Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 394748: solve for r
r^2 + 3r = 1
Click here to see answer by robertb(5830)

Question 394747: x^2 + 14x + 4 = 0
Solve for x
Click here to see answer by robertb(5830)

Question 394729: I really don't know how to set this up to get my answer....Please someone Help!!

A temporary agency offers two payment options for administrative help:
Option1: $25 daily fee plus $10/hour; or
Option 2: No daily fee but $15/hour.
Let x = total hours worked.
a) Write a mathematical model representing the total temp cost, C, for a four-day temporary administrative assistant in terms of x for the following:
Option 1: C=_________________
Option 2: C=_________________

b) How many total hours would the temp need to work in the four day period for the cost of option 1 to be less than option 2. Set up an inequality and show your work algebraically using the information in part a. Don�t forget about the daily fee in Option 1 (it�s a four day proposition!). Do not assume an eight hour workday. Any number of hours per day is possible.
Answer:

Show your work here:
Lisa
Click here to see answer by mananth(16946)

Question 394940: A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeowner cannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally. [Show work.]
Click here to see answer by Earlsdon(6294)

Question 394991: Give exact and approximate solutions to three decimal places.

The exact solutions are x=____
(Use radicals as needed. Use a comma to separate answers.)
The approximate solutions to 3 decimal places are x=____
(Use a comma to separate answers.)
Click here to see answer by ewatrrr(24785)

Question 394992: Find the x-intercepts and y-intercepts for f(x).

The x-intercept(s) is(are) ____.
The y-intercept(s) is(are) ____.
(Type an ordered pair. Type an integer or a decimal. Round to the nearest tenth. Use a comma to separate answers as needed.)
Click here to see answer by ewatrrr(24785)

Question 394985: a)Solve
-What are the solutions?
x=____
(Simplify your answer. Type exact answers, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
b)Find the x-intercepts of .
-What are the x-intercepts?
(Type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.}
Click here to see answer by scott8148(6628)

Question 394980: Give exact and approximate solutions to three decimal places.

What are the exact solutions?
x=____
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
**There are no approximate solutions since the solutions are integers.
Click here to see answer by scott8148(6628)

Question 395045: Find all solutions of the equation x^2−3x+8=0 and express them in the form a+bi:
First with the input b<0
Then with the input b>0

Click here to see answer by stanbon(75887)

Question 395135: Please help me solve this equation:
Click here to see answer by stanbon(75887)

Question 395135: Please help me solve this equation:
Click here to see answer by richard1234(7193)

Question 395138: Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).

a. Does the graph of this equation open up or down? How did you determine this?

Click here to see answer by richard1234(7193)

Question 395151: write 6x^2-17x+13=20x^2-32 in standard form then solve.
Click here to see answer by mananth(16946)

Question 395154: use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth.
question 1 : 2a^2-46a+252=0
question 2 : x^2-4x=5
please answer these . thanks
Click here to see answer by mananth(16946)

Question 395277: Give exact and approximate solutions to three decimal places.

What are the exact solutions?
x=____
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
**There are no approximate solutions since the solutions are integers.
Click here to see answer by Earlsdon(6294)

Question 395290: A model rocket is launced into the air and follows a parabolic path described by the function h(t)=-5t^2 + 40t +2, where t is time in seconds after the rocket is launched and h(t) is the height of the rocket above the ground in metres. Algebraically determine the maximum height reached by the rocket and the time it takes the rocket to reach it's maximum height.
Click here to see answer by stanbon(75887)

Question 395287: A football is kicked in the air and lands on the ground 32m from where it was kicked. If the maximum height reached by the ball is 14m, determine the transformational form of the quadratic function representing the path of the football while it is in the air.
Click here to see answer by jrfrunner(365)

Question 395314: I am totally confused by the factoring results my text says is the answer: The equation is
3x^2 + x - 2 = 0
They say the factor of this is
(3x - 2)(x + 1)
Why isn't it -1, +2? Isn't the product of -2 suppose to equat the sum of 1 ?
Please show me why their answer is correct? I even tried using the ac Method with no results.
Click here to see answer by ewatrrr(24785)

Question 395297: A rectangular skating rink has length 22m and width 30m. The rink is made larger by extending the width and length by the same amount such that the area of the new rink is 825 m^2. Create a quadratic equation to models this situation and use it to determine the new dimensions of the new rink.

