New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'mananth'
mananth answered: 12270 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299, >>Next
Polynomials-and-rational-expressions/371054: Hello. I am having trouble with solving inequalites and graphing them and putting them into set builder and interval notation.
2(x+4)<5x+3(x+2).
So far i have gotten 2x+8<8x+6.
Thank you for the help.
1 solutions
Answer 264357 by mananth(12270)   on 2010-11-14 20:13:31 (Show Source):
You can put this solution on YOUR website!2(x+4)<5x+3(x+2).
2x+8<8x+6
add -2x to both sides
2x-2x+8<8x-2x+6
8<6x+6
-6 -6
2<6x
/6
2/6
1/3
...
x>1/3
..
(1/3, OO)
..
{x|x>1/3}
...
m.ananth@hotmail.ca
|
Polynomials-and-rational-expressions/371043: A circular pool is surrounded by a brick walkway 3 m wide. Find the radius of the pool if the area of the walkway is 198 m^2.
1 solutions
Answer 264352 by mananth(12270) on 2010-11-14 20:04:33 (Show Source):
You can put this solution on YOUR website!let the radius of the pool be x
radius of pool + walkway = x+3
..
area of pool + walkway = pi*(x+3)^2
area of pool = pi*x^2
..
area of walkway = 198 m^2
pi(x+3)^2-pi*x^2= 198
/pi
(x+3)^2-x^2=198/pi
x^2+6x+9-x^2=198/pi
6x+9 = 63
-9 -9
6x=63-9
6x=54
x= 9m radius of the pool
...
m.ananth@hotmail.ca
|
Travel_Word_Problems/371019: Solve the problem. On a recent trip, Sarah's car traveled 20 mph faster on the first 140 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarah's car on the first part of the trip.
1 solutions
Answer 264350 by mananth(12270) on 2010-11-14 19:58:45 (Show Source):
You can put this solution on YOUR website!let speed on second leg be x mph
speed on first leg = x+20
..
second leg distance = 80 miles
first leg distance = 140 miles
..
time first leg + time second leg = 4 hours
...
t= d/t
80/x + 140/(x+20)=4
(80(x+20)+140x)/x(x+20)=4
80x+1600+140x=4x(x+20)
220x +1600 = 4x^2+80x
4x^2+80x-220x-1600=0
4x^2-140x-1600=0
/4
x^2-35x-400=0
solve for x using quadratic formula
discriminant = 2825
x1= (35+sqrt(2825))/2
x2 will be negative so to be ignored
= 44.07 mph on the second leg.
first leg speed = x+20 = 64.07 mph
..
m.ananth@hotmail.ca
|
Travel_Word_Problems/371015: An airplane travels against a 52.5 mph wind in 5 hours and it makes the return trip with the same wind in 2 hours. Find the speed of the plane in still air.
1 solutions
Answer 264336 by mananth(12270) on 2010-11-14 19:24:00 (Show Source):
You can put this solution on YOUR website!An airplane travels against a 52.5 mph wind in 5 hours and it makes the return trip with the same wind in 2 hours. Find the speed of the plane in still air.
..
let plane speed in still air be x mph
wind speed = 52.5 mph
..
Against wind speed = x-52.5
with wind speed = x+52.5
..
distance is the same
against wind time = 5 hours
with wind time = 2 hours
..
5(x-52.5) = 2(x+52.5)
5x-262.5=2x+105
5x-2x=262.5+105
3x= 367.5
/3
x=122.5 mph the speed of plane
...
m.ananth@hotmail.ca
|
Unit_Conversion_Word_Problems/370982: Squares are cut from the corner of a rectangular sheet of metal 30 inches by 50 inches. The four sides are then turned up and soldered. How large are the squares if the volume open metal box is 2,392 cubic inches? 4,000 cubic inches?
1 solutions
Answer 264330 by mananth(12270) on 2010-11-14 19:09:10 (Show Source):
You can put this solution on YOUR website!dimensions of plate = 30 by 50
let he square cut has edge x cm.
the length will reduce to 30-2x
width will reduce to 50-2x
height of box when folded will be x
..
Volume of box = L*W*H= 2392
x(50-2x)(30-2x)=2392
4x(25-x)(15-x)= 2392
4x(375-25x-15x+x^2)=2392
4x(x^2-40x+375)=2392
/4
x(x^2-40x+375)=2392/4
x^3-40x^2+375x-598=0
solve for x
you will get x=2 the width cut
so the squares are 2 by 2 in
...
m.ananth@hotmail.ca
|
Graphs/370960: Y=0.12x+0.76
0.11x-Y=0.85
1)Are these lines intersecting parellel or perpendicular?
