Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 177827: Quadratic Equations
The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the legs is 28cm. Find the length of each leg of the triangle.

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Question 177834: Quadratic Equations
Write a quadratic equation with the given roots.
a)5, and -2
b)-3 over 4, and -2 over 3

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Question 177834: Quadratic Equations
Write a quadratic equation with the given roots.
a)5, and -2
b)-3 over 4, and -2 over 3

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Question 177832: Quadratic Equations
20) The perimeter of a rectangle is 8m and its area is 2m^2. Find the length and width of the rectangle to the nearest tenth of a metre.
Thank you

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Question 177774: Analytic Geometry
On a street map, the coordinates of the two fire stations in a town are A(10, 63) and B(87, 30). A neighbour reports smoke coming from the kitchen of a house at C(41,18).
a) Which fire station is closer to this house?
b) Describe how to use geometry software to asnwer part a).

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Question 177861: If a pro-basketball player has a vertical leap of 35 in, what is his hang time? Use the hang time function of V=48T^2.
Hang time in seconds.
Please help, thank you.

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Question 177862: Jeff can mow his lawn in 4 hours time. His sister can mow the same lawn in 3 hours. How much time would it take them if they mowed it together?
Could you please help with this one? Thank you.

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Question 177862: Jeff can mow his lawn in 4 hours time. His sister can mow the same lawn in 3 hours. How much time would it take them if they mowed it together?
Could you please help with this one? Thank you.

Click here to see answer by nerdybill(7384) About Me 

Question 177806: Quadratic Relations
A basketball shot is taken from a horizontal distance of 5m from the hoop. The height of the ball can be modelled by the relation h=-7.3t^2+8.25t+2.1, where h is the height, in metres, and t is the time, in seconds, since the ball was released.
a) From what height was the ball released?
b) What was the maximum height reached by the ball?
c) If the ball reached the hoop in 1 s, what was the height of the hoop?

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Question 177876: Here is one that I am struggling with the directions.
Find the polynomial for the perimeter and the area. Do not factor.
there is a rectangle with the length labeled z+5 and the width is labeled z.
I think the perimeter would be 2z+2(z+5) and the area may be z(z+5). Thanks

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

Question 177880: Solve. s^2+3s-54+0
I think I use the quadratic equation to solve this. I did and got the answers of -3Plus or minus the square root of -207 all divided by 2. Is this right? Thank you for your help.

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Question 177791: Analytic geometry
Determine the shortest distance from the point H(5,2) to the line through points J(-6,4) and K(-2,-4).

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Question 177883: solve.
x^2+18x-4=0. Do I use the quadratic equation or do I factor this to solve it?
Please and thank you for your help

Click here to see answer by Alan3354(69443) About Me 

Question 177776: Use analytic geometry to classify the quadrilateral with vertices D(10,0), E(2,4), F(-8,-6), and G(6,-8). Explain your reasoning and show all your work.
Click here to see answer by Fombitz(32388) About Me 

Question 177874: Please help. Solve for x, and simplify answers. 4x(x-2)-5x(x-1)=2.
I have the problem simplified to -x^2-8x+3=0 (I think this is correct) then I think I use the quadratic equation and I got: 8+square root of 76 divided by -2 and 8-square root of 76 divided by -2.
Do I divide by two?

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Question 177884: Please help.
Factor out the GCF.
7x^7-49x^6+56x^5=0

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Question 177853: Solve by completing the square. Show your work.[please]

29. 2x2 - 6x + 1 = 0
30. -x2 - 8x + 5 = 0

31. 9x2 - 18x - 1 = 0
32. -4x2 + 8x - 3 = 0

Click here to see answer by jim_thompson5910(35256) About Me 
Question 177853: Solve by completing the square. Show your work.[please]

29. 2x2 - 6x + 1 = 0
30. -x2 - 8x + 5 = 0

31. 9x2 - 18x - 1 = 0
32. -4x2 + 8x - 3 = 0

Click here to see answer by gonzo(654) About Me 

Question 177764: Linear System
A boat took 5 h to travel 60km up a river, against the current. The return trip took 3 h. Find the speed of the boat in still water and the speed of the current.

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Question 177756: Linear System
Solve each linear system using the method of substitution.
a) y=6-3x
y=2x+1
b) 5x-y=4
3x+y=4

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Question 177918: Evaluate the discriminant of each equation. How many real and imaginary
solutions does each have?

37. x2 + 5x + 6 = 0
38. 3x2 - 4x + 3 = 0



39. -2x2 - 5x + 4 = 0
40. 16x2 - 8x + 1 = 0

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Question 177932: What is the vertex of the parabola given by y=x^2+4x+3?
Click here to see answer by EMStelley(208) About Me 

Question 177941: please solve each matriz..
1. [3 4] [3]
[-1 -1]x=[2]


2. [6 2] [8 1]
[-1 4]-x [1 3]



3. x+[1 3 6] [8 1 0]
[-1 2 1]= [14 3 -1]


4. [-3 -2] [8 -1]
[1 1] x=[6 0]


5. 4x+3 [3 2] [10 8]
[1 -2]= [5 -2]


6. 2x=1/4[-6 2]
[8 -8]

