Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 281633: Jack mowes the lawn in 4hrs and mary mowes the lawn in 7 hours. How long would it take them to both mow the yard?
Click here to see answer by checkley77(12844)

Question 281657: A ball falls off the top of a roof 320 feet above the ground. The formula h= -16t^2 + 16t +320 describes the height of the ball above the ground, h, in feet, t seconds after the fall begins. How long will it take the ball to strike the ground.
Click here to see answer by Greenfinch(383)

Question 281772: If sides of a square are lengthened by 5cm, the area becomes 169cm^2. Find the length of a side from the original square.
Click here to see answer by richwmiller(17219)

Question 281773: x^1/2*y^1/6*z^1/5
Write as a single radical expression using rational exponents only.
Click here to see answer by stanbon(75887)

Question 281775: find the lenght of the side not given in the triangle
b=1, c=sqrt 17
What is a?
Click here to see answer by Alan3354(69443)

Question 281865: find a polynomial for the perimeter and area of a rectangle when the long side is d+7 and the short side is d.
perimeter=?
area=?
Click here to see answer by mananth(16946)

Question 281863: s^3-8s/s^2-64
Need all numbers for which expression is undefined.
Click here to see answer by subudear(62)

Question 281864: s^3-8s/s^2-64
Need all numbers for which expression is undefined.
Click here to see answer by nerdybill(7384)

Question 281952: Factor out the largest common factor.
5x(3x - 5) + 2(3x - 5)
Please help with this one.
Click here to see answer by richwmiller(17219)

Question 281957: Factor by grouping, if possible. Show all necessary work.
x^3 + 3X^2 - 2x - 6
where to start, I have no clue.
Click here to see answer by stanbon(75887)

Question 281983: Factor completely. Show all work necessary.
6x^2 + 17x +12
Click here to see answer by richwmiller(17219)

Question 282048: write 8.35x10^7 in decimal notation.

Click here to see answer by Mathematicians(84)

Question 282067: find the length of the side not given in a general right triangle where a and b are the short sides and c is the long side.
b=1, c=sqrt 17
What is the length of a?
a=?
Click here to see answer by solver91311(24713)

Question 282082: Factor completely. Show all work necessary.
4x^2-9
Click here to see answer by richwmiller(17219)

Question 282086: Solve using the principle of zero products.
(y + 17)(y + 5) (y + 3) = 0
Click here to see answer by richwmiller(17219)

Question 282087: Solve by factoring and using the principle of zero products. Show all work necessary.
4x^2 - 12x = 16
Click here to see answer by richwmiller(17219)

Question 282084: I am having trouble with this problem thank you.
Find the ordered pair for the vertex.
y=4x^2-16x+20
I've tried using the quadratic equation and my answer was 2 and 6.
I've also tried factoring the polynomial like this:
4(x^2-4x+5) = (x-5)(x+4) and could not get the last digit in equation to be positive. Please help I am really struggling with this.
Do I need to use the formula: -b/2a?
Thank you in advance for all your help.
Marlo
Click here to see answer by solver91311(24713)

Question 282173: We can never find zeros by solving the quadratic equation.
True or false?
All quadratic functions will factor so finding the zeros by graphing is not needed.
True or false?
Click here to see answer by richwmiller(17219)

Question 282200: finding the roots by using the quadratic formula
please solve
Click here to see answer by Mathematicians(84)

Question 282185: Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x. I need all possible answers and the work this was so confusing.
f(x) = 7x^2 - 2
Click here to see answer by dabanfield(803)

Question 282225: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x^2 - 12x + 34 = 0
Click here to see answer by Mathematicians(84)

Question 282231: use the quadratic formula to determine the x-intercept problem = f(x)=1/4x^2
Click here to see answer by oberobic(2304)

Question 282233: 3x^3+4x^2-32x=0
Click here to see answer by oberobic(2304)

Question 282242: solve the equation by finding square roots if necessary round to nearest
7x squared -8 = 20.
can you show me the steps?
Click here to see answer by rfer(16322)

Question 282311: 16x^2-4x+4=0
What is the alue of the discriminant?
Click here to see answer by xachu4u(10)

Question 282341: A group plans to share the cost equally for a $200,000 plane,the group wants to find 5 more people to join ,so that the cost will decrease $2,000 per person .How people are currently in the group.

