New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'ankor@dixie-net.com'
ankor@dixie-net.com answered: 15608 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 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829 , 13830..13859 , 13860..13889 , 13890..13919 , 13920..13949 , 13950..13979 , 13980..14009 , 14010..14039 , 14040..14069 , 14070..14099 , 14100..14129 , 14130..14159 , 14160..14189 , 14190..14219 , 14220..14249 , 14250..14279 , 14280..14309 , 14310..14339 , 14340..14369 , 14370..14399 , 14400..14429 , 14430..14459 , 14460..14489 , 14490..14519 , 14520..14549 , 14550..14579 , 14580..14609 , 14610..14639 , 14640..14669 , 14670..14699 , 14700..14729 , 14730..14759 , 14760..14789 , 14790..14819 , 14820..14849 , 14850..14879 , 14880..14909 , 14910..14939 , 14940..14969 , 14970..14999 , 15000..15029 , 15030..15059 , 15060..15089 , 15090..15119 , 15120..15149 , 15150..15179 , 15180..15209 , 15210..15239 , 15240..15269 , 15270..15299 , 15300..15329 , 15330..15359 , 15360..15389 , 15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629, >>Next
Miscellaneous_Word_Problems/749959: In the absence of air resistance, the trajectory of a cannon ball fired from ground level at 1200 feet per second and at an angle of 45o can be approximated as
y=x-1/45,000x^2
where y is the height above the ground and x is the distance from the cannon.
A. Find the vertex of the parabola described by this equation
B. What is the maximum height of the cannon ball?
C. What is the range of the cannon ball (the range is the horizontal distance to the point of impact at ground level)?
I'm a bit confused on how to find all these! Any help is appreciated thanks! 1 solutions
Answer 456273 by ankor@dixie-net.com(15623) on 2013-05-17 21:50:17 (Show Source):
You can put this solution on YOUR website!In the absence of air resistance, the trajectory of a cannon ball fired from ground level at 1200 feet per second and at an angle of 45 degrees can be approximated as
y=x-  x^2
WRite this in the standard form: y = ax^2 + bx + c
y =  x^2 + x
where y is the height above the ground and x is the distance from the cannon.
A. Find the vertex of the parabola described by this equation
Find the axis of symmetry which is x = -b/(2a)
x =  =  = +22500
:
B. What is the maximum height of the cannon ball?
Replace x with 22500 in the original equation, find y
y =  22500^2 + 22500
y = +11250 ft max height
:
C. What is the range of the cannon ball (the range is the horizontal distance to the point of impact at ground level)?
At impact, y = 0, occurs twice the value of the axis of symmetry
x = 2(22500) = 45000 ft
:
Graphically
|
Age_Word_Problems/749797: John is 5 years older than bob. Three years ago he was twice as bob. How old is john? 1 solutions
Answer 456215 by ankor@dixie-net.com(15623) on 2013-05-17 15:45:38 (Show Source):
You can put this solution on YOUR website!John is 5 years older than bob.
j = b+5
:
Three years ago he was twice as bob.
j-3 = 2(b-3)
j - 3 = 2b - 6
j = 2b - 6 + 3
j = 2b - 3
replace j with (b+5)
b + 5 = 2b - 3
5 + 3 = 2b - b
b = 8 yr is Bob's age
:
How old is john?
j = 8 +5
j = 13
:
:
Check solutions in the statement:
"Three years ago he was twice as bob."
13 - 3 = 2(8-3); confirms our answer
|
Age_Word_Problems/749305: A father is four times as old as his son and his daughter is five years younger than her brother. If their combined ages amount to 73 years, find the age of each 1 solutions
Answer 456110 by ankor@dixie-net.com(15623) on 2013-05-16 21:17:55 (Show Source):
You can put this solution on YOUR website!A father is four times as old as his son and his daughter is five years younger than her brother.