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Question 177945: A quadratic function has a vertex(-3,0) and opens down. What is the nature of the roots?
a) imaginary and equal
b) imaginary and unequal
c) real and equal
d) real and unequal

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Question 177945: A quadratic function has a vertex(-3,0) and opens down. What is the nature of the roots?
a) imaginary and equal
b) imaginary and unequal
c) real and equal
d) real and unequal

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Question 177943: What is the general form of : y=-3(x-2)^2 -4
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Question 177935: Evaluate the discriminant of each equation. How many real and imaginary
solutions does each have?(please help me with this.. i realy need it done in like a very fast time.. please please))
37. x2 + 5x + 6 = 0
38. 3x2 - 4x + 3 = 0
39. -2x2 - 5x + 4 = 0
40. 16x2 - 8x + 1 = 0

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Question 177930: Find the transformational form of the quadratic function having vertex (-3,4) and x-intercept (-6,0).
Click here to see answer by Mathtut(3670) About Me 

Question 177927: The Smith's have 160 meters of fencing available to build a rectangular garden. One side of the garden touches a side of the house and doesn't need any bordering. Algebraically find the dimensions that will give the maximum area.
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Question 177922: A rectangular pool measures 8m by 4m. A deck of unifrom width is to be built all the way around the pool such that the total area of the pool and deck will be 96m^2. Set up and solve a quadratic equation to determine the width of the deck.
Click here to see answer by Mathtut(3670) About Me 

Question 177929: A baseball is hit and follows a parabolic path described by the function y=-3x^2+18x+1, where x represents the time in seconds after the ball is hit and y represents the ball's height in meters from the ground. Algebraically determine the maximum height and the time at which the ball reaches its maximum height.
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Question 177920: Algebraically find the EXACT ROOTS in simplest form for: x/-7=(x+1)/(x-11)
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Question 178012: Linear System
Use graphing to find the point of intersection of each pair of lines.
Thank you sooo much

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Question 178029: Linear System
Use the graphing to find the point of intersection of each pair of lines.
b) y=1/2x-4
y=2x-1
f) x+y-4=0
5x-y-8=0
Can you pleaseeeeee do both of them because i have to do a, c, d, e, and g for that i need to understand b and f okay thank you sooo much

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Question 178030: Linear System
Solve each linear system using the method of substitution.
c) 5x-y=4
3x+y=4
Thank you sooo much

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Question 177924: A paper airplane follows a parabolic path with h=-1/4t^2+t+3, where h is the height in meters, and t is the time in seconds. Algebraically determine how long it takes for the paper airplane to hit the ground.
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Question 178074: Analytic geometry
11) Determine the shortest distance from the origin to the line represented by y=1/2x-2. (PLEASE)
Thank you very much

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Question 178080: Quadratic relations
7) Sketch a graph of each quadratic. Label the x-intercepts and the vertex.
b) y=2(x-3)(x+1) pleaseeeeeeeeeeee
thank you very muchhhhhhhhhhhh

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Question 178078: Quadratic Relations
39) The vertex of a parabola is (-2,-4). One x-intercept is 7. What is the other x-intercept? (PLEASE)
Thank you very muchhhhhhhhhhhh

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Question 178100: 1. If tn=2n-3, for what value of 'n'is tn=5?
Is it -1,1,4 OR 7??????? I think the answer is 4 or 7????????
2. Which sequence represents an exponential function????
a) {1,6,11,16,21,...}
b) {16,8,4,2,1,...}
c) {2,8,18,32,50,...}
d) {1,8,27,64,125,...} I think it is (b)???
3. Which function represents a geometric sequence?
a) {3*4,3*4^2, 3*4^3,3*4^4,...}
b) {3+4,3+4+4,3+4+4+4,...}
c) {3*4,3*5,3*6,3*7,...}
d) {3+4,3+4^2,3+4^3,...}

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Question 178100: 1. If tn=2n-3, for what value of 'n'is tn=5?
Is it -1,1,4 OR 7??????? I think the answer is 4 or 7????????
2. Which sequence represents an exponential function????
a) {1,6,11,16,21,...}
b) {16,8,4,2,1,...}
c) {2,8,18,32,50,...}
d) {1,8,27,64,125,...} I think it is (b)???
3. Which function represents a geometric sequence?
a) {3*4,3*4^2, 3*4^3,3*4^4,...}
b) {3+4,3+4+4,3+4+4+4,...}
c) {3*4,3*5,3*6,3*7,...}
d) {3+4,3+4^2,3+4^3,...}

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Question 178088: Quadratic Equations
Write a quadratic equation with the given roots.
b) -3/4, -2/3 Pleaseeeeeee
Thanks a lottttttt

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Question 178105: solve for x: cx=a^2+1

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Question 178103: Which represents the range for -(y+3)=(x-4)^2 :
a){y such that y is less than or equal to -3,y belongs to a set of real numbers}
b){y such that y is greater than or equal to 4, y belongs to a set of real numbers}
c){y such that y is less than or equal to 3, y belongs to a set of real numbers}
d){y such that y is less than or equal to -4, y belongs to a set of real numbers}
I hope someone canhelp me, I always have trouble with these:(

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Question 178031: Linear System
c) 4k+3h=12
4k-h=4

Thanks a lot

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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