Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 1117462: Demonstrate that the roots of the following equation are rational
abc�x� + 3a�cx + b�cx - 6a� - ab + 2b� = 0

Click here to see answer by greenestamps(13198)

Question 1117528: it takes pump A two hours less time than Pump B to empty a swimming pool. Pump A is started at 8:00 am and pump B is started at 10:00. At 12:00 pm, 60% of the pool is empty when pump B book down. How much time at 12 pm would it take pump A to empty the pool?

Click here to see answer by Fombitz(32388)

Question 1117563: It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each machine to manufacture10,000 parts alone?
Click here to see answer by greenestamps(13198)

Question 1117665: A line passes through the points(-8,-7)
and has a slope of 5/4

Write an equation in slope-intercept form for this line.
Click here to see answer by josmiceli(19441)

Question 1117671: Amy, Chau, and Juan have a total of 90
in their wallets. Amy has 5
more than Chau. Juan has 3
times what Amy has. How much do they have in their wallets?

Click here to see answer by ikleyn(52777)

Question 1117664: A line passes through the points (-8,-7)
and has a slope of 5/4

Click here to see answer by josgarithmetic(39617)

Question 1117664: A line passes through the points (-8,-7)
and has a slope of 5/4

Click here to see answer by Alan3354(69443)

Question 1117664: A line passes through the points (-8,-7)
and has a slope of 5/4

Click here to see answer by MathLover1(20849)

Question 1117676: Rick paddled up the river, spent the night camping, and then paddled back. He spent 10 hours paddling and the campground was 24 miles away. If Rick kayaked at a speed of 5 mph, what was the speed of the current (in mph)?
Click here to see answer by josgarithmetic(39617)

Question 1117686: B^2-4x > -1 means the root is real. True or false?

Click here to see answer by josgarithmetic(39617)

Question 1117686: B^2-4x > -1 means the root is real. True or false?

Click here to see answer by ikleyn(52777)

Question 1117778: Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. (Let x be the independent variable and y be the dependent variable.)
a. Vertex (-4,9); Point (0,25)
b. Vertex (-2,9); Point (-5,0)
Click here to see answer by greenestamps(13198)

Question 1117968: Tom has a backyard that is 100 ft. by 60 ft. He plans to install a rectangular swimming pool bordered by a concrete walkway of uniform width. He wants the area of the pool to take up 1/2 of the area of the entire backyard. Determine the width of the walkways (x). Round your answer to 2 decimals
Click here to see answer by greenestamps(13198)

Question 1117981: Determine whether or not the following points fall on the graph of f(x)=-3x^2+6x+5.
Point 1. (3,-4)
Point 2.(-1,4)
Explain
Click here to see answer by Alan3354(69443)

Question 1117982: When a quadratic function is graphed, it will produce a parabola. Describe the difference between a Minimum Vertex and a Maximum Vertex of a parabola.
Explain
Click here to see answer by rothauserc(4718)

Question 1117979: Learning to find Maximum and Minimum Values for Applications of Quadratic Functions in my Algebra class and the only question on my homework that is giving me trouble is this one:
One number is 6 less than twice a second number. Find a pair of such numbers so that their product is as small as possible.
The two numbers are:
The smallest possible product is:
I can't seem to figure out how to set the equation up. Please help!
Click here to see answer by Podrius(1)

Question 1117988: Using the formula s = 5.45√d for the speed (s) I'm miles per hour with which an object dropped from a height of d feet strikes the ground.
A) A pair of pliers is dropped from a roof 32 feet high. How fast will it be traveling when it hits the ground?
B) A bullet is shoot 400 feet up into the air. With what speed will it strike the ground?
Click here to see answer by solver91311(24713)

Question 1117977: Using the formula s= 5.45√d for speed(s) in Ikea per hour with an object dropped from a height of d feet strikes the ground.
A) A pair of pliers is dropped from a roof 32 feet high. How fast will it be traveling when it hits the ground?
B) A bullet is shoot 400 feet up into the air. With what speed will it strike the ground
Click here to see answer by Alan3354(69443)

Question 1118073: What is the equation of the blue parabola shown? (6,1)(5,-2)
Click here to see answer by josgarithmetic(39617)

Question 1118073: What is the equation of the blue parabola shown? (6,1)(5,-2)
Click here to see answer by Shin123(626)