If their combined ages amount to 73 years, find the age of each
:
Let f = father's age
let s = son's age
let d = daughter's age
:
Write an equation for each statement:
:
"A father is four times as old as his son"
f = 4s
:
"his daughter is five years younger than her brother."
d = s-5
:
"their combined ages amount to 73 years,"
f + s + d = 73
replace f with 4s, replace d with (s-5)
4s + s + (s-5) = 73
6s = 73 + 5
6s = 78
s = 78/6
s = 13 yrs is son's age
:
I'll let you find f and d, check your solutions in the total age
|
Miscellaneous_Word_Problems/749662: If 3/4 of a number is 48, then what is 5/8 of that same number? I need to figure out the answer before Friday of this week so can you please help me? 1 solutions
Answer 456107 by ankor@dixie-net.com(15623) on 2013-05-16 21:09:42 (Show Source):
You can put this solution on YOUR website!If 3/4 of a number is 48, then what is 5/8 of that same number?
:
Let n = "a number"
the equation for the statement," 3/4 of a number is 48,"
 n = 48
multiply both sides by 4
3n = 4(48)
3n = 192
n = 192/3
n = 64 is the number
:
"what is 5/8 of that same number?"
 *64 =
Cancel 8 into 64
5 * 8 = 40
|
Linear_Equations_And_Systems_Word_Problems/749612: A kicker on a football team scores 1 point for making an extra point and 3 points for making a field goal. The kicker makes a total of 8 extra points and field goals in one game. He scored a total of 12 points in the game.
I have to write 2 equations representing the situation and solve them. I think I will be able to solve them but I can't come up with the equations.
1x + y =8
3x + y =12, is all I am able to come up with.
Your time is greatly appreciated. (: 1 solutions
Answer 456097 by ankor@dixie-net.com(15623) on 2013-05-16 19:38:34 (Show Source):
You can put this solution on YOUR website!A kicker on a football team scores 1 point for making an extra point and 3 points for making a field goal. The kicker makes a total of 8 extra points and field goals in one game. He scored a total of 12 points in the game.
I have to write 2 equations representing the situation and solve them. I think I will be able to solve them but I can't come up with the equations.
1x + y =8
3x + y =12
:
rewrite it to
3x + y = 12
x + y = 8
-------------Subtraction eliminates y, find x
2x = 4
x = 4/2
x = 2 field goals
I'm sure you can find the extra points
|
Linear-equations/749355: please help me with this word problem:
Two stations A and B are 90km apart and on a highway.A car starts from A and another from B at the same time.If they go in the same direction, they meet after 9 hours and if they go in opposite directions,they meet after 1 2/7 (one- two by seven hours)hours, find the speeds of both the cars. 1 solutions
Answer 456036 by ankor@dixie-net.com(15623) on 2013-05-16 15:53:53 (Show Source):
You can put this solution on YOUR website!Two stations A and B are 90km apart and on a highway.
A car starts from A and another from B at the same time.
If they go in the same direction, they meet after 9 hours and
if they go in opposite directions, they meet after 1 2/7 hours,
find the speeds of both the cars.
:
Change 1 2/7 hrs to 9/7 hrs
:
Let x = Car from A's speed
Let y = Car from B's speed
:
A distance equation when going towards each other
 x +  y = 90
multiply by 7
9x + 9y = 630
:
A distance equation when going the same direction
9x = 9y + 90
9x - 9y = 90
:
Use elimination here
9x + 9y = 630
9x - 9y = 90
---------------addition eliminates y, find x
18x = 720
x = 720/18
x = 40 km/hr speed of the Car from A
then
9(40) + 9y = 630
9y = 630 - 360
9y = 270
y = 270/9
y = 30 km/hr speed of the car from B
:
:
You can confirm this
9(40) - 9(30) = 90
|
pythagorean/749499: Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. Which of the following equations could be used to find the direct distance to her aunt's house? 1 solutions
Answer 456020 by ankor@dixie-net.com(15623) on 2013-05-16 14:38:17 (Show Source):
You can put this solution on YOUR website!Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. Which of the following equations could be used to find the direct distance?
:
This is a pythag triangle equation where the legs are 15 and 36
The direct distance (d) is the hypotenuse
:
d = 
:
|
Permutations/749386: Plz some1 help me to solve this problem:
An 8 litre cylinder contains a mixture of oxygen
and nitrogen, the volume of oxygen being 16% of
the total volume. A few litres of the mixture is
released and an equal amount of nitrogen is added.
Then the same amount of the mixture as before is
released and replaced by nitrogen for the second
time. As a result, the oxygen content becomes 9% of
the total volume. How many litres of mixture is
released each time?
