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Question 1209045: If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $12$ dollars, then I'll have four times as much money as he will have. How much money does my brother currently have (in dollars)?
Click here to see answer by math_tutor2020(3816)

Question 1209047: An aquarium tank is \frac{1}{6} full of water. When 2 gallons of water are added, the tank becomes \frac{3}{5} full. What is the total capacity of the aquarium tank, in gallons?
Click here to see answer by ikleyn(52776)

Question 1209049: Five times a number is divided by 7 more than that number. If the result is 8, then what was the original number?
Click here to see answer by ikleyn(52776)

Question 1209046: Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 56 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
Click here to see answer by math_tutor2020(3816)

Question 1209048: Solve for $x$:
\frac{3x+12}{x+4} = \frac{4x^2 + 8x + 18x^2}{2x^2}.
Click here to see answer by math_tutor2020(3816)

Question 1209053: Fill in the blanks so that the resulting equation has no solutions:
___ + ___ = ___ + ___

Click here to see answer by ikleyn(52776)

Question 1209182: Four cubes of ice with an edge of 4 centimeters each are left to melt in a cylindrical glass with a radius of 6 cm. how high will the water rise when they have melted?
Click here to see answer by math_tutor2020(3816)

Question 1209193: what is the constant in this algebra expression 26n+3b-3
Click here to see answer by ikleyn(52776)

Question 1209051: Find all real numbers $a$ that satisfy
\frac{1}{a^3 + 7} -7 = -\frac{a^2}{a^3 + 7}.
Click here to see answer by yurtman(42)

Question 1209052: Find all values of $a$ that satisfy the equation
\frac{a}{4} + 1 = \frac{a + 4}{a^2} + 7.
Click here to see answer by yurtman(42)

Question 1209204: Points A,B and C are three vertices of an isosceles triangle in which AC=BC. The coordinates of A and B are(2,1) and (6,-3) respectively and the equation of AC is 4x-7y+15=0. Find the coordinates of C.
Click here to see answer by greenestamps(13198)

Question 1205173: Consider the following system of linear equations
𝑥 + 3𝑦 + 2𝑧 − 𝑤 = −1
−3𝑥 − 7𝑦 + (𝑝 − 6)𝑧 + 2𝑤 = 1
2𝑥 + 𝑝^2𝑧 + 𝑝𝑤 = 𝑞^2
where 𝑝 and 𝑞 are real numbers.
Using Gaussian elimination, determine all possible values of 𝑝 and 𝑞 such that the system has infinitely many solutions with two free variables and solve the systems
Click here to see answer by ElectricPavlov(122)

Question 1207013: 4. Discrete independent random variables X and Y are given by the following laws of distribution:
X 0 3 Y - 2 - 1 2
P 0,3 0,7 P 0,2 0,4 0,4
Find M (X + Y) by two ways: 1) composing the law of distribution of X + Y; 2) using the property: M (X + Y) = M (X) + M (Y).
Click here to see answer by ElectricPavlov(122)

Question 1200776: Let y be defined implicitly by the equation ln(5y)=3xy. Use implicit differentiation to find the second derivative of y with respect to x.
d^2y/dx^2 =
Simplify fully please!
Click here to see answer by asinus(45)

Question 1209298: Engineering is an art and a science, to what extent do you agree/disagree with this statement?
Click here to see answer by ikleyn(52776)

Question 1199332: Use the gradient rise method©to optimize the function f(x,y)=6xy−(19x^2+3y^2)−36x−14y+13 with starting point x0=(−3,−4) and λ=0.01.
The first two points of the iteration are
x1=(-2.46 , -4.08 ) CORRECT
x2=(-2.13 , -4.1228 ) CORRECT
The main function is in
xopt=(952717619 , -150328908.2) WRONG
The optimal value of the function is
fopt=____

Click here to see answer by textot(100)

Question 1199331: Use the gradient method to find the maximum of the function f(x,y)=54y−(5x^2+9y^2)+70x−319 with initial point x0=(8,5) and λ=0.08. (The number λ is also known as step size or learning rate.)
The first two points of the iteration are
x1=(7.2,2.12) CORRECT
x2=(-2.40032,37.2096) WRONG
The maximum of the function is in (you may need to change the value of λ to achieve convergence):
xopt=(___,___)
The maximum value of the function is
fopt=_____

Click here to see answer by textot(100)