Question 1118097: What is the equation of a parabola whose vertex is (-6,0) and whose graph is half as tall as y=x^2 and opens upside down? Include y= as part of your answer
Click here to see answer by ikleyn(52777)

Question 1118147: Use technology to find the quadratic regression curve through the given points. HINT [See Example 5.] (Round all coefficients to four decimal places.)
{(-2, 2), (-3, 1), (-4, -1), (-5, 0)}
Click here to see answer by greenestamps(13198)

Question 1118185: Find the value of "a" such that the equation ax^2 + 2x + 4 = 0 has exactly one solution.
I'm not sure how to go about solving this problem. Any help is much appreciated.

Click here to see answer by ikleyn(52777)

Question 1118184: You operate a gaming Web site, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was 570 log-ons per month. When you lowered the price to $2.50, the demand increased to 855 log-ons per month.
(a) Construct a linear demand function for your Web site and hence obtain the monthly revenue R as a function of the log-on fee x.
R(x)=
(b) Your Internet provider charges you a monthly fee of $40 to maintain your site. Express your monthly profit P as a function of the log-on fee x. HINT [See Example 4.]
P(x)=
Determine the log-on fee you should charge to obtain the largest possible monthly profit.
x = $
What is the largest possible monthly profit?
$
Click here to see answer by Boreal(15235)

Question 1118187: Please Help Me With This Question find the gradient of the curve y=x^2+5x-3 at the point x=2
Click here to see answer by Boreal(15235)

Question 1118191: The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are.
x −2 −1 0 1 2
f(x) 0.5 1.5 4.5 13.5 40.5
g(x) 12 6 3 1.5 0.75
Click here to see answer by ikleyn(52777)

Question 1118201: X(x+2)=20
Click here to see answer by josgarithmetic(39617)

Question 1118227: Vertex 1/8 passes through 3/12
Click here to see answer by greenestamps(13198)

Question 1118227: Vertex 1/8 passes through 3/12
Click here to see answer by Alan3354(69443)

Question 1118241: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE.)
f(x) = 2-2e^x/x; a=0

Click here to see answer by greenestamps(13198)

Question 1118188: You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $10 per guest and averaged 250 guests per night. The next week you charged $11 per guest and averaged 240 guests per night.
(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.
q(p) =
(b) Find the nightly revenue R as a function of the cover charge p.
R(p) =
(c) The club will provide two free non-alcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $2,000. Find the cost C as a function of the cover charge p.
C(p) =
(d) Now find the profit in terms of the cover charge p.
P(p) =

Determine the entrance fee you should charge for a maximum profit.
p = $ per guest
Click here to see answer by greenestamps(13198)

Question 1118298: 3x-2x^2=7
Click here to see answer by josgarithmetic(39617)

Question 1118369: Twenty reasons to visit Fiji

Click here to see answer by ikleyn(52777)

Question 1118369: Twenty reasons to visit Fiji

Click here to see answer by Shin123(626)

Question 1118397: The length of swimming pool is 8m longer than its width and the area is 103m
Click here to see answer by josgarithmetic(39617)

Question 1118408: A realty developers sells residential lots for Php 4000 per. square meter plus a processing fee of Php 25000. ONE OF THE LOTS. THE REALTY DEVELOPERS IS SELLING COST PHP 625,OOO
Click here to see answer by josgarithmetic(39617)

Question 1118409: Edna paid at least Php1,200 for a pair of pants and blouse,The cost of pair is Php600 more than the costof the blouse
Click here to see answer by josgarithmetic(39617)

Question 1118409: Edna paid at least Php1,200 for a pair of pants and blouse,The cost of pair is Php600 more than the costof the blouse
Click here to see answer by ikleyn(52777)

Question 1118413: How did you know if the equation is not quadratic?
Click here to see answer by josgarithmetic(39617)

Question 1118414: How did you know if the equation is not quadratic?
Click here to see answer by josgarithmetic(39617)

Question 1037220: how get sqrt(3+sqrt(5-sqrt(13+sqrt(48)))) show than (sqrt(2)+sqrt(6))/2
helpme please

Click here to see answer by Rishikesh1501(1)

Question 1118427: z^2-4z=0
Click here to see answer by ankor@dixie-net.com(22740)

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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, 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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