1 solutions
Answer 456017 by ankor@dixie-net.com(15623) on 2013-05-16 14:33:04 (Show Source):
You can put this solution on YOUR website!An 8 litre cylinder contains a mixture of oxygen
and nitrogen, the volume of oxygen being 16% of
the total volume. A few litres of the mixture is
released and an equal amount of nitrogen is added.
Then the same amount of the mixture as before is
released and replaced by nitrogen for the second
time. As a result, the oxygen content becomes 9% of
the total volume. How many litres of mixture is
released each time?
:
let x = amt of mixture released each time, also the amt of nitrogen added
:
We know that if the mixture is 16% oxygen, it is 84% nitrogen
then 9% oxygen means we have 91% nitrogen
:
Write the decimal equation in the terms of nitrogen
.84(8-2x) + 2x = .91(8)
6.72 - 1.68x + 2x = 7.28
-1.28x + 2x = 7.28 - 6.72
.32x = .56
x = .56/.32
x = 1.75 liters of the mixture is released each time.
|
Quadratic_Equations/749246: Have a project with Angry Birds where you have to find the equation of a parabola for the bird's flight path in various situations. I have to pick a point at the origin and a pint on the x axis for the pig to be placed and find the flight path (equation). How would i do this? I chose for points:
Bird placed at (0,0)
Pig placed at (5,0)
I dont understand what to do after this please help. 1 solutions
Answer 455895 by ankor@dixie-net.com(15623) on 2013-05-15 21:16:41 (Show Source):
You can put this solution on YOUR website!Have a project with Angry Birds where you have to find the equation of a parabola for the bird's flight path in various situations.
I have to pick a point at the origin and a point on the x axis for the pig to be placed and find the flight path (equation).
How would i do this? I chose for points:
Bird placed at (0,0)
Pig placed at (5,0)
:
We need another point, 0,0 is of no use, lets choose 3,4 as a point
:
Using the form ax^2 + bx + c = y
We are using origin so we can ignore c, just find a and b
:
Write an equation for each point, find a and b
:
Point: 5,0
25a + 5b = 0
and
Point 3,4
9a + 3b = 4
:
Multiply the 1st equation by 3, the 2nd equation by 5
75a + 15b = 0
45a + 15b = 20
------------------subtraction eliminates b, find a
30a = -20
a = -20/30
a = -.67
Use the 1st equation to find b
25(-.67) + 5b = 0
-16.67 + 5b = =
5b = 16.67
b = 16.67/5
b = 3.33
:
The equation: y = -.67x^2 + 3.33x
looks like this
|
Rate-of-work-word-problems/749081: If four men working at the same rate can do 2/3 of a job in 40 minutes, how many minutes would it take one man working at this rate to do 2/5 of the job? 1 solutions
Answer 455886 by ankor@dixie-net.com(15623) on 2013-05-15 20:48:03 (Show Source):
You can put this solution on YOUR website!If four men working at the same rate can do 2/3 of a job in 40 minutes,
then the number of minutes (m)to complete the job is:
 m = 40
2m = 3 * 40
2m = 120
m = 60 min for four men to do the job
therefore
4 * 60 = 240 man-minutes to do the job
:
how many minutes would it take one man working at this rate to do 2/5 of the job?
1m =  *240
1m = 96 minutes for 1 man to do 2/5 of the job
|
Travel_Word_Problems/749075: Two runners start running at the same time from the start/finish line of a 400 meter oval track. One runner runs laps of 1 minute 15 seconds and the other runs laps of 1 minute 45 seconds. How long will it be before the runners cross the finish line at the same time? 1 solutions
Answer 455786 by ankor@dixie-net.com(15623) on 2013-05-15 16:22:27 (Show Source):
You can put this solution on YOUR website!Two runners start running at the same time from the start/finish line of a 400 meter oval track.
One runner runs laps of 1 minute 15 seconds and the other runs laps of 1 minute 45 seconds.
How long will it be before the runners cross the finish line at the same time?
:
Change the times to seconds:
Runner one laps in 75 sec
Runner two laps in 105 sec
:
Find the least common multiple of 75 and 105 by prime factoring.