Note: the length of one side and the width of one side, not all the way around.
Please help me.
Click here to see answer by ankor@dixie-net.com(22740)

Question 395305: solve and find the value for x which satisfies the equation
2x^2-4=7x

Click here to see answer by jim_thompson5910(35256)

Question 395382: 1. 5/2x^2-3/2x-1/4=0
2. 12m^2-192=0
if you could write out how to do it it would help me so much thanks
Click here to see answer by jim_thompson5910(35256)

Question 395421: If the numerical value of the area of a rectangle is 19 more than 2 times the perimeter, and the length is 2 more than the width, what is the width?
Area = L * W
2x + 19
w = X
l = X + 2
X(X + 2) = 2x + 19 ?
x^2 + 2x = 2x + 19 + x + 2

Click here to see answer by jrfrunner(365)

Question 395429: When the area of a rectangle is 3 times the length and the lenght is 1 more than twice the width, what are the demensions?
I know somthing is missing in my formula. Please help? Thanks.
A = L*W
W = x
L = 2x + 1
x(2x + 1) = 3(2x + 1)
2x^2 + x = 6x + 3
2x^2 + 5x + 3
(2x + 3)(x+1)

Click here to see answer by stanbon(75887)

Question 395357: write a quadratic equation having the given numbers as solutions
-5 and -3
Click here to see answer by MathLover1(20849)

Question 395439: Give exact and approximate solutions to three decimal places.
X^2+12X+36=64
Click here to see answer by jim_thompson5910(35256)

Question 395293: The sum of two numbers is 10 and the sum of their squares is a minimum. Algebraically determine the function that models the sum of their squares and use it to find the two numbers.
Click here to see answer by robertb(5830)

Question 395288: An Olympic ski jumper skis off a spring board. Her height h, in meters, above the ground, t seconds after she jumps, is given by h(t)= -4.9t^2 + 20t +15. Algebraically determine the approximate instantaneous rate of change in her height at 2 seconds and describe what is happening at that time.
Click here to see answer by ankor@dixie-net.com(22740)

Question 395569: find the vertex, the line of symmetry, and the maximim or minimum value of the quadratic function, and graph the function on paper.
f(x) = 2x^2+2x+4
what is the x-coordinate of the vertex? (type a simplified fraction)
Click here to see answer by lwsshak3(11628)

Question 395613: Find the vertex and x-intercept(s) for the quadratic function.
f(x)= -3x^2+2x+3
Round to the nearest hundredth if necessary.
If there is more than one x-intercept, separate them with commas.
Click here to see answer by ewatrrr(24785)

Question 395575: find the x-intercepts and y-intercepts
f(x) = -x^2 +2x+15
The x-coordinates of the intercepts are x= ___
Click here to see answer by ewatrrr(24785)

Question 395567: find the vertex, the line of symmetry, and the maximim or minimum value of the quadratic function, and graph the function on paper.
f(x) = 3x^2-18x+14
what is the vertex (type an ordered pair)
Click here to see answer by ewatrrr(24785)

Question 395560: find the vertex, the line of symmetry, and the maximim or minimum value pf f(x). Graph the function.
f(x)= -(x+9)^2-4
the vertex is (type an ordered pair)
Click here to see answer by ewatrrr(24785)

Question 395555: find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function.
f(x)= -5(5+3)^2 + 8
the vertex is (type an ordered pair)
Click here to see answer by ewatrrr(24785)

Question 395566: find the vertex, the line of symmetry, and the maximim or minimum value of the quadratic function, and graph the function on paper.
f(x) = x^2 -10x-4
what is the vertex (type an ordered pair)
Click here to see answer by ewatrrr(24785)

Question 395572: Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) = 0.1x^2 - 1.6x + 8.78, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bucycle?
The shop should build ___ bicycles?
Click here to see answer by jrfrunner(365)

Question 395630: To calculate the quadratic equation given 3 sides A,B,C your program should be interactive [hint-x=[-b+vb2-4ac]/2a
Click here to see answer by richard1234(7193)

Question 395652: Please walk me thru this problem, especially the process for determining each of the factors:
Solve: 5x^2 - 8x +3 = 0. My text says that the factors are (5x-3)(x-1). I don't understand how they got this. thank you.
Click here to see answer by ewatrrr(24785)

Question 395655: Please walk me thru this problem, especially how they got their factors:
Solve: 3x^2 + x - 2 = 0. They say that the factors are(3X-2)(X+1). Thank you..
Click here to see answer by ewatrrr(24785)

Question 395690: Hello. I am stumped on a homework assignment. I have to solve a quadratic equation using two methods. I have solved the equation using factoring and now have to figure out how to solve it by completing the square method. The equation I have is z^2+z-2=0. Any help would be greatly appreciated.
Thank you.
Click here to see answer by Alan3354(69443)

Question 395574: A carpenter is building a rectangular room with a fixed perimeter of 304 ft. What dimensions would yield the maximum area? What is the maximum area?
The length that would yield the maximum area is ___ ft.
Click here to see answer by solver91311(24713)

Question 395731: Help please. I have an assignment to find a real world situation where quadratic equations are used. I don't have trouble finding them, just the ones I do find I have no idea how to explain. I really appreciate any help!
Explore and find a real-world application of a quadratic equation, whether it is from the realm of physics, finance, or anything else. Write a paragraph about what you find. In your description,
* show the equation.
* explain what the variable represents in real terms.
* describe what the equation models in real terms.
Click here to see answer by richard1234(7193)

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