Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 204167: One principle used by the ancient
Greeks to get shapes that are pleasing to the eye in art
and architecture was the Golden Rectangle. If a square
is removed from one end of a Golden Rectangle, as shown
in the figure, the sides of the remaining rectangle are
proportional to the original rectangle. So the length
and width of the original rectangle satisfy
L/W = W/L-W
An artist wants her painting to be in the
shape of a golden rectangle. If the length of the painting is
36 inches, then what should be the width?
So far the only thing I have is 36/w = w/36-w. I can't find an example in my book that looks like this equation. I am missing a step somewhere.
Click here to see answer by scott8148(6628)   |
Question 204189: 1) The sum of the squares of two consecutive integers is 613. What are the integers?
Let x be one integer. Therefore x +1 is the next integer.
x^2+(x+1)^2= 613
2)The length of a rectangle is four more than the width. If the area of the rectangle is 621 m2, find the width and length of the rectangle.
Let w be the width. Therefore w + 4 is the length.
W(w +4) = 621
Click here to see answer by RAY100(1637) |
Question 204189: 1) The sum of the squares of two consecutive integers is 613. What are the integers?
Let x be one integer. Therefore x +1 is the next integer.
x^2+(x+1)^2= 613
2)The length of a rectangle is four more than the width. If the area of the rectangle is 621 m2, find the width and length of the rectangle.
Let w be the width. Therefore w + 4 is the length.
W(w +4) = 621
Click here to see answer by Theo(3472)  |
Question 204190: hi these question are from a worksheet....plzz kindly help
1) A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165m². What is the width of the flower bed?
Let x be the width of the flowerbed
(8+2x)(4+2x)=165
2) Can x (x – 5) = 0 be solved by dividing both sides of the equation by x?
Explain your answer.
3)Write a quadratic equation whose roots are 5 and –3.
Click here to see answer by Earlsdon(6288) |
Question 204283: Open-Top Box: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and foldiing up the ssides. If the area of the base is to be 80 square inches, then what size square should be cute from each corner
Click here to see answer by solver91311(16897)  |
Question 204338: Form each of the following:
1. a linear equation in one variable
2. a linear equation in two variaables
3. a quadratic equation
4. a polynomial of three terms
5. an exponential function
6. a logarithmic function
Click here to see answer by stanbon(57415) |
Question 204443: hi can you plzz help me with this question...thanks!
The path of a basketball shot can be modeled by the equation h = -0.09d² + 0.9d + 2 where h is the height of the basketball, in metres, and d is the horizontal distance of the ball from the player, in metres.
a) What is the maximum height reached by the ball?
b) What is the horizontal distance of the ball from the player when it reaches its maximum height?
c) How far from the floor is the ball when the player releases it?
Click here to see answer by Earlsdon(6288) |
Question 204501: I would like to know if I did these questions right.
For the first one I have this:
Do exponential functions only model phenomena that grow, or can they also model phenomena that decay?
Explain what is different in the form of the function in each case.
Yes they also model decay, for example you can use them to model the decay of radioactivity. The only difference is that there will be a negative index.
Example of function of growth: y = ae^(kt)
Example of function of decay: y = ae^(-kt)
And for the second one I have:
A cell divides into two identical copies every 4 minutes. How many cells will exist after 5 hours?
f(t) = 2^(t/4)
after 5 hours: 5 * 60 = 300
f(t) = 2^(300/4)
f(t) = 2^75
f(t) = 3.78(10^22)
Are these correct and if not can you please explain them to me
Click here to see answer by alicealc(281) |
Question 204658: hi, I was hoping you can help me on this:
A rectangular lawn measures 8m by 6m. The owner wants to get a uniform border of trees along two adjacent sides of the lawn. If the tress cover an area of 8m^2, how wide is the border?
Click here to see answer by ichudov(499)  |
Question 204664: Hi, I was hoping you can help me on this:
The perimeter of a professional NBA basketball court is 300 feet. If the length of the court is two feet more than triple the width, find the length and the width of the blocked off court.
