Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 1209303: If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4 - 5t^2 + 14t + 55?
Click here to see answer by Edwin McCravy(20054)

Question 1209303: If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4 - 5t^2 + 14t + 55?
Click here to see answer by AnlytcPhil(1806)

Question 1209303: If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4 - 5t^2 + 14t + 55?
Click here to see answer by timofer(104)

Question 1209309: Find all real values of p such that
2(x+6)(x-p)\]
has a minimum value of -4 over all real values of x.
Click here to see answer by ikleyn(52778)

Question 1199775: Find the equilibrium quantity and the equilibrium price.
p = -2x^2 + 80 and p = 15x + 30
Click here to see answer by textot(100)

Question 1209318: Find the real number k such that f(x) = f(k - x) for all real numbers x, where
f(x) = 3x^2 - 4x - 2x^2 + 19x.
Click here to see answer by ikleyn(52778)

Question 1209319: Let f(a,b) = 2a - 3b^2 + 7 + 5a^2 - 10a. If f(k,-3) = -10, then what is k?
Click here to see answer by ikleyn(52778)

Question 1209316: Find the value of a for which there is exactly one real value of $x$ such that f(x) = a, where
f(x) = x^2 + 4x - 31 + 4x^2 - 13x + 25.
Click here to see answer by ikleyn(52778)

Question 1209401: Let a be a real number such that a - \frac{1}{a} = 1. Compute a^3.
Click here to see answer by ikleyn(52778)

Question 1209497: Find the range of values of k for which the expression 3 - 4k - (k+3)x - x^2 will be negative for all real values of x.
[the answer is 3 < k < 7]
Click here to see answer by ikleyn(52778)

Question 1192306: A marketing firm estimate that n months after the introduction of a client of new product f(n) thousand households will use it, where

Click here to see answer by CPhill(1959)

Question 1191505: ▱
upper left: A
lower left: D
Upper right: B
lower right: C
Centre: E
1.) Given: AB=(3x-5) cm, BC=(2y-7) cm, CD=(x+7) cm and AD=(y+3) cm.
∠BAD measures (2a+25)∘ while ∠BCD measures (3a-15)∘.
a. what is the value of a
b. what is m∠BAD?
c. What is m∠CBA?
2.) Diagonals AC and BD meet at E. DE is 8cm and AC is 13 cm
a. How long is BD?
b. How long is AE?

Click here to see answer by CPhill(1959)

Question 1189926: Given:
Room1 : length=4m : width=3m
Room2 : length=6m : width=4m
Tiles:
Glossy1 : 0.5m x 0.5m cost $8/tile
Glossy2 : 1m x 1m cost $10/tile
Non glossy1: 0.5m x 0.5m cost $5/tile
Non glossy2: 1m x 1m cost $7/tile
How to formulate 2 quadratic inequalities involving the dimensions of the floor of the rooms and the measure and costs of the tiles. Then graph the solution sets of these inequalities.

Click here to see answer by CPhill(1959)

Question 1209534: Find the range of values of k for which the expression 3 - 4K - (k+3)x - x^2 will be negative for all real values of x.
[the answer is 3 < k < 7]
Click here to see answer by CPhill(1959)

Question 1186902: The owner of a small clothing company wants to create a mathematical model for the company’s daily profit,
p, in dollars, based on the selling price, d, of the dresses made. The owner has noticed that the maximum daily profit
the company has made is $1200. This occurred when the dresses were sold for $65 each. The owner also noticed that
selling the dresses for $50 resulted in a profit of $900.
a. Using a quadratic relation to model this problem, create an equation for the company’s daily profit.
b. If he set the price to be $60, what would the profit be?

Click here to see answer by CPhill(1959)

Question 1209581: Please help me this qeation 4x^-9y^=19 & 2x+3y one linear one quedratic
Click here to see answer by ikleyn(52778)

Question 1209592: The solutions to the equation
6x^2 + 10x = -2x^2 - 12x - 17
can be written in the form $x=\frac{P \pm \sqrt Q}{R}$, where $P$ and $R$ are relatively prime integers and $R > 0$.