75: 3*5*5
105: 3*7*5
LCM: 3*5*5*7 = 525 seconds they will cross the finish line at the same time
(That's 8 min 45 sec)
:
Runner one completes exactly 525/75 = 7 laps
Runner two completes exactly 525/105 = 5 laps
|
Equations/748833: Its been WAY too long since I did algebra. Trying to help my son with an equation but I just cannot remember how this stuff works...
what is the simplest form of x+3 over x3-x2-6x divided by x2-9 over x2+x-12?
Little help, please? 1 solutions
Answer 455655 by ankor@dixie-net.com(15623) on 2013-05-14 21:51:40 (Show Source):
You can put this solution on YOUR website!what is the simplest form of:

-------------

:
Remember when you divide fractions, invert the dividing fraction and Multiply
 * 
:
Factor as much as we can
 * 
:
the first denominator can be factored again
 * 
:
Cancel x+3 and x-3, in the 2nd denominator
 * (x+4) =  ; about all you can do with it.
:
:
It's not an equation, expressions are what they are
|
Systems-of-equations/748794: Solve the given nonlinear system by the addition method.
4x^2–2y^2= –2
x^2+4y^2=40
Please show me the steps. thank you so much!! 1 solutions
Answer 455654 by ankor@dixie-net.com(15623) on 2013-05-14 21:32:56 (Show Source):
You can put this solution on YOUR website!Solve the given nonlinear system by the addition method.
4x^2 – 2y^2= –2
x^2 + 4y^2 = 40
:
Multiply the 1st equation by 2, add to the 2nd equation
8x^2 – 4y^2= –4
x^2 + 4y^2 = 40
--------------------Addition eliminates y^2, find x^2
9x^2 = 36
divide both sides by 9
x^2 = 4
x = +/- 
x = +2,
x = -2
:
Find y using the 2nd equation, we know x^2 = 4
4 + 4y^2 = 40
4y^2 = 40 - 4
4y^2 = 36
divide both sides by 4
y^2 = 9
y = +/- 
y = +3
y = -3
:
Check our solutions in the 1st equation
4(4) - 2(9) = -2
|
Geometry_Word_Problems/748721: Carl is making a rectangular dog run. He has 36 one yard sections of fence that he plans to use to keep his dog inside. He wants the run to be as long as possible. what is the longest whole-number length he can use for the run?
Thank you for your help as I am unable to assist my daughter with this question. 1 solutions
Answer 455648 by ankor@dixie-net.com(15623) on 2013-05-14 21:13:08 (Show Source):
You can put this solution on YOUR website! Carl is making a rectangular dog run. He has 36 one yard sections of fence that he plans to use to keep his dog inside. He wants the run to be as long as possible. what is the longest whole-number length he can use for the run?
:
Assuming the run will be 1 section wide at each end.
That leaves 34 ea 1 yard sections for the lengths
He needs two sides of: 34/2 = 17 sections in the length
:
Check by finding the perimeter: 17 + 1 + 17 + 1 = 36 sections
|
Rate-of-work-word-problems/748787: Tiburcio can paint a certain room in 1 day. His daughter Alma can paint it in 2 days. After Tiburcio has been working for several hours, his daughter helped him and together they finished the job in 3 hours. How many hours did Tiburcio work alone? Assume an 8-hour working day. 1 solutions
Answer 455646 by ankor@dixie-net.com(15623) on 2013-05-14 21:02:50 (Show Source):
You can put this solution on YOUR website!Tiburcio can paint a certain room in 1 day.
His daughter Alma can paint it in 2 days.
After Tiburcio has been working for several hours, his daughter helped him and together they finished the job in 3 hours.
How many hours did Tiburcio work alone?
Assume an 8-hour working day.
:
Let t = time that Ti worked alone
Let the completed job = 1 (a painted room)
:
A shared work equation, (time in hrs)
 +  = 1
multiply by 16, cancel the denominators, resulting in:
2(t+3) + 3 = 16
2t + 6 + 3 = 16
2t = 16 - 9
2t = 7
t = 7/2
t = 3.5 hrs worked by Ti alone
:
:
See if that checks out on a calc:
 +  =
.8125 + .1875 = 1
|
Age_Word_Problems/748520: The average age of a board of 10 advisors of a company is the same as it was 3 year back on account of the replacement of one of the older advisors by younger men.what is the difference between older and younger man? 1 solutions
Answer 455639 by ankor@dixie-net.com(15623) on 2013-05-14 20:02:11 (Show Source):
You can put this solution on YOUR website!The average age of a board of 10 advisors of a company is the same as it was 3
year back on account of the replacement of one of the older advisors by younger men.
what is the difference between older and younger man?
