Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

Tutors Answer Your Questions about Expressions-with-variables (FREE)

Question 251885: The sum of the integers from 1 to n is n(n+1) over 2. The sum of the squares of the integers from 1 through n is n(n+1)(2n+1) over 6 . The sum of the cubes of the integers from 1 through n is n^2(n+1)^2 over 4 . Use the appropriate expressions to find the following values.
A. The sum of the integers from 1 to 30.
i just dont underatand what it wants me to do, i looked in the book but i cant find any examples to help explain what i am suppose to even solve. I am just not sure where i should even start.
Click here to see answer by richwmiller(9144)

Question 252056: Two cyclists start biking from a trails start 3 hrs apart. The second cyclist travels at 10 mph and starts 3 hours after the first cyclist who is traveling at 6 mph. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started cycling. I know d=rt. I tried
d=10(t-3)/6t?

Click here to see answer by richwmiller(9144)

Question 252066: write a system of equations for the following:
a rectangle is 3 times longer than it is wide. Perimeter is 44cm
I know the dimensions, but not how to write a system of equations
Click here to see answer by richwmiller(9144)

Question 252174: 1\3(c+1)=1\6(3c-5)
Click here to see answer by drk(1908)

Question 251202: solve for x and express the solution in intervals.x^3-3x+2<=0
Click here to see answer by drk(1908)

Question 251143: I am trying to figure out the least common multiple of 35a^2b^2,5a^5b^5, 14a^2b^5
I believe it is the number 5, but do I do with the variables and exponents. I do not see anything like this problem in my text. Please help me solve and understand.
Click here to see answer by nyc_function(2733)

Question 249893: how do you graph this equation*? ..
or what do i do to start off so i can graph it?
*y = x + 2
Click here to see answer by Alan3354(31518)

Question 252389: i dont have a problem its more of a question with expression i know you have to do the same opperation to each side but how do you figure out wich number to use, allong with what action * - + or/?
Click here to see answer by richwmiller(9144)

Question 250807: when solving 3x^2=75 do you multiply 3 times x then square it, or do you multiply three times the squared number to find 75
Click here to see answer by edjones(7569)

Question 252484: please help me solve this question.
( 3x^-2 y^5 over p^-3)^-2 (3x^-2 over y)^2

Click here to see answer by drk(1908)

Question 250837: use elimination to solve each system of equations.
2.4x+y=-9
4x+2y=-10
Click here to see answer by drk(1908)

Question 252572: 14x+(8x+4)=180
Click here to see answer by rfer(12730)

Question 250794: At the basketball game, they charge $4 for each ticket and they expect to make $75 in concessions. The team must pay the two referees $100 each and pay the ticket taker $25. Each fan gets a free noise maker that costs the team $0.25 each. How many tickets must be sold to break even?
Click here to see answer by checkley77(12569)

Question 252590: Solve for x: 2x over 3 minus 2x+3 over 5 = x-5 over 3

Click here to see answer by drk(1908)

Question 252590: Solve for x: 2x over 3 minus 2x+3 over 5 = x-5 over 3

Click here to see answer by checkley77(12569)

Question 252593: 3x+6 over 4x+12 DIVIDED BY x^2-4 over x+3
Click here to see answer by drk(1908)

Question 252593: 3x+6 over 4x+12 DIVIDED BY x^2-4 over x+3
Click here to see answer by jim_thompson5910(28715)

Question 252600: Solve for x:
2x over 3 +4 = x-5
Click here to see answer by jim_thompson5910(28715)

Question 252602: If 3ax+b=c, then what does x equals
Click here to see answer by ankor@dixie-net.com(15746)

Question 252608: the length of the hypotenuse of a right triangle is 34 inches and the length of one of its legs is 16 inches. what is the length in inches of the other leg of this right triangle?
Click here to see answer by drk(1908)

Question 252675: 4x+4y=32
x+4y=8
Click here to see answer by richwmiller(9144)

Question 251399: The life expectancy of Americans has been steadily increasing primarily due to medical advancements and awareness of maintaining a healthy lifestyle.
Life expectancies at birth for men and women can be modeled by the following functions:
W(x)= 0.126x + 76.74
M(x) = 0.169x + 69.11
W(x) represents the life expectancy of women and M(x) represents the life expectancy of men. The x represents the years since 1975. (x=0 corresponds to the year 1975, x=5 corresponds to 1980, and so on).
Complete the following table:

