Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 1159323: A picture frame holds an 8-inch by 10-inch photograph. The frame adds a border x inches wide around three sides of the photo. On the fourth side, the frame is wider to accommodate a decoration on the frame. The forth side is (3x-1) inches wide, as shown in the figure.
a) write a quadratic expression for the combined area of the frame in terms of x.
b)if the border on the three matching sides in 1 inch, what is the combined area of the frame?
c)if the combined area of the frame is 165 square inches, find x.
Click here to see answer by ikleyn(52781)   |
Question 1165819: Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs, the cost of each chair, $y is given by y = x2 - 14x + 80.
a. Find x such that the cost of each chair is the same as when Mr. Lim
ordered 5 chairs.
b. Find the number of chairs in a batch he needs to orders such that the cost
per chair is less than $45.
Click here to see answer by greenestamps(13200)  |
Question 1165819: Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs, the cost of each chair, $y is given by y = x2 - 14x + 80.
a. Find x such that the cost of each chair is the same as when Mr. Lim
ordered 5 chairs.
b. Find the number of chairs in a batch he needs to orders such that the cost
per chair is less than $45.
Click here to see answer by ikleyn(52781) |
Question 1165818: Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs, the cost of each chair, $y is given by y = x^2 - 14x + 80.
a. Find x such that the cost of each chair is the same as when Mr. Lim
ordered 5 chairs.
b. Find the number of chairs in a batch he needs to orders such that the cost
per chair is less than $45.
Click here to see answer by ikleyn(52781) |
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 ikleyn(52781) |
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 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 ikleyn(52781) |
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 1210274: Maricopa's Success scholarship fund receives a gift of $ 100000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 5.5 % interest, and stocks pay 6.7 % interest. Maricopa Success invests $ 40000 more in bonds than in CDs. If the annual income from the investments is $ 5590 , how much was invested in each account?
Click here to see answer by mccravyedwin(407)  |
Question 1210274: Maricopa's Success scholarship fund receives a gift of $ 100000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 5.5 % interest, and stocks pay 6.7 % interest. Maricopa Success invests $ 40000 more in bonds than in CDs. If the annual income from the investments is $ 5590 , how much was invested in each account?
Click here to see answer by ikleyn(52781) |
Question 1210274: Maricopa's Success scholarship fund receives a gift of $ 100000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 5.5 % interest, and stocks pay 6.7 % interest. Maricopa Success invests $ 40000 more in bonds than in CDs. If the annual income from the investments is $ 5590 , how much was invested in each account?
Click here to see answer by Edwin McCravy(20055)  |
Question 1165727: a satellite dish has a shaped of a paraboloid. If the receiver of the satellite dish is placed at the focus 2.53 ft from the vertex, write an equation for the cross-section of the satellite dish. Assume that the focus is on the positive x-axis and its vertex at the origin.
Click here to see answer by ikleyn(52781) |
Question 1170219: When lithium fluoride is dissolved in water, the equation of the solubility constant (Ksp) is
Ksp = [Li+] × [F-].
The value of Ksp for lithium fluoride is 0.00184 mol2/L2.
If the concentration of fluorine, [F-], is 0.0060 mol/L more that the concentration of lithium, [Li+], what is the concentration of lithium, [Li+], in the solution?
Round your answer to 2 significant figures.
Click here to see answer by CPhill(1959) |
Question 1170322: Formulate a quadratic equation then answer what is asked in the problem.
John can answer all the problem solving in the activity in Math 9 module within 24 hours alone. But Justine can answer it 4 hours more than John. How long will it take Justine to answer? How many hours to finish answering the activity if they worked together?
Click here to see answer by ikleyn(52781) |
Question 1170322: Formulate a quadratic equation then answer what is asked in the problem.
John can answer all the problem solving in the activity in Math 9 module within 24 hours alone. But Justine can answer it 4 hours more than John. How long will it take Justine to answer? How many hours to finish answering the activity if they worked together?
Click here to see answer by josgarithmetic(39617) |
Question 1171510: Show the mathematics of designing and constrcting a parabolic arch that is 10 meters across the base and 10 meters tall (measured from the ground to the vertex at the bottom of the keystone). Remember: -4a(y-k)=(x-h)^2
a) Place an axis system on this parabola
b) Find the function for this parabola
c) Make a chart of values for functional heights spaced 1 meter apart
d)How far down from the vertex is the focal point?
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 ikleyn(52781) |
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) |
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 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 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 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 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 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 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 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 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 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(52781) |
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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
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