:
Let a = the average age
:
let y = age of the younger man
:
 = 
multiply both sides by 10
10a - 30 = 9a + y
10a - 9a = y + 30
a = y + 30
:
30 years between older and younger man
|
logarithm/748328: express in terms of logarithms of A,B and c: log(a to the 3 power times B divided b the square root of c)
I need to know what steps to take to get the answer. Thank you! 1 solutions
Answer 455506 by ankor@dixie-net.com(15623) on 2013-05-14 07:54:23 (Show Source):
You can put this solution on YOUR website!express in terms of logarithms of A,B and c:
log(a to the 3 power times B divided by the square root of c)

:

Can also be written
3*log(A) + log(B) -  log(c)
|
Age_Word_Problems/748158: Crisner is 3 years older than her niece Josephine. In 7 years she will be six seventh of her age. How old are they? 1 solutions
Answer 455473 by ankor@dixie-net.com(15623) on 2013-05-13 21:46:55 (Show Source):
You can put this solution on YOUR website!): Crisner is 3 years older than her niece Josephine.
In 7 years she will be six seventh of her age.
How old are they?
:
Let c = C's age now
Let j = J's age
;
Write an equation for each statement
:
"): Crisner is 3 years older than her niece Josephine."
c = j + 3
:
"In 7 years she will be six seventh of her age."
j + 7 =  (c+7)
Get rid of that annoying fraction, mult both sides by 7
7(j+7) = 6(c+7)
7j + 49 = 6c + 42
7j = 6c + 42 - 49
7j = 6c - 7
replace c with (j+3) from the 1st statement
7j = 6(j+3) - 7
7j = 6j + 18 - 7
7j - 6j = 11
j = 11 yrs is J's age
then
11 + 3 = 14 yrs is C's age
;
;
see if that works
j + 7 =  (c+7)
11 + 7 =  (14+7)
18 =  (21)
7 cancels into 21
18 = 6(3)
|
Systems-of-equations/747750: Meenakshi: ‘How old are you ,Mom’
Mom: ‘Let me think, Meenakshi, well our three ages add up exactly seventy years’
Meenakshi: That it a lot, is not it? And how old are you Dad?
Dad: Just Six times as old as you, my daughter.
Meenu: Shall I ever be half as old as you, Dad?
Dad: ‘Yes , Meenakshi, when that happens our three ages will add up to exactly twice as much as today’
1 solutions
Answer 455263 by ankor@dixie-net.com(15623) on 2013-05-12 21:25:52 (Show Source):
You can put this solution on YOUR website!This problem will not solve with given values, I am going to change it so it does.
:
Meenakshi: ‘How old are you ,Mom’
Mom: ‘Let me think, Meenakshi, well our three ages add up exactly seventy-two years’
Meenakshi: That it a lot, is not it? And how old are you Dad?
Dad: Just Six times as old as you, my daughter.
Meenu: Shall I ever be half as old as you, Dad?
Dad: ‘Yes , Meenakshi, when that happens our three ages will add up to exactly twice as much as today’
:
Let m = Mom's present age
Let n = Meena's age
Let d = Dad's age
:
Write an equation for each statement
:
" our three ages add up exactly seventy-two years’"
m + n + d = 72
:
"Dad: Just Six times as old as you, my daughter."
d = 6n
:
"Shall I ever be half as old as you, Dad. when that happens our three ages will add up to exactly twice as much as today’
:
From this statement we know that the total of the 3 people increases by 72 yrs
Therefore each person's age has to increase by 72/3 = 24 yrs
now the equation is:
d + 24 = 2(n+24)
d + 24 = 2n + 48
d = 2n + 48 - 24
d = 2n + 24
Replace d with 6n
6n = 2n + 24
6n - 2n = 24
4n = 24
n = 24/4
n = 6 yrs old is Meena's present age
then
6(6) = 36 yrs is Dad's age
and
6 + 36 + m = 72
m = 72 - 42
m = 30 yrs is Mom's present age
:
:
Check: 36 + 30 + 6 = 72
|
Graphs/747569: Complete the square as an aid in graphing: y = x^2 + 4x - 2
After completed the square, graph the parabola.
