Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 1208234: what is the height of the coin when it is tossed? -16x^2+96x+112
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Question 1208234: what is the height of the coin when it is tossed? -16x^2+96x+112
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Question 1208274: After reducing by an equal amount the length and width of a rectangle which were originally 8cm and 5cm respectively.The area of the new rectangle is 18cm square.Find the dimensions of the rectangle

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Question 1208346: The daily cost to a printer is modeled by the function C(x)=3x+1800 where C(x) is the total daily cost and x is the number of copies printed. Find C(4000), and interpret its meaning.
C(4000)=
This value represents
The number of copies manufactured when the daily cost is 4000
The product of the daily cost and the number of copies
The daily cost when 4000 copies are printed
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Question 1208477: how to evaluate 7 to the power of 2 - 3 to the power of 2 + 4

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Question 1208477: how to evaluate 7 to the power of 2 - 3 to the power of 2 + 4

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Question 1208477: how to evaluate 7 to the power of 2 - 3 to the power of 2 + 4

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Question 1208624: The vertices of △ABC are A(4, 4), B(-6, 2), and C(2, 0). Find an equation in slope y-intercept form for the median from vertex A.
Click here to see answer by math_tutor2020(3816) About Me 
Question 1208728: Solve by completing the square.

x^2 + (2/3)x - 1/3 = 0

Let me see.
x^2 + (2\3)x = 1/3
[(2/3) ÷ 2]^2 = 1/9
x^2 + (2/3)x + 1/9 = 1/3 + 1/9
x^2 + (2/3)x + 1/9 = 4/9
(x + 1/3) (x + 1/3) = 4/9
(x + 1/3)^2 = 4/9
Taking the square square on both sides, I get
x + 1/3 = 2/3 & x + 1/3 = -2/3
Now solve for x by setting x + 1/3 to equal 2/3 and then -2/3.
x + 1/3 = 2/3
x = 2/3 - 1/3
x = 1/3
And
x + 1/3 = -2/3
x = -2/3 - 1/3
x = -3/3
x = -1
You say?
Click here to see answer by timofer(104) About Me 
Question 1208728: Solve by completing the square.

x^2 + (2/3)x - 1/3 = 0

Let me see.
x^2 + (2\3)x = 1/3
[(2/3) ÷ 2]^2 = 1/9
x^2 + (2/3)x + 1/9 = 1/3 + 1/9
x^2 + (2/3)x + 1/9 = 4/9
(x + 1/3) (x + 1/3) = 4/9
(x + 1/3)^2 = 4/9
Taking the square square on both sides, I get
x + 1/3 = 2/3 & x + 1/3 = -2/3
Now solve for x by setting x + 1/3 to equal 2/3 and then -2/3.
x + 1/3 = 2/3
x = 2/3 - 1/3
x = 1/3
And
x + 1/3 = -2/3
x = -2/3 - 1/3
x = -3/3
x = -1
You say?
Click here to see answer by MathTherapy(10551) About Me 
Question 1208761: Dear Genii
I have what I fear is a rather silly question. The other day I came across this question on a GCSE maths paper:
x-y = k
x^2+y^2-9=0
These simultaneous equations have exactly one set of solutions.
Show that k = +/_3root2 (I don't know hoe to put the square root sign in.
I have never come across questions like this before and I have no idea what this method/technique is called; I have no idea why it is used and I have no idea about how to solve such questions. I would very much appreciate it if someone could tell me what this technique is called, why it is used and where I might find instructions about how to use it.
Marcus Clayson
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Question 1208779:
Find k such that the equation x^2 - kx + 4 = 0 has a repeated real solution.



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Question 1208778: Show that the product of the roots of a quadratic equation is c/a.
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Question 1208778: Show that the product of the roots of a quadratic equation is c/a.
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Question 1208778: Show that the product of the roots of a quadratic equation is c/a.
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Question 1208780: Show that the real solutions of the equation ax^2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx^2 + bx + a = 0. Assume that b^2 - 4ac is greater than or equal to 0.