Click here to see answer by greenestamps(13198)

Question 1209591: What are all solutions to the equation x^2 + 3x - 10 = 18x - 15?
Click here to see answer by josgarithmetic(39617)

Question 1209609: Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.
Click here to see answer by math_tutor2020(3816)

Question 1209609: Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.
Click here to see answer by ikleyn(52778)

Question 1209639: What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?

f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

Your answer should be a list of numbers and should not include variable names, nor should it include $y$-coordinates.
Click here to see answer by ikleyn(52778)

Question 1209647: Suppose f(x) is a quadratic function such that f(1) = -24, f(4) = 10, and f(3) = 60.

Determine the value of f(-1).
Click here to see answer by CPhill(1959)

Question 1209641: Find all nonzero constants $a$ such that
ax^2 + 7x + 2 = 5x^2 + 23x - 12
has only one distinct root.

Click here to see answer by CPhill(1959)

Question 1209638: What is the equation of the line of symmetry of the parabola $y = f(x)$.
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
Click here to see answer by CPhill(1959)

Question 1209637: For parts (a) through (d), let f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

What is the vertex of the parabola y = f(x)?

Enter your answer as a coordinate pair, that is, as $(x,y)$ where $x$ and $y$ are replaced by numbers.
Click here to see answer by CPhill(1959)

Question 1209636: Complete the square: 3x^2 + 8x + 9 - 4x^2 + 25x + 19
Click here to see answer by CPhill(1959)

Question 1209634: Complete the square: x^2 - 10x + 21 + 3x^2 - 2x + 8.
Click here to see answer by CPhill(1959)

Question 1209652: GetThere Airlines currently charges $200$ dollars per ticket and sells $40{,}000$ tickets a week. For every $10$ dollars they increase the ticket price, they sell $300$ fewer tickets a week. How many dollars should they charge to maximize their total revenue?
Click here to see answer by CPhill(1959)

Question 1209648: Determine the range of the function $(x) = -4x^2-8x-6 + 3x^2 - 17x + 10. Enter your answer in interval notation.
Click here to see answer by CPhill(1959)

Question 1181712: A rocket is being launched vertically over a point 𝐴 on the ground with
a velocity of 550 𝑚𝑖Τℎ𝑟. Twenty five miles away from point 𝐴 on the
ground, there is a photographer video-taping the launch. At what rate
is the angle of elevation of the camera changing when the rocket
achieves an altitude of 25 miles?
Click here to see answer by CPhill(1959)

Question 1180642: 1. A programmer is writing the code for a new interactive basketball game. She is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modelled by the quadratic relation, h = - 0.2d2 + 3d + 6, where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter. Both distances are measured in feet. A programmer is writing the code for a new interactive basketball game. She is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modelled by the quadratic relation, h = - 0.2d2 + 3d + 6, where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter. Both distances are measured in feet.
a.Create a own quadratic relation that would model the path of a shot from a distance of 15 feet that would hit the rim of the basketball net. Explain how you obtained the answer.
Click here to see answer by CPhill(1959)

Question 1180625: The probability P(x) of an event happening is equal to the number of ways N(x) an event can come out favorably, divided by the number of all possible ways S(x) the event can turn out, P(x)= N(x)/S(x). Managers of a baseball stadium decide to hand out progressively more free baseball caps to random attendees with each successive game, according to the function x+5, where x = 1 for the first game, x = 2 for the second game, and so on. This causes more fans to attend, according to the function 2x+3. Compose a probability function P(x) denoting the probability that a fan in attendance on day x will receive a baseball cap. State its domain and range, in practical terms (think about games and baseball caps).
Click here to see answer by CPhill(1959)

Question 1180550: A programmer is writing the code for a new interactive basketball game. She is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modelled by the quadratic relation, h = - 0.2d2 + 3d + 6, where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter. Both distances are measured in feet.

