Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 186289: If there is any way you can help, please do, I am soooo lost.
Show the equation that you used to solve each problem. Be sure to say what quantity each variable represents.

1. A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?
2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.

4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?

Click here to see answer by stanbon(57361)

Question 186313: THESE ARE FOURTH GRADE MATH QUESTIONS: PLEASE HELP ME I'M PUZZLED ON THIS

1. AT A PARTY, LOU ATE 6 FEWER APPETIZERS THAN SUSAN. CHRIS ATE 8 MORE THAN LOU. MITCHELL ATE 5 FEWER THAN CHRIS. MITCHELL ATE A TOTAL OF 5 APPETIZERS. HOW MANY DID SUSAN HAVE?
2. THE TIGERS FOOTBALL TEAM GAINED 12 YARDS ON THEIR SECOND PLAY. ON THEIR THRID PLAY, THEY LOST 24 YARDS. ON THEIR FOURTH PLAY, THEY GAINED 31 YARDS AND WERE STOPPED AT THEIR 42-YARD LINE. AT WHAT YARD LINE WERE THEY AFTER THE FIRST PLAY?

Click here to see answer by vleith(2825)

Question 186440: Find the solution: 2x2 + 6x + 5 = 0.
Click here to see answer by jim_thompson5910(28595)

Question 186442: how to factor t2 + 4t-st-4s
Click here to see answer by checkley77(12569)

Question 186469: A fraternity charters a bus for a ski trip at a cost of $360. When 6 more students join the trip, each person's cost decreases by $2. How many students were in the original group of ravelers?
Click here to see answer by josmiceli(9686)

Question 186455: write the expression 9x^2-9x+1 in the form a(x+b)+c where a, b, and c are real numbers.
Hence, state whether the function y = 9x^2-9x+1 has a maximum or minimum value.
state the value of x at which this maximum or minimum value occurs
Click here to see answer by feliz1965(151)

Question 186482: What is the answer to f(x) = -3x2
Click here to see answer by josmiceli(9686)

Question 186633: Hi there,
It would be great if someone could help me solve the following question as I am not too strong on transformations and it would be a huge help if someone could explain the solution to the following question.
Given the equation y=2^x, predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
Click here to see answer by vleith(2825)

Question 186632: Hi there,
I was finishing my Quadratics homework and had a problem that I couldn't seem to be able to graph. Could someone please help me with this question.
Sketch y=-1/4(2)^x-4+5 by first including a table describing its major features.
Click here to see answer by Alan3354(30993)

Question 186635: The following question is very hard and I honestly do not understand how to do it. I am supposed to do it for a homework assignment and its worth 8 marks. Could someone please help me with this? I would be really grateful.
Given y=1/5log^3(9x-36)^15-13, apply the laws of logarithms to change the form of the equation. Graph the function by first stating the basic function and then describe what transformation applied in order. Specifically describe what happens to the domain, range, asymptotes, x-intercept, and vertical stretch or compression. Confirm your result by graphing both equations using a graphing technology of your choice.
Click here to see answer by Alan3354(30993)

Question 186696: Please Help me with this problem. I am very confused. Determine whether the following equation have a solution or not? √2 x² - 4x – 7 √2 = 0
Click here to see answer by nerdybill(6962)

Question 186812: Jessica pulled the plug in her bathtub and it started to drain at a rate of L=-5T sqared-8T+120 where L represents the number of litres of water in the bathtub and T represents the number of minutes since the plug was pulled.
How long will it take for all of the water in the tub to drain out?
How many litres of water were in the tub originally?
my name is Chantal and I know how to find the vertex and the roots but I wasn't at school to learn these word problems. Can you help me?
The vertex is(-.8, 123.2)
The roots are -5.763869458 and 4.163869458
This is not in a text book
Click here to see answer by Alan3354(30993)

Question 186740: When an arrow is shot in the air, the height of the arrow h(t),at time t, t>or equal to 0, is determined by the equation h(t)= -4tsquared +16t+1.For which interval of time is the height of the arrow greater than or equal to 11 meters?
I figured out the vertex (2,17) and roots are in decimals-.0615528128 and 4.061552813. I believe the 4.061552813 is how long it takes to go up and down, reaching 17 meters going up, but I don't know how long for 11 meters. I missed on how to do this I was sick all week and have no one to explain it to me. Please help me. Chantal Laroche
Click here to see answer by ankor@dixie-net.com(15656)

Question 186702: I am confused as to how an quadratic equation can be used in our every day lives? I need an example such as when cooking.
Click here to see answer by ankor@dixie-net.com(15656)

Question 186794: This is a story problem and i have to find two equations.
one is linear and one is quadratic.
here is the problem:
"Two very lucky twin brothers have very wealthy parents who offered them very generous allowances at the tender age of 8 years old. the boys had 2 choices. under Option 1, they could take a monthly allowance of $100 this year (year 0) and expect a $100 raise every year until they turn 18 (year 10). Under option 2 they could take a monthly allowance of $5 this year (year 0), and the amount would double every year until they turn 18 (year 10). What are the equations that would represent each option?"
Click here to see answer by Edwin McCravy(8909)

Question 186813: Translate the folowing into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions?
Click here to see answer by ankor@dixie-net.com(15656)

Question 186831: I am very confused. Determine whether the following equation have a solution or not? √2 x² - 4x – 7 √2 = 0''.

