where:

F (p) = - 1/50 P^2 + 2P+ 20... 0 ≤ P≤ 100. Find the máximum- weight.

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Question 633467: solve
16x^4+47x^2=3






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Question 633466: sketch graph of quadratic function
f(x)=x^2-2x-3


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Question 633466: sketch graph of quadratic function
f(x)=x^2-2x-3


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Question 633466: sketch graph of quadratic function
f(x)=x^2-2x-3


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Question 633475: In two hpurs, a motorboat can travel 8 miles down a river and return 4 miles back. If the river flows at a rate of 2 mph, what is the rate of the boat in still water?
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Question 633522: Joan Arlington has twice as much money invested at 5% simple annual interest as she does at 4%. If her yearly income from the two investments is $252, how much does she have at each rate?
Click here to see answer by richwmiller(17219) About Me 

Question 633631: Equations of quadratic form
4x to the 4th power-10xsquare plus 9=0 I'm not sure whata numbers to factor

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Question 633640: I need help with a few problems that I have been working on but I can't seem to get exactly what it is I need, which is understanding how to work these problems and show my work. Please and thank you for any help you can offerme at this time.

Problem # 1: In this problem it asks to find the vertex, the line symmetry, and the maximum or minimum value of f(x). Graph the function. f(x)=1/3(x+6)^2+4.
Problem # 2: Find the variation constant and equation of variation where y varies directly as x and y=12 when x=2.
Problem #3: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. sq rt u-sq rt /sq rt u+sq rt v
Problem #4: Convert to decimal notation. 8.91*10^7
Problem #5: In a right triangle, find the length of the side not given. b=1, c=sq rt 10. The third length of the third side is?



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Question 633665: two hundred eighty meters of fencing is
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Question 633736: Solve
X^2-6x+7=0

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Question 633816: Find the x-coordinate of the vertex of the function given below.
y=(x-7)(x+5),I tried doing the opposites but when I typed in the answer it said it was numerically incorrect. Could you please help, thanks

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

Question 633953: Determine which set of ordered pairs (x, y) represents y as a function of x.
(A){(1, 2), (6, 7), (6, 1), (7, 6)}, (B){(1, 2), (2, 1), (7, 7)}

(C){(1, 2), (2, 6), (1, 7)}, (D){1, 2, 6, 7}


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Question 633964: write a quadratic equation with integral coefficients given the following number as roots. 6, -2/3
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Question 633951: Find the slope-intercept form of the equation of the line passing through the points:
(8, -6), (4, -2)

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Question 634041: Find the quadratic equation.
1. x = -1/3; x = 5/2

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Question 634273: please help me solve this equation {{[ (3/x-6)-(x/x-8)+(x^2+24/x^2-14x+48)
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Question 634452: what is the solution set for 2x^2-7x+6=0
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Question 634452: what is the solution set for 2x^2-7x+6=0
Click here to see answer by MathTherapy(10551) About Me 

Question 634449: I am a little confused on how to solve this. I need to solve and give exact and approximate solution to three decimal places. Any help, showing steps, would be really appreciated so I can understand how to do this type of problem. THanks.
y^2-18y+81=25

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Question 634449: I am a little confused on how to solve this. I need to solve and give exact and approximate solution to three decimal places. Any help, showing steps, would be really appreciated so I can understand how to do this type of problem. THanks.
y^2-18y+81=25

Click here to see answer by josmiceli(19441) About Me 

Question 634618: I know that the solutions of this problem are imaginary, but I don't think I solved it right. The problem is x^2+7x+14 and I believe the imaginary solutions are -7+iradical-7/2 and -7-iradical-7/2. Are these right?
Click here to see answer by ewatrrr(24785) About Me 

Question 634677: what is the equation form in vertex form
y-3x2 - 12x +7

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Question 634538: Please, make this expression a perfect square trinomial. then factor the resulting PST. +x%5E2-7x+
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Question 634539: please, make the expression a perfect square trinomial. Then factor the resulting PST. +x%5E2%2B3x+
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Question 634728: Which of the following quadratic equations has solutions x=6a and x=-3b?
A. x^2-18ab=0
B. x^2-x(3b-6a)-18ab=0
C. x^2-x(3b+6a)+18ab=0
D. x^2+x(3b-6a)-18ab=0
E. x^2+x(3b+6a)+18ab=0

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Question 634899: x^2+4x+2=0
solve it

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Question 634871: 2x^2 + 8 =7x
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Question 634986: I'm stumped. Thank you for your help.
in a diving siblings showcase, 11-year old hannah takes off from a 24.61 foot platform with an initial velocity of 9.7 ft/sec at the same time her brother tyler, who is 3.5 years older, takes off from a 32.81 foot platform with an initial velocity of 4.51 ft/sec. Who enters the water first? By how much? Round to the nearest hundredth.

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Question 634987: Q.1) The question reads "solve the equation x^2-1=8 by using the graph."
The graph has an open (upward facing) parabola. It has a y-intercept of -1; x-intercept's at -1, 1.
How do I answer this question? I'm not sure what I need to do...
Q.2) The question reads "express the following as a compound inequity and graph"
it states "x" is between -4 to 6.
There is a graph.
How do I properly answer this on the graph?
Thank you.

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Question 635220: Find the vertex of the parabola:
f(x) = x^2 - 12x -4

Click here to see answer by solver91311(24713) About Me 

Question 635204: An arrow is shot into the air and its path is modeled by the function h(x) = -4.9t2 + 34.3t - 49 where "h" is the height of the arrow (given in meters) at any given time t (given in seconds). Find the number of seconds necessary for the arrow to reach its maximum height.
Thanks, it means a lot! :)

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Question 635228: A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the equation P = -25x^2 + 450x. What number of clerks will maximize the profit?
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Question 635346: Solve by completing the square. x^2-11x+30=0.
HELP!
Thanks!

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Question 635345: A flat square piece of cardboard is used to construct an open box. Cutting a 3 feet by 3 feet square off of each corner and folding up the edges will yield an open box (assuming these edges are taped together). If the desired volume of the box is 147 cubic feet, what are the dimensions of the original square piece of cardboard?
Click here to see answer by mananth(16946) About Me 

Question 635381: (6+5sqrt3)(1- sqrt3)= ? simplify thanks for your help
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Question 635380: (sqrt x + sqrt 7)^2
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Question 635426: Suppose that the equation p(x) = -5x^2 + 600x +100 (where x represents the number of items sold), describes the profit function for a certain business. How many items should be sold to maximize the profit?
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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