Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 722822: An architect is designung a building with a right triangle footprint. The hypotenuse of the triangle is 80 feet longer than one leg of the triangle and 40 feet longer than the other leg. Use Pythagorean Theorem to find the dimensions of the footprint of the building.
Click here to see answer by KMST(5328)

Question 722631: Could you please show me the steps to factoring and solving the problem below?
Also, could you please show me how to check my solution back into the original equation?
Could you please show me the final solutions as decimal approximations carried out to the third decimal place.
If possible and applicable, could you please show me how to incorporate the following four math vocabulary words into my steps?
-Quadratic formula
-Factoring
-Completing the square
-Discriminant
1. 2m^(2) - m - 15 = 0
Click here to see answer by mananth(16946)

Question 722944: Expand and factor the expression x(x−1)−30.
(b) Solve the equation x(x−1)=30. If there is more than one correct answer, enter your answers as a comma separated list. If there are no answers, enter NONE.
Click here to see answer by DrBeeee(684)

Question 723272: I don't understand how to solve this equation: -4x^2-24x+36=0 leaving your answer in radicals... I ended up with 24 plus/minus square root of 1152 over 8. but I don't know how to simplify it. Can you please help me?
Click here to see answer by Alan3354(69443)

Question 723242: x^2-3x+4
Click here to see answer by checkley79(3341)

Question 723390: how to determine the vertex and zeros of the equation y= 1/4(x+2)^2-5
Click here to see answer by stanbon(75887)

Question 723451: M^2-8m-37=-4
I'm not even sure how to start I think I am supposed to complete the square
^2 means the number is squared
Click here to see answer by mananth(16946)

Question 723461: n^2-20n+102=3
I believe this is completing the square
^2 means the number is square
Click here to see answer by richwmiller(17219)

Question 723487: Rectangle is 240 square inches. The length is 15 inches. What is the width?
Click here to see answer by ahmadsolehin(6)

Question 723515: An arrow shot vertically into the air from ground level with a crossbow reaches a maximum height of 324 feet after 4.5 seconds of flight. Let the quadratic function d(t) represent the distance above ground (in feet) t seconds after the arrow is released. (If air resistance is neglected, a quadratic model provides a good approximation for the flight of a projectile.)
(A) Find d(t)
(B) At what times (to two decimal places) will the arrow be 250 feet above the ground?

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

Question 723561: S solve the quadratic equation by completing the square 3r^2+2r-2=0
Click here to see answer by mananth(16946)

Question 723752: Factor the expression
4x^2-19x-30
Click here to see answer by stanbon(75887)

Question 723733: For what values of c do the equations y=x2+2x-3 and y=c have no point in common?
Click here to see answer by KMST(5328)

Question 723678: Convert the quadratic function into its standard form, identify the vertex,the x and y intercepts and graph the function and all its components. label all components on the graph
y=3xsquared + 2x-8 (i.e y=3^x2 +2x-8)
Click here to see answer by josgarithmetic(39613)

Question 723863: 5. Will this profit function have a maximum, if so, what is it?
To find the maximum, I will use the formula;
P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ≥ 0.

these are the numbers to use in this function
90 34419
80 33936
70 33451
60 32964
50 54975

Click here to see answer by stanbon(75887)

Question 724015: Please help me with these problems:
Finding the maximum y-value on the graph of y=f(x).
My problem is f(x)= -x^2+8x+7
Using quadratic formula to find any x-intercepts on graph of equation. My problem is y=x^2+6x-1.
and
To solve by completing the square what value should be added to each side of equation with problem x^2+16x=-4.
Thanking you in advance for your help.
Click here to see answer by stanbon(75887)

Question 724081: (2a+1)(a+3)+3=0
Click here to see answer by jsmallt9(3758)

Question 724161: Factorise
(2x+3y)^(2)(�5)(2x+3y)�14
Click here to see answer by Alan3354(69443)

Question 724223:
A company's costs, in millions of dollars, are given by the equation. C=x^2-3x-27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items?
I tried substitution 1,000 and 1,500 into the given equation but I was told that was wrong. I do not know where to begin with this problem. HELP PLEASE!!
Click here to see answer by checkley79(3341)

Question 724099: 6sin^2x-sinxcosx+2cos^2x=o
Click here to see answer by jsmallt9(3758)

Question 724302: In the formula h(t)= -16t^2+vt+s, what does the "-16" represent?
Click here to see answer by stanbon(75887)