Click here to see answer by user_dude2008(1861)

Question 186860: HELP PLEASE!! Determine whether the following equation have a solution or not? √2 x² - 4x – 7 √2 = 0''. This is the way I done it but I am not sure if I did the equdratic portion correctly. I get confused on having to divide the equation by 2(√2). The square root is what is confusing me.
2 solutions because the discriminate = 72 which is > 0
b² - 4ac
= (-4)² - 4(√2) (-7√2)
= 16 – 4(2) (-7)
= 72
Solution 1:
X = -b ±√b² - 4ac /2a
X = -(-4) + √72 /2(√2)
X = 4 + 8.485281374 /2.828427125

X = 4.414213562

Solution 2:
X = -b ±√b² - 4ac /2a
X = -(-4) - √72 /2(√2)
X = 4 – 8.485281374/2.828427125
X = -1.585786437

Click here to see answer by vleith(2825)

Question 186856: the numerator of a fraction is 3 less than the denominator. when both the numerator and denominator are increased by 4, the fraction is increased by 12/77. find the original fraction.
Click here to see answer by vleith(2825)

Question 186915: fatoring 6x2-7x-20
Click here to see answer by checkley77(12569)

Question 186875: I need help please. How do you form a quadratic equation from this?
If x=-3 and x=4, then form a quadratic equation.
Click here to see answer by ankor@dixie-net.com(15656)

Question 186943: please help me solve by factoring.

4x^2-11x+6=0 and show work so i can do this on my own tomorrow. thanks

Click here to see answer by jim_thompson5910(28595)

Question 186951: please solve by factoring...i got stuck near the end.

3x^2+8x+4=0

thanks
Click here to see answer by jim_thompson5910(28595)

Question 186990: 5n^2 = -8n -2
Click here to see answer by stanbon(57361)

Question 186991: find the function value
f(x) =x^2-5x-2
find f(-2)
Click here to see answer by jim_thompson5910(28595)

Question 186994: 2y^ 2 -6y= 3
Click here to see answer by stanbon(57361)

Question 187003: please help me factor and solve

x^2-21x-100=0

thank you...please show work
Click here to see answer by user_dude2008(1861)

Question 187002: please solve by factoring.

y^2-4y=45
Click here to see answer by user_dude2008(1861)

Question 186995: A = 3 pie a^2
solve for a
Click here to see answer by user_dude2008(1861)

Question 186983: x ^2 + 7x- 18 = 0
Click here to see answer by sowmya(32)

Question 187006: please help factor and solve.

12a^2=5a+28

thank you
Click here to see answer by jim_thompson5910(28595)

Question 187007: please help me solve and factor.

m^2+9m=0

thank you
Click here to see answer by jim_thompson5910(28595)

Question 187009: please factor and solve

12z^2+z=6
Click here to see answer by jim_thompson5910(28595)

Question 187015: Iva is trapped in a house which has walls 15 feet high. Fire fighters will rescue him by putting a ladder of length L feet at a distance x feet from the wall. They require x/L=1/2 solve exactly for x and L.
Click here to see answer by jojo14344(1512)

Question 186992: x+ 40/x = -13
Click here to see answer by rapaljer(4667)

Question 186981: 6m ^2 - 12m = 0
Click here to see answer by rapaljer(4667)

Question 187045: please factor out this quadratic

9x+x^2+20=0

thanks
Click here to see answer by Alan3354(30993)

Question 187039: what are the solutions of the equation x'2-8x=240
a.) -20 and -12
b.) -20 and 12
c.) 20 and -12
d.) 12 and 20
Click here to see answer by vleith(2825)

Question 186989: a ^2 -2a = 35 = 0
Click here to see answer by rapaljer(4667)

Question 187102: Hello I was doing my homework on quadratic functions and I have a question on a problem that my teacher never went over before.

1. Find a quadratic function that includes each set of values.
(1,-2),(2,-2),(3,-4)

Please show me work because I would like to know how to do it. Thank You

Click here to see answer by nerdybill(6962)

Question 187107: What are the roots for the equation 4xsquared+25=20x? I tried making the equation look like this:4xsquared-20x=-25 and I got x=40,0, but the 40 didn't equal what the original eqaution was.
Click here to see answer by scott8148(6628)

Question 187157: Apply Slope, Midpoint and Length Formulas
4. Verify that the quadrilateral with vertices P(2, 3), Q(5, -1), R(10, -1), and S(7, 3) is a rhombus.
Can you please help me with this question because i do not know how to verify it. It would be kind if you verify so i can understand it and can do the other question.
Click here to see answer by jim_thompson5910(28595)

Question 187159: Apply Slope, Midpoint and Length Formulas
5. The vertices of a quadrilateral are K(-1, 0), L(1, -2), M(4, 1), and N(2, 3). Verify that
a) KLMN is a rectangle
b) the lengths of the diagonals of KLMN are equal
Can you please help me with this question? thank you!!!
Click here to see answer by jim_thompson5910(28595)

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