Click here to see answer by mananth(16946)

Question 282408: Factor completely. Remember to look first for a common factor. Check by multiplying. If a polynomial is prime, state this.
27m^2 - 36 + 12
This is what I have got so far if I am heading in the right direction please let me know and what I do next if not help me figure this one out.
27m^2 - 36 + 12
=3(9x^2 - 12x + 4)
=3[(3x)^2 - 4*3 + 2^2]
That's all I got so far.
Click here to see answer by richwmiller(17219)

Question 282415: One hundred twenty pounds of weight is placed at one end of a 10ft lever and 25 pounds is place at the other end. How far from the 120 lb weight should the fulcrum be placed to have a balanced system?
Click here to see answer by dabanfield(803)

Question 282422: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
The product of two consecutive positive integers is 272. Find the integers.
Click here to see answer by richwmiller(17219)

Question 282317: 5th root of 21
rewrite with rational exponents
Click here to see answer by dabanfield(803)

Question 282449: Find the solutions of 4ix^2-4ix+5i=0 using the quadratic formula.
Click here to see answer by solver91311(24713)

Question 282516: The base of a triangle is 11 cm more than its height. The area is 90cm^2. What is the measure of the height?
Click here to see answer by checkley77(12844)

Question 282490: rewrite with positive exponents (3xy)^-8/9
Click here to see answer by user_dude2008(1862)

Question 282557: Please help me solve this equation r2-5r+6 it has a bar in between it,and both Rs or to the 2nd powers -
r2-4
Click here to see answer by user_dude2008(1862)

Question 282463: Find the real or imaginary solutions
w^2=-225
Click here to see answer by user_dude2008(1862)

Question 282469: Identify the degree of each term of the polynomial.
-9x^3+6x^2+9x+2
first term, second term, third term, fourth term
Click here to see answer by user_dude2008(1862)

Question 282540: i need help and a couple of things explained better if possible
this is what my textbook says:
By drawing a suitable graph, find the roots of these quadratic functions. Check each root by substitution:
this is what we have been told to find by our teacher
where does x�-x=0 cut the y-intercept
where it cuts the x-axis
locate the turning point (an axis of symmetry)
i dont know how to do any of it so there is nothing i can write to show what i have done so far ?
thanks if you get back to me x
Click here to see answer by richwmiller(17219)

Question 282494: f(x)=1/5(x+7)^2+3
what is the vertex?
Does it open up or down?
Click here to see answer by user_dude2008(1862)

Question 282571: Jack usually mows his lawn in 3 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together?
Simplify-type an integer, proper fraction, or mixed number.
Click here to see answer by solver91311(24713)

Question 282570: Not sure if this falls into the category of quadratics, but here's the question, if someone can check my calculations?
Problem: Find the solution set for the equation:
[4/(6x+1)]^(1/2) - x/(x-1)=0
My solution:
use sqrt (4/(6x+1)) - x/(x-1)=0
square both sides, get
4/(6x+1)-(x/(x-1)^2=0
Cross multiply to get:
4(x^2-2x+1)=x^2(6x+1)
Multiply and condense:
6x^3-3x^2+8x-4=0
Factor to:
(2x-1)(3x^2+4)=0
For 2x-1=0, get 1/2 for x
For 3x^2+4=0, no solution, since x has to be negative number, but squared only gives positive
Does this seem right?
Click here to see answer by jim_thompson5910(35256)

Question 282576: If the sides of a square are lengthened by 7cm, the area becomes . Find the length of a side of the original square.
The length of a side of the original square ____cm
Click here to see answer by richwmiller(17219)

Question 282574: For the following equation, state the value of the discriminant and then describe the nature of the solutions.

What is the value of the discriminant?
A) The equation has 2 imaginary solutions
B) the equation has 2 real solutions
C) The equation has 1 real solution
Click here to see answer by richwmiller(17219)

Question 282591: Use the quadratic formula to solve the equation.

Click here to see answer by jim_thompson5910(35256)

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