a. How high was the ball when the shooter shot it?
b. What was the maximum height obtained by the ball?
c. A rim of a basketball net is 10 feet high. For what distance was the ball above the rim of the basketball net?
d. How far would the shooter have to be away from the rim of the basketball net for the ball to hit the rim of the basketball net and possibly go in?
e. Create a graphical model, using technology, to verify your calculations.
d. Create your own quadratic relation that would model the path of a shot from a distance of 15 feet that would hit the rim of the basketball net. Explain how you obtained your answer.
mathlover1 pls help
Click here to see answer by CPhill(1959)

Question 1178461: The table shows the sales of two companies for the year 2000 and the targeted sales after 10 years.
Company

Sales in 2000 (millions of AFN)

Sales target for 2010 in (millions of AFN)
A

2.00

2.60
B

2.70

3.10

Let x represent the number of years since 2000 and y represent sales in millions of AFN.
Write the system of equations to represent the sales of the two companies.
Solve the system using the elimination method and interpret the solution.
Show all your steps
Click here to see answer by CPhill(1959)

Question 1178048: The hire purchase price of a refrigerator is 6000. The deposit of 500 is made and the remainder is paid in equal monthly payments of 2500.
a) if the cash price is 4000, express as a percentage of the cash price, the extra cost of buying on hire purchase.
b) what is the interest rate (simple interest) charged on this transaction
Click here to see answer by CPhill(1959)

Question 1209791: Factor 15x3 - 5x2 + 6x - 2 by grouping. What is the resulting expression?
(5x2 + 2)(3x - 1)
(5x2 - 2)(3x + 1)
(15x2 + 2)(x - 1)
(15x2 - 2)(x + 1)
Click here to see answer by math_tutor2020(3816)

Question 1174395: Factory A has produced a product for the common users. The total variable cost per unit is
RM 10. The fixed cost is RM 6 200 in a year and the yearly revenue (in RM) is derived by
function R(x) = R(x) = - 2x^2+260x+500, given that x is the number of productions.
(a) Find the production level for breakeven point of factory A.
(b) State the range of number of productions where the factory A should produce to have profit.
(c) State the range of number of productions when the factory A has a loss more than RM 500.
Click here to see answer by CPhill(1959)

Question 1174372: A vehicle driver has to pay an annual road tax of RM 810 and RM 90 for insurance. His vehicle
can travel 500 kilometres to one gallon which costs 100 cents per gallon. The vehicle is
compulsory to be sent for service for every 5 000 kilometres travelled at a cost of RM 1 000, and
depreciation is calculated in cent by multiplying the square of the mileage by 0.1.
(a) If he covers x kilometres in a year, obtain an expression for the total cost in travelling x
kilometres and the average total cost per kilometre.
(b) Show that the total cost of travelling is RM 1 992 when the average total cost per kilometre
is minimized.
Click here to see answer by CPhill(1959)

Question 1174261: A vehicle driver has to pay an annual road tax of RM 810 and RM 90 for insurance. His vehicle
can travel 500 kilometres to one gallon which costs 100 cents per gallon. The vehicle is
compulsory to be sent for service for every 5 000 kilometres travelled at a cost of RM 1 000, and
depreciation is calculated in cent by multiplying the square of the mileage by 0.1.
(a) If he covers x kilometres in a year, obtain an expression for the total cost in travelling x
kilometres and the average total cost per kilometre.
(b) Show that the total cost of travelling is RM 1 992 when the average total cost per kilometre
is minimized.
Click here to see answer by CPhill(1959)

Question 1171702: The profit P(x) that company earn for selling x number of toy cars can be modelled by
P(x) =25x^2 +1000 -3000.
1. Write an inequality that models the problem if the profit P has to be at least php 5000
2. what could be the range of possible values of x
3. how many toy cars must be sold for a profit of at least php 5000
4. how many toy cars must be sold to obtain the maximum profit
5. how much is the maximum profit

Click here to see answer by CPhill(1959)

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