Question 724434: An object's height, in meters, when thrown vertically from the ground at a velocity of 80m/s is given by the equation H=-4.9t^2+80t. Ignoring wind resistance, what is the height of the ball after 2 seconds? 3 seconds? 10 seconds?
In this problem I substituted the seconds in the given equation, but I was told that was incorrect....HELP PLEASE!!!
Click here to see answer by stanbon(75887)

Question 724451: An object's height, in meters, when thrown vertically from the ground at a velocity of 80m/s is given by the equation H=-4.9t^2+80t. Ignoring wind resistance, how many seconds will it take the object to return to the ground? in other words, when is H=0?
In this problem, I set the equation equal to 0 then I used the quadratic formula but that was wrong....HELP PLEASE!!!
Click here to see answer by jsmallt9(3758)

Question 724480: A company's costs, in millions of dollars, are given by the equation, C=x^2-3x-27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? and 1,500 items are sold?
I tried substituting 1,000 and 1,500 in the given equation but I was told that was wrong!!! HELP!!
Click here to see answer by jsmallt9(3758)

Question 724427: 1) (x-y-1)^2 + (x+y-7)^2=0 find x+y
Click here to see answer by jsmallt9(3758)

Question 724601: A company's costs, in millions of dollars, are given by the equation, C=x^2-3x-27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? and 1,500 items are sold?
So far I have used 1 and 1.5 and substituted into the equation but I am getting negative numbers is that correct?
Click here to see answer by stanbon(75887)

Question 725038: A company's costs, in millions of dollars, are given by the equation, C=x^2-3x-27, where x is the number of items sold, in thousands. How many items must be sold for the costs to be zero?

Click here to see answer by lwsshak3(11628)

Question 725129: Is this a quadratic equation? there's only one 'x'. How do i solve this problem? 2(x-3)^2-50=0.
Click here to see answer by Alan3354(69443)

Question 725129: Is this a quadratic equation? there's only one 'x'. How do i solve this problem? 2(x-3)^2-50=0.
Click here to see answer by josmiceli(19441)

Question 725237: x^2-x=6
Click here to see answer by erika514(39)

Question 725361: The height of a projectile, over time, launched from an initial height of 50 feet can be modeled by the quadratic function, h(x) = -16t2 + 96t + 50, where h(x) is the height of the projectile and t is time, in seconds. If the maximum height reached by the projectile is 344 feet, how long does it take for the projectile to reach its maximum height?
Thanks!
Click here to see answer by Alan3354(69443)

Question 725483: Ms. S. has a rectangular flower garden that measures 15 by 20 meters. She wishes to build a concrete walk of uniform width around the garden. Her budget for the project allows her to buy enough concrete to cover an area of 74 square meters. How wide can she build the walk?
Click here to see answer by mananth(16946)

Question 725517: x^2 - 4x = -3
Click here to see answer by mananth(16946)

Question 725545: I need step by step answers please for this one H=-16t^2+25
Click here to see answer by jsmallt9(3758)

Question 725781: how would you solve x^2+3x-9
Click here to see answer by Alan3354(69443)

Question 725980: Find the equation of the quadratic function whose graph passes through the point (-1,3) and has vertex (2,-4) .
?
Click here to see answer by josmiceli(19441)

Question 725933: When solving the quadratic equation x2 - 8x + 12 = 0, the solutions are x = 2 and x = 6. If you examine the quadratic function y = x2 - 8x +12, how can you use the solution of the corresponding quadratic equation to determine the x-intercepts of the quadratic function?
Click here to see answer by KMST(5328)

Question 726129: simplify 8(x-5)-x+2
Click here to see answer by checkley79(3341)

Question 726264: How do you write a math problem in Standard form?
Click here to see answer by stanbon(75887)

Question 726375: x� +x+12=0
Click here to see answer by Adittadas4@gmail.com(2)

Question 726602: I need help sloving this problem -5x�^2-4x-11= if x=-1
Click here to see answer by jim_thompson5910(35256)

Question 726659: the sydney harbour bridge has its main steel arch in the shape of a parabola. The longest vertical support, situated 135m from its origin is 182.25m high. The road is situated 50m above the base of the pylon. There are 19 vertical steel cables equally spaced between the road and the arch. Fins the equation of the parabolic arch in the form y=ax2 + bx
Click here to see answer by DrBeeee(684)

Question 726700: Two pipes can fill up water tank in 6 hours and 40 minutes. Find the time each will take to fill the tank if one of the two pipes can fill it is three hours less than the other.
Click here to see answer by checkley79(3341)

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