Question 1196276: If m=(1 -1 K)
4 7 3
-1 12 -2
Evaluate in term of K the determinant of m
Hence,if x=(x)
Y
Z
Solve the equation mx=(1)
11
21
When K=Z,by the lot method
Click here to see answer by ElectricPavlov(122)

Question 1196378: Jonathan obtained his degree and started his own consulting company in January of 2010. At the end of each month he began saving R2 480.00 in his account and requested the bank to quarterly debit three month sum of his exact savings towards his individual retirement account for a total period of ten years. The retirement account earned interest at 11% per annum, compounded quarterly. The amount that was available to him after ten years in the retirement account is
Click here to see answer by ElectricPavlov(122)

Question 1200420: 29% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
Click here to see answer by ElectricPavlov(122)

Question 1194207: https://ibb.co/jwFWQpm
Click here to see answer by proyaop(69)

Question 1194207: https://ibb.co/jwFWQpm
Click here to see answer by ikleyn(52776)

Question 1209345: Let x be a real number such that 625x = 9. Then 125x = ___.
Click here to see answer by ikleyn(52776)

Question 1209345: Let x be a real number such that 625x = 9. Then 125x = ___.
Click here to see answer by math_tutor2020(3816)

Question 1209345: Let x be a real number such that 625x = 9. Then 125x = ___.
Click here to see answer by MathTherapy(10551)

Question 1193663:
5.Suppose 80,000 is due at the end of 4 years with interest at 10% compounded quarterly. If money is worth 14% compounded quarterly, what is the value of obligation;
a.Now,
b.At the end of 3 years, and
At the end of 6.5 years
Click here to see answer by proyaop(69)

Question 1193566: Determine the discounted value now of $5200 due in 40 months if money is worth 6.5% compounded quarterly.
Click here to see answer by yurtman(42)

Question 1209361: How many values greater than 7000 can be formed using the digits 3, 5, 7, 8, 9 without repetition?
Click here to see answer by math_tutor2020(3816)

Question 1209361: How many values greater than 7000 can be formed using the digits 3, 5, 7, 8, 9 without repetition?
Click here to see answer by ikleyn(52776)

Question 1209379: Kiko planted eggplant seeds for two days. On the first day, there were k seeds sprouted while on the next day, the seeds sprouted were 5 more than thrice the number of eggplants seeds sprouted on the first day.
Click here to see answer by ikleyn(52776)

Question 1209396: can a fourth power integer be expressed as a sum of two distinct non zero integers squared where all terms are relatively primes?
Click here to see answer by Edwin McCravy(20054)

Question 1209421: Car A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 60 mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet?
Click here to see answer by ikleyn(52776)

Question 1209456: Odd Perfect Numbers.
Descartes suggested (and later confirmed by Euler) that if an odd perfect number does exist, it must be of the form 𝑁=𝑃𝑀^2 where 𝑃 is prime and M a positive
odd >1.
Because a perfect number equals the sum of it's proper devisers, we can rewrite the above equation as:
𝑁=𝑃𝑀^2=𝑃+𝑃𝑀+𝑀^2+𝑀+1
𝑃*𝑀^2-𝑃𝑀-𝑃=𝑀^2+𝑀+1
𝑃(𝑀^2-𝑀-1) = 𝑀^2+𝑀+1
𝑃=(𝑀^2+𝑀+1)/(𝑀^2−𝑀−1)
It's clear from the last derivation, as M grows, in the limit P will tend to 1,
because the values of M+1 and M-1 would be negligible compared to M^2 as M grows. This mean 𝑁=𝑃𝑀^2 has no positive integer solutions.
Was Descartes wrong or am I missing something?
Click here to see answer by ikleyn(52776)

Question 1209461: The line y= mx + c is tangent to the curve x^2 + y^2 = 4. Prove that 4m^2 = c^2 - 4
Click here to see answer by math_tutor2020(3816)

Question 1209461: The line y= mx + c is tangent to the curve x^2 + y^2 = 4. Prove that 4m^2 = c^2 - 4
Click here to see answer by greenestamps(13198)

Question 1209465: There are two differnet triples of positive integers (a,b,c) and (d,e,f) such that a^2 + b^2 + c^2 = 90 and d^2 + e^2 + f^2 = 90. Find the sum a+b+c+d+e+f
Click here to see answer by ikleyn(52776)

Question 1209476: 2X -4 *X *2
Click here to see answer by ikleyn(52776)

Question 1209476: 2X -4 *X *2
Click here to see answer by timofer(104)

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, 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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, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580