2) Use the equation of the lines to determine if they are parellel.
1 solutions
Answer 264312 by mananth(12270) on 2010-11-14 18:20:46 (Show Source):
You can put this solution on YOUR website!Y=0.12x+0.76
0.11x-Y=0.85
re write the equation in slope intercept form
y=0.11x-0.85
...
compare the two lines.
if the lines are parallel the slopes should be same.
They are not so they are not parallel.
..
If the lines are perpendicular then the slopes should be negative reciprocal of each other. they are not.
so they are neither perpendicular.
..
solve the two equations
..
Y-0.12x=0.76
0.11x-Y=0.85
...
add the two equations
-0.01X=1.61
X=-161
..
plug value of x to get y
Y-0.12*-161=0.76
Y=-18.56
...
m.ananth@hotmail.ca
|
Equations/370684: How do you compute algebraically (not by graphing) the intercepts of any function?
For example, what are the x-intercept(s) and y-intercept(s) of 2x – 5y = 8 without graphing the equation? Remember that intercepts are points and points are written as ordered pairs.
1 solutions
Answer 264251 by mananth(12270) on 2010-11-14 09:03:10 (Show Source):
You can put this solution on YOUR website!2x – 5y = 8
...
For y intercept plug x=0
0-5y=8
/-5
y=-8/5
The co-ordinates are (0,-8/5)
..
For x intercept
plug y = 0
2x+0=8
x= 4
(4,0) are the co-ordinates
..
m.ananth@hotmail.ca
|
Coordinate-system/370674: Write an equation of the line with the given slope and the given y-intercept. Leave the answer in the slope-intercept form.
-2/3 , y-intercept (0, 5)
1 solutions
Answer 264248 by mananth(12270) on 2010-11-14 08:22:16 (Show Source):
|
Linear-systems/370678: 9x - (5x-5) = 37
How do I solve and what is the x
1 solutions
Answer 264247 by mananth(12270) on 2010-11-14 08:18:30 (Show Source):
You can put this solution on YOUR website!9x - (5x-5) = 37
First step is to remove the parenthesis
whenever there is negative sign before the parenthesis all the signs of the terms in the parenthesis become opposite.
9x-5x+5 = 37
4x+5 = 37
-5 -5
4x= 37-5
4x=32
/4
x= 8
...
m.ananth@hotmail.ca
|
Coordinate-system/370667: Here is my final question for now.
A line k passes through the points (4,2) and (-4,4. A second line h poasses through the points (-8,1) and (8, -3), is line k parallel to line h? Why or why not? (Note--parenthesis in this case do no mean multiply).
1 solutions
Answer 264245 by mananth(12270) on 2010-11-14 08:14:47 (Show Source):
You can put this solution on YOUR website!(4,2) and (-4,4. A second line h poasses through the points (-8,1) and (8, -3), is line k parallel to line h?
..
slope of line k = (4-2)/(-4-4)
=2/-8
=-1/4
..
slope of line h =(-3-1)/(8+8)
=-4/16
=-1/4
..
slopes are same so they are parallel
...
m.ananth@hotmail.ca
|
test/370648: I know this is kinda basic bt I need help reducing mixed numbers to fractions urrrrg
1 solutions
Answer 264234 by mananth(12270) on 2010-11-14 07:03:30 (Show Source):
You can put this solution on YOUR website!The steps are simple. A practical approach
..
4 1/5
..
5*4 +1 /5
=21/5
...
6 3/4
4*6+3/4
=27/4
...
3 1/9
9*3+1 /9
28/9
..
Observe the pattern and you will walk through.
...
m.ananth@hotmail.ca
|
Exponential-and-logarithmic-functions/370658: by selling a towel for rs. 126.90, a man loses 6%, for how much should he sell to gain 4%
1 solutions
Answer 264233 by mananth(12270) on 2010-11-14 06:57:32 (Show Source):
You can put this solution on YOUR website!He loses 6% on the sale
..
SP = selling price
CP = cost price
..
SP = 94 when CP = 100
SP== 126.90 CP=?
..
CP= 126.90*100/94
=135.
..
He wants 4 % profit
..
4% of 135 = (4/100)*135= Rs 5.40.
Add it to CP
135+5.40 = 139.40. will be SP
...
m.ananth@hotmail.ca
|
Exponents/370651: what is the solution on this problem??
simplify the following!
(2 raised to the power of -1 + 3 raised to the power of -1 /2 raised to the power of -1 - 3 raised to the power of -1)raised to the power of -1
please answer...