Click here to see answer by Earlsdon(6288) |
Question 204660: Can you help me solve this word problem: 1) A house owner wants to build a swimming pool in his backyard. The dimensions of the pool he wants to build is 60m by 40m. If the area of his backyard is only 40m^2, then what is the width of his backyard?
Click here to see answer by Alan3354(30993)  |
Question 204681: how do you know if a quadratic equation will have one, two or no solutions? If only given the solution, how do you find a quadratic equation? Is it possible to have different quadratic equations with the same solution?
Click here to see answer by stanbon(57415) |
Question 204672: Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?
Click here to see answer by nerdybill(6963)  |
Question 204724: solve by using quadratic formula (((6x2+3x-18=0)))
my answer is x=-2 3/2
-b+- sq root of b^2-4ac/2a
a=6
b=3
c=18
so -3+-sqrt[9-4(6)(-18)]/12
-3+-sqrt(441)/12
(-3+-21)/12 and x=(-3-21)/12
x=-3+21/12 and x=-3-21/12
x=18/12=3/2 and x=-2
this is how I came up with this answer is this right?
Click here to see answer by lazi(15) |
Question 204725: solve by using quadratic formula (((6x2+3x-18=0)))
my answer is x=-2 3/2
-b+- sq root of b^2-4ac/2a
a=6
b=3
c=18
so -3+-sqrt(9-4(6)l-18/12
-3t-sqrt9441)/12
-3+-21/12 and x=-3-21/12
x=-3+21/12 and x=-3-21/12
x=18/12=3/2 and x=-2
this is how I came up with this answer is this right?
Click here to see answer by Earlsdon(6288) |
Question 204725: solve by using quadratic formula (((6x2+3x-18=0)))
my answer is x=-2 3/2
-b+- sq root of b^2-4ac/2a
a=6
b=3
c=18
so -3+-sqrt(9-4(6)l-18/12
-3t-sqrt9441)/12
-3+-21/12 and x=-3-21/12
x=-3+21/12 and x=-3-21/12
x=18/12=3/2 and x=-2
this is how I came up with this answer is this right?
Click here to see answer by Alan3354(30993) |
Question 204736: y=x^2 + 4x -5 =0
a) without solving the equation or factoring, determine the solution(s) to the equation. x^2 +4x -5 =0
b) does this function have a maximum or minimum?
c) what are the coordinates of the vertex in (x,y) form?
d) what is the equation of the line of symmetry?
Click here to see answer by stanbon(57415) |
Question 204830: I am having problems with this question, please could you help me to understand it?
I open a bottle of champagne and release the cork vertically from the bottle. The height in metres of the cork above the level of the ground at time (t) seconds is modelled by the equation
h = 1 + 8t - 5t^2.
a) find the height of the cork after 0.8s....i have the answer of 4.2m for this.
b) find the time when the cork is at ground level (h = 0)......i have the answer of 1.72s for this.
c) explain what the maximum value of t is for which this function is a plausible model for the height of the cork?....i don't understand this question.
hope you can help me by explaining how to do this
thank you
Dawn
Click here to see answer by nerdybill(6963) |
Question 204879: I need help with this quadratic equation please:
When a ball is thrown, its height in meters h after t seconds is given by the equation h= vt-5t^2 where v is the initial upwards velocity in meters per second. If meters per second, find all values of t for which h=1 meter. Do not round any intermediate steps. Round the answer to 2 decimal places.
My try: Not even sure where to start..
Click here to see answer by Alan3354(30993) |
Question 204893: When graphing a linear inequality, how do you know if the inequality represents the area above the line?
What are the necessary and sufficient conditions for inequalities to represent an area in the first quadrant?
Click here to see answer by stanbon(57415) |
Question 204936: I need a real life example of a quadratic function.
Equation:
x represents ____________________
y represents _____________________
First point: (x1,y1). ________________
Second point: (x2,y2). ________________
Thank you
Click here to see answer by stanbon(57415) |
|
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
|
