Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 1177487: If a^(1/2)-a^(-1/2)=1, show that a+a^-1=3
Click here to see answer by MathTherapy(10549)

Question 1177572: The equation x²+ px +4 = 0, where p and q are constants, has roots -1 and 4. a) Find the values of p and q.
b) Using these values of p and q. find the value of r, where r is a constant, and the equation x² + px + r=0 has equal roots.
Click here to see answer by ikleyn(52748)

Question 1177575: The quadratic equation x² + kx + 36=0 has
two different real roots. Find the set of possible values of k.
Click here to see answer by ikleyn(52748)

Question 1177738: Mr Lim will pay $ y to Michael and $80 less than Michael to Jack monthly for x months. The total amount will be received by Michael in x months is $2400.
In the next coming x months, each of them are given $20 more than the money they receive in the previous x months monthly. Given that the total amount will be received by both of them together in the next x months is increased by 12.5% compared to the total amount will be received by both of them in the previous x months. Calculate the values of x and y.
Click here to see answer by Theo(13342)

Question 1177750: Two pipes can fill a tank in 50 minutes if both are turned on. If only one is used, it would take 20 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank?
Click here to see answer by josgarithmetic(39613)

Question 1177772: At a certain time of day, a tree that is x meters tall casts a shadow that is x−28 meters long. If the distance from the top of the tree to the end of the shadow is x+8 meters long, what is the height, x, of the tree?
Click here to see answer by josgarithmetic(39613)

Question 1177799: A video camera is placed on a 120 m tall building. The angle of depression from the camera to the base of another building is 36o. The angle of elevation from the camera to the top of the same building is 47o.
How far apart are the two buildings? Round your answer to the nearest meter. Show work.

How tall is the building viewed by the camera? Round your answer to the nearest meter. Show work.

Click here to see answer by mananth(16946)

Question 1177833: A landscape architect is planning a circular flower
bed that will be surrounded by a ring of paving
stones, 25 cm wide. The area of the ring of paving
stones will be half the area of the flower bed.
Determine the radius of the flower bed, to the
nearest centimetre.
Click here to see answer by mananth(16946)

Question 1177873: Solve for x: x^2+xp-p^2

answer is ((-1/2)p)(-1+√5). (ignoring the negative value)

Click here to see answer by ewatrrr(24785)

Question 1177865: Bob is renting an apartment so he can get out on his own! He's excited he gets to stay in his own place! He's even keeping it clean. Bob has $4,700 saved up when he finds the apartment. The apartment complex asks Bob to make a deposit before his first month's rent. Use the table and the graph to figure out the monthly rent along with some other important information about Bob.
Interpret the table and the graph so that you can answer the following true or false statements.

True False
Bob's deposit is $500. - Bob's deposit is $500. - Bob's deposit is $500.
Bob pays $500 per month for rent. - Bob pays $500 per month for rent. - Bob pays $500 per month for rent.
After month eight Bob has $400 left. - After month eight Bob has $400 left. - After month eight Bob has $400 left.
Bob's money will last long enough for him to pay for nine months of rent. - Bob's money will last long enough for him to pay for nine months of rent. - Bob's money will last long enough for him to pay for nine months of rent.
The equation that models Bob's Apartment Money is y=−500x+4,400. - The equation that models Bob's Apartment Money is y is equal to negative 500 x plus 4 comma 400. - The equation that models Bob's Apartment Money is y is equal to negative 500 x plus 4 comma 400.
Bob has $3,400 after paying his third month's rent. - Bob has $3,400 after paying his third month's rent. - Bob has $3,400 after paying his third month's rent.
The equation that models Bob's Apartment Money is linear. - The equation that models Bob's Apartment Money is linear. - The equation that models Bob's Apartment Money is linear.
The y-intercept of the graph is $4700. - The y-intercept of the graph is $4700. - The y-intercept of the graph is $4700.
The x-intercept is a little before nine months - The x-intercept is a little before nine months - The x-intercept is a little before nine months
x
(# of months)
y
(money left)
Before Bob found the apartment $4,700
0 (paid for the deposit) $4,400
1 $3,900
2 $3,400
3 $2,900
4 $2,400
5 $1,900
6 $1,400
7 $900
8 $400
9 - $100
10 - $600
Click here to see answer by ikleyn(52748)

Question 1178157: Write a quadratic equation in the form x^2+bx+c=0 that has the roots -7 and 10
Click here to see answer by MathLover1(20849)

Question 1178163: The length of a rectangle is 3m less than twice the width, and the area of the rectangle is 14m^2 . Find the dimensions of the rectangle.
Click here to see answer by mananth(16946)

Question 1178173: Solve the following system of equations.
2 x+ 3 y = 4
5 x - 5 y = -15
Answer: (x,y) =
Click here to see answer by mananth(16946)

Question 1178173: Solve the following system of equations.
2 x+ 3 y = 4
5 x - 5 y = -15
Answer: (x,y) =
Click here to see answer by ikleyn(52748)

Question 1178173: Solve the following system of equations.
2 x+ 3 y = 4
5 x - 5 y = -15
Answer: (x,y) =
Click here to see answer by MathLover1(20849)

Question 1178175: Solve the following system of equations.
2 x - 5 y = -13
3 x+ 2 y = 9
Answer: (x, y) =
Click here to see answer by MathLover1(20849)

Question 1178175: Solve the following system of equations.
2 x - 5 y = -13
3 x+ 2 y = 9
Answer: (x, y) =
Click here to see answer by greenestamps(13195)