Please show all work so I can understand.
1 solutions
Answer 455057 by ankor@dixie-net.com(15623) on 2013-05-11 21:21:51 (Show Source):
You can put this solution on YOUR website!Complete the square as an aid in graphing: y = x^2 + 4x - 2
Subtract 2 from both sides
x^2 + 4x + ___ = 2
Find the value that completes the square.
This is half of coefficient of x, squared, therefore 2^2 = 4, add to both sides
x^2 + 4x + 4 = 2 + 4
x^2 + 4x + 4 = 6
Which is
(x+2)^2 = 6
Find the square root of both sides
x + 2 = +/- 
Two solutions
x = -2 -  ; about -4.45
and
x = -2 -  ; about +.45
:
After completed the square, graph the parabola.
we know the parabola crosses the x axis at +.45 and -4.45, looks like this
|
Travel_Word_Problems/747566: Albert raced 4 tims as fast as Bernhard. In fact, Albert raced 48 miles in 3 hours less than it took Bernhard to race 30 miles. How fast did each of them race? What were the times of each racer? 1 solutions
Answer 455051 by ankor@dixie-net.com(15623) on 2013-05-11 20:04:37 (Show Source):
You can put this solution on YOUR website!Albert raced 4 times as fast as Bernhard.
In fact, Albert raced 48 miles in 3 hours less than it took Bernhard to race 30 miles.
How fast did each of them race?
What were the times of each racer?
:
Let s = B's racing speed
then
4s = A's speed
:
Write a time equation; time = dist/speed
:
B's time - A's time = 3 hrs
 -  = 3
mult by 4s to clear denominators, resulting in:
4(30) - 48 = 3(4s)
120 - 48 = 12s
72 = 12s
s = 72/12
s = 6 mph, is B's speed
then
4(6) = 24 mph is A's speed
:
Their times
30/6 = 5 hrs for B
48/24 = 2 hrs for A
--------------------
differs: 3 hrs
|
Volume/747248: the dimensions of the larger balloon is twice those of the smaller balloon. if the volume of the smaller balloon is 50 cubic inches, what is the volume of the larger balloon? 1 solutions
Answer 454952 by ankor@dixie-net.com(15623) on 2013-05-11 08:30:50 (Show Source):
You can put this solution on YOUR website!the dimensions of the larger balloon is twice those of the smaller balloon.
if the volume of the smaller balloon is 50 cubic inches, what is the volume of the larger balloon?
:
Find the ratio of the volumes of the two balloons
:
 
-----------
 
:
 
-----------
 
Cancel like terms and we are left with

Volume of the larger balloon: 8 * 50 = 400 cu/in
|
logarithm/747473: Hi tutors,
I have a log question which I'm sure is pretty simple, except to me.
Solve this equation for x. log base3 x =1.1
When they ask for this, am I looking for an actual answer or putting it into exponential form?
Thanks for your assistance and explanations. 1 solutions
Answer 454944 by ankor@dixie-net.com(15623) on 2013-05-11 07:42:08 (Show Source):
|
�t�e�s�t/747477: 1296 plants are to be planted in a garden in such a way that each row contains as may plants as is the number of rows.Find the number of rows and the number of rows and the number of plants in each row. 1 solutions
Answer 454943 by ankor@dixie-net.com(15623) on 2013-05-11 07:36:06 (Show Source):
You can put this solution on YOUR website!1296 plants are to be planted in a garden in such a way that each row contains as many plants as is the number of rows.
Find the number of rows and the number of plants in each row.
:
 = 36 rows, 36 plants in each row
|
Numbers_Word_Problems/747275: When 8 is added to the number that is produced by doubling the number x, the result is equal to 8 times the number that is 5 less than x. What is the value of x? 1 solutions
Answer 454942 by ankor@dixie-net.com(15623) on 2013-05-11 07:32:06 (Show Source):
You can put this solution on YOUR website!When 8 is added to the number that is produced by doubling the number x,
the result is equal to 8 times the number that is 5 less than x.
What is the value of x?
;
2x + 8 = 8(x-5)
|
|