Counting the Years Year
1975 1980 1985 1990 1995 2000
x, years since 1975 0 5 10 15 20 25
W(x)
M(x)

Click here to see answer by mathhater404(3)

Question 252977: solve for x: 4/x=1/5
Click here to see answer by Greenfinch(383)

Question 252978: an airplane flew for 4.23 hours with a 25.5km/h tail wind. the return flight against the same tail wind took 4.97 hours. find the speed of the plane in still air.
Click here to see answer by richwmiller(9144)

Question 252981: to deliver a package a messenger must travel at a speed of 60mi/h on land and then use a motor boat who's speed is 20 mi/h in still water. The messenger goes by land to a dock and then travels on a river against a current of 4 mi/h . He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours. How far did the messenger travel by land and how far by water.
Please help with step by step instructions for problem solving.. THANKS...
Click here to see answer by Greenfinch(383)

Question 253036: A three- digit number divisible by 5 has a hundreds digit that is 2 more than the tens digit. If the number is 43 times the sum of the digit, what is the number?
Click here to see answer by richwmiller(9144)

Question 253048: Fame is 10 years older than EJ. Five years ago, EJ was two years more than 1/4 as old as Fame. What are their present ages?
Click here to see answer by richwmiller(9144)

Question 253057: how do i divide big numbers because i don't know how to divide big numbers
Click here to see answer by richwmiller(9144)

Question 253046: A speed boat traveling 60kph left the port 5 minutes after a fishing boat sailed. If it overtakes the fishing boat after 2 hours, find the rate of the fishing boat.
Click here to see answer by richwmiller(9144)

Question 253040: A 400g solution made up of 40% sugar must be added to a 2oog solution. What should be the percentage of sugar in 200g of solution in order to produce a 38% sugar solution?
Click here to see answer by nerdybill(7003)

Question 253038: Two years ago, Anton was a three times as old as his sister, Nathalie. In 4 years, he will be only twice his sister's age. Find their present ages.
Click here to see answer by richwmiller(9144)

Question 253035: The sum of two-digit number is 13. When 9 is subtracted from the original number, the resulting number is the reverse of the original number. What is the new number?
Click here to see answer by richwmiller(9144)

Question 253125: Marvic is 20 years older than Fe.Seven years from now, Marivie will be thrice as old as Fe. Find their present ages.
*please answer my question with just one variable.,thnX
Click here to see answer by ankor@dixie-net.com(15746)

Question 253163: y+2x=-1
y-4=-2x

first equation:y plus 2x equals negative 1.
second equation: y minus 4 equals negative 2x.
Click here to see answer by Alan3354(31518)

Question 253163: y+2x=-1
y-4=-2x

first equation:y plus 2x equals negative 1.
second equation: y minus 4 equals negative 2x.
Click here to see answer by Edwin McCravy(8999)

Question 253253: write two verbal expressions for n-5
Click here to see answer by drk(1908)

Question 253248:
Click here to see answer by drk(1908)

Question 253286: Erin's age is 3 times Warren's. In 4 years she will be twice as old as he will be. How old is each now?
so far I have {E+4 = 2(w x 3 + 4)}
Click here to see answer by Greenfinch(383)

Question 253286: Erin's age is 3 times Warren's. In 4 years she will be twice as old as he will be. How old is each now?
so far I have {E+4 = 2(w x 3 + 4)}
Click here to see answer by josmiceli(9817)

Question 253286: Erin's age is 3 times Warren's. In 4 years she will be twice as old as he will be. How old is each now?
so far I have {E+4 = 2(w x 3 + 4)}
Click here to see answer by richwmiller(9144)

Question 253291: Janine has job offers at two companies. One company offers a starting salary of $28,000 with a raise of &3,000 each year. The other company offers a starting salary of $36,000 with a raise of $2,000 each year.
a. After how many years would Janine's salary be the same with both companies?
b. What would that salary be?
-----------------------------------------
please help me i am having the hardest time with this question, thank you.
Click here to see answer by checkley77(12569)

Question 253304: 4n+6-2n=2(n+3)
Click here to see answer by drk(1908)

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