Question 1178175: Solve the following system of equations.
2 x - 5 y = -13
3 x+ 2 y = 9
Answer: (x, y) =
Click here to see answer by ikleyn(52748)

Question 1178174: Solve the following system of equations.
2 x - 5 y = -13
3 x+ 2 y = 9
Answer: (x, y) =
Click here to see answer by MathLover1(20849)

Question 1178174: Solve the following system of equations.
2 x - 5 y = -13
3 x+ 2 y = 9
Answer: (x, y) =
Click here to see answer by ikleyn(52748)

Question 1178178: Solve the following system of equations.
5 x - 4 y = 1
-10 x + 8 y = -2
Please write your solution(s) in the ordered-pair form.
If there is no solution, please type "None".
If there are infinitely many solutions, then type "Infinitely Many Solutions".
Click here to see answer by ikleyn(52748)

Question 1178241: Solve the following system of equations.
-3 x+ 3 y = -2
9 x - 9 y = -6
Please write your solution(s) in the ordered-pair form.
If there is no solution, please type "None".
If there are infinitely many solutions, then type "Infinitely Many Solutions".
Answer: (x,y) =
Click here to see answer by ikleyn(52748)

Question 1178249: Solve the following system of equations.
\begin{array}{rl}
\frac{3}{4} x + \frac{-1}{6} y & = \frac{1}{2} \\
\\
\frac{-1}{4} x + \frac{-1}{2} y & = 2
\end{array}
Click here to see answer by ikleyn(52748)

Question 1178185: b Expand f(x) = (x − α) (x − β) and show that Δ = (α − β )^2
Hence show that the zeroes are x = α and x = β (as expected) and that the vertex is
(α + β)/2, −((α − β)/2)^2).
Click here to see answer by greenestamps(13195)

Question 1178634: A ball is thrown straight up from a rooftop 432 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down. The graph of the formula is shown. Determine when the ball's height will be 378 feet and identify the solution as a point on the graph.
h=-16t^2+30t+432

Click here to see answer by MathLover1(20849)

Question 1178727: Add: ( 7a^{6}b^{2}+3a^{4}b^{4}+2 ) + ( -2a^{6}b^{2}+2a^{4}b^{4}-5 )

Click here to see answer by MathLover1(20849)

Question 1178832: Two companies working together can clear a parcel of land in 18 hours. Working alone, it would take Company A 10 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round your answer to the nearest tenth.)
Click here to see answer by greenestamps(13195)

Question 1178877: the height of a ball thrown upward after a given amount of time is h = - 4.9t ^ 2 + 29.4t + 1 where h represents the height of the ball in metres , and t represents the time elapsed since the ball has been thrown . Determine the maximum height of the ball and at what time this occurs a) What is the maximum height reached by the ball? b ) How long is the ball above a height of 40 m ? c) When does the ball hit the ground ?
Click here to see answer by Solver92311(821)

Question 1178898: Grade 10- The height of a ball thrown upward after a given amount of time is h = - 4.9t ^ 2 + 29.4t + 1 where h represents the height of the ball in metres , and t represents the time elapsed since the ball has been thrown . Determine the maximum height of the ball and at what time this occurs. What is the maximum height reached by the ball? How long is the ball above a height of 40 m ? When does the ball hit the ground?
Click here to see answer by Boreal(15235)

Question 1178899: Grade 10 solve using the quadratic formula- The height of a ball thrown upward after a given amount of time is h = - 4.9t ^ 2 + 29.4t + 1 where h represents the height of the ball in metres , and t represents the time elapsed since the ball has been thrown . Determine the maximum height of the ball and at what time this occurs. What is the maximum height reached by the ball? How long is the ball above a height of 40 m ? When does the ball hit the ground?
Click here to see answer by Solver92311(821)

Question 1178958: Trying to solve this question Quadratic Equation word problem.
A rectangle is 2 meters longer than it is wide. If the area of the rectangle is 35 square meters what is the width?
Click here to see answer by mananth(16946)

Question 1179141: An aircraft flew a distance of 3800 Km from Singapore to Perth in Australia at an average speed of v Km/h.
(a) Write down an expression in terms of v, for the time taken in hours for the journey.
The aircraft returned by the same route at anaverage speed of (v+50) Km/h.
(b) Write down an expression in terms of x, for the time taken in hours for the return journey.
(c) Given that the difference in time between the two journeys is 20 minutes, form an equation in v and show that it reduces to V²+50v-570000=0
Click here to see answer by mananth(16946)

Question 1179148: the distance between London and New York is 320 Km. A train takes x hours to travel between London and New York.
(a) Write down an expression in terms of x, for the average speed of the train [1]
(b) A car takes 2 ½ hours longer than a train to travel between London and New York. The average speed of the train is 80 Km/h greater than the average speed of the car. Form an equation in x and show that it simplifies to

Click here to see answer by josgarithmetic(39613)

Question 1179215: A company has a total of 228 employees in the marketing and sales offices. For every five people employed in marketing, there are fourteen people employed in sales. How many people in the office work in marketing? How many people in the office work in sales?
Click here to see answer by ikleyn(52748)

Question 1179219: Write an algebraic equation for the following problem and then solve it.
Princess Margaret hospital received a shipment of 13-milligram doses of a medicine. Each 13-milligram package was repacked into two smaller doses of unequal size and labeled packet A and packet B. The hospital then used 19 doses of packet A and 17 doses of packet B in one week. The hospital used a total of 243 milligrams of the medicine during that week.
How many milligrams of the medicine are contained in each A packet? In each B packet?
Click here to see answer by MathLover1(20849)

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