1 solutions
Answer 264232 by mananth(12270) on 2010-11-14 06:50:47 (Show Source):
|
Numbers_Word_Problems/370467: The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 10 less than three times the larger. Find the numbers.
1 solutions
Answer 264219 by mananth(12270) on 2010-11-14 04:43:55 (Show Source):
You can put this solution on YOUR website!The larger of two numbers is 8 more than twice the smaller. The sum of the numbers is 10 less than three times the larger. Find the numbers.
..
let the numbers be x & y. x is larger.
x=2y+8
x-2y=8........................1
...
x+y =3x-10
-2x+y=-10.....................2
multiply (1) by 2
2x-4y=16
add it to (2)
-2x+2x-4y+y=-10+16
-3y=6
/-3
y=-2
..
x-2y =8 from (1)
plug value of y
x-2*-2=8
x+4=8
x=8-4
x=4
...
-2, 4 are the numbers
...
m.ananth@hotmail.ca
|
Travel_Word_Problems/370470: A boat moves 9 kilometers upstream in the same amount of time it moves 17kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still water.
1 solutions
Answer 264218 by mananth(12270) on 2010-11-14 04:37:13 (Show Source):
You can put this solution on YOUR website!let rate of boat in still water be x km/h
rate of current = 9km/h..
upstream rate = x-9 km/h
downstream rate = x+9 km/h
..
upstream distance = 9 km
downstream distance = 17 km
..
time down stream = time upstream
9/(x-9)= 17/(x+9)
9(x+9)=17(x-9)
9x+81=17x-153
9x-17x=-153-81
-8x=-234
x= -234/-8
x= 29.5 km/h
...
m.ananth@hotmail.ca
|
Rate-of-work-word-problems/370611: A heating system can increase the temperature of a classroom by 3 degrees Celsius per hour. If the class room temperature is 15 degrees Celsius when the timer starts the heating system during the night, which of the following equations provides a mathematical model for the temperature after t hours.
A.Temperature= 3t-15
B. Temperature= 3t+15
C. 3t/15
D. 3t times 15
/= fraction
1 solutions
Answer 264212 by mananth(12270) on 2010-11-14 04:13:52 (Show Source):
|
Equations/370594: 3 / x^2 - 25 = 1 / x + 5 + 2 / x - 5
Solve the equation for the variable
1 solutions
Answer 264202 by mananth(12270) on 2010-11-14 02:25:05 (Show Source):
You can put this solution on YOUR website!3 / (x^2 - 25) = 1 / (x + 5) + 2 / (x - 5)
..
It is advisable that the numerator and the denominator be separated by brackets.
..
3 / (x^2 - 25) = 1(x-5)+2(x+5) / (x^2-25)
...
3 / (x^2 - 25) = 1(x-5)+2(x+5) /(x^2-25)
..
3/(x^2-25)=x-5+2x+10/(x^2-25)
..
3/(x^2-25)= 3x+5/(x^2-25)
3=3x+5
3-5=3x
-2=3x
x=-2/3
..
|
Quadratic_Equations/370628: A train travels 360km at a uniform speed. If the speed had been 5km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train
1 solutions
Answer 264194 by mananth(12270) on 2010-11-14 00:55:51 (Show Source):
You can put this solution on YOUR website!distance = 360 km
..
let speed be x
then time taken = d/r
t=360/x
..
if speed is increased by 5 km/h
speed will be (x+5)km/h
..
distance is the same
t= 360/(x+5)
..
time with original speed - time with increased speed = 1
..
360/x - 360/(x+5)=1
LCD= x(x+5)
(360(x+5)-360x) /x(x+5)=1
360x+1800-360x=x(x+5)
x^2+5x = 1800
x^2+5x-1800=0
x^2+45x-40x-1800=0
x(x+45)-40(x+45)=0
(x-40)(x+45)=0
x= 40 mph the original speed.
...
m.ananth@hotmail.ca
|
real-numbers/370610: Find a number that is 68 greater than three times its opposite
1 solutions
Answer 264193 by mananth(12270) on 2010-11-14 00:42:52 (Show Source):
You can put this solution on YOUR website!Find a number that is 68 greater than three times its opposite
..
Let the number be x
..
the opposite of this number will be (-x)
..
3 times the opposite of the number = 3*(-x)=-3x
..
add 68
we get
(-3x)+68
x = (-3x+68)
add 3x to both sides
3x+x=68
4x=68
..
divide by 4
4x/4 = 68/4
x= 17 the required number
...
m.ananth@hotmail.ca
|
|