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Question 1208801: Let c be a real number. What is the maximum value of c such that the graph of the parabola y = 1/5 x^2 has at most one point of intersection with the line y = cx?
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Question 1208802: Find the value of $a$ for which there is exactly one real value of $x$ such that $f(x) = a,$ where
f(x) = x^2 + 4x - 31
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Question 1208864: a baseball team held a fundraising car wash. They charged $4 for each car and $6 for each truck. They washed 50 cars and trucks and collected $210. How many of each type of vehicle did they wash?
Click here to see answer by josgarithmetic(39617) About Me 
Question 1208864: a baseball team held a fundraising car wash. They charged $4 for each car and $6 for each truck. They washed 50 cars and trucks and collected $210. How many of each type of vehicle did they wash?
Click here to see answer by timofer(104) About Me 
Question 1208864: a baseball team held a fundraising car wash. They charged $4 for each car and $6 for each truck. They washed 50 cars and trucks and collected $210. How many of each type of vehicle did they wash?
Click here to see answer by greenestamps(13198) About Me 
Question 1208902: Find the quadratic formula online. Solve the formula for c.
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Question 1208902: Find the quadratic formula online. Solve the formula for c.
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Question 1208902: Find the quadratic formula online. Solve the formula for c.
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Question 1208922: If 6k^2 + k = 2 and k > 0, find the value of k.
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Question 1208922: If 6k^2 + k = 2 and k > 0, find the value of k.
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Question 1208922: If 6k^2 + k = 2 and k > 0, find the value of k.
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Question 1209023: The minimum cost of maintaining an overhead crane depends on the number of hours the crane is in operation. The cost is given by the relation C=6t^2 - 36t +154, where C represents the cost in hundreds of dollars and t represents the time in hours that the crane has been operated. a) What is the minimum cost of maintaining the crane? (b) Find the number of hours the crane operates for this minimum maintenance cost.
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Question 1209024: The minimum cost of maintaining an overhead crane depends on the number of hours the crane is in operation. The cost is given by the relation C=6t^2 - 36t +154, where C represents the cost in hundreds of dollars and t represents the time in hours that the crane has been operated. a) What is the minimum cost of maintaining the crane? (b) Find the number of hours the crane operates for this minimum maintenance cost.
THANKS
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Question 1209039: a rectangular field is to be divided up into 3 equal sections, enclosed by 160m of fencing. the field is beside a barn, and the fencing will attach to the wall of the barn. the wall of the barn requires no fencing. determine the dimensions of the entire rectangular field that will result in the maximum area
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Question 1209108: I'm thinking of a number. My number has the property that its square is equal to 270 more than five times the number. Enter all numbers that have this property.
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Question 1209117: One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
-x^2 + 18x + 81
3x^2 - 6x + 9
8x^2 - 32x + 32
25x^2 - 30x - 9
x^2 - 14x + 196
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Question 1209117: One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
-x^2 + 18x + 81
3x^2 - 6x + 9
8x^2 - 32x + 32
25x^2 - 30x - 9
x^2 - 14x + 196
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Question 1209114: A box has a certain length, width, and height. The length of the box is equal to twice its width, as well as equal to 8 less than its height. If the total surface area of the box is 480, then what is the height of the box?
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Question 1209115: Wilma and Greg were trying to solve the quadratic equation
x^2 + bx + c = 0.
Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 5 and 15. Greg wrote down the wrong value of c (but his value of b was correct), and found the roots to be -5 and -7. What are the actual roots of x^2 + bx + c = 0?
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Question 1209115: Wilma and Greg were trying to solve the quadratic equation
x^2 + bx + c = 0.
Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 5 and 15. Greg wrote down the wrong value of c (but his value of b was correct), and found the roots to be -5 and -7. What are the actual roots of x^2 + bx + c = 0?
Click here to see answer by ikleyn(52778) About Me 
Question 1209123: Let a and b be the roots of x^2 + 7x - 4 = 0. Find (a + 3)/(b + 3) + (b + 3)/(a + 3).
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Question 1209123: Let a and b be the roots of x^2 + 7x - 4 = 0. Find (a + 3)/(b + 3) + (b + 3)/(a + 3).
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Question 1209150: Find all real values of s such that x^2 + sx + 144 - 6x + 3x^2 is the square of a binomial.
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Question 1209149: For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial?
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Question 1209143: y=4x 8x−4y=-40

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Question 1209148: Find all real values of t that satisfy the equation
(t^2 - 13)^2 = 144 + 8t^2
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Question 1209147: Solve for c in (c - 7)^2 = 81 + 20c.
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Question 1209154: An acorn falls from a tree that is 75 feet tall. What is the height of the acorn 1 second after it was dropped? Use the vertical motion model, h=-16t^2 + 75 where t is the time in seconds and h is the height in feet.
Height:_ feet
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Question 1209169: For what real values of k does the quadratic 12x^2 + kx + 27 = 0 have nonreal roots? Enter your answer as an interval.
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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