New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'fractalier'
fractalier answered: 2101 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, >>Next
expressions/39538: Simply each of the following expressions where possible (pg. 150)
I can't really type it out on my computer but the numbers are on the left side of the letter.
6x2y3 + 9x2y3
________________________________
3x2y2
1 solutions
Answer 24995 by fractalier(2101)   on 2006-05-26 12:24:27 (Show Source):
You can put this solution on YOUR website!From
(6x^2y^3 + 9x^2y^3) / 3x^2y^2
we can combine the numerator and cancel where we can...we get
(6x^2y^3 + 9x^2y^3) / 3x^2y^2 =
15x^2y^3 / 3x^2y^2 =
5y
|
Equations/39428: 2y/x^2+2x+1 + x/x^2-1
1 solutions
Answer 24993 by fractalier(2101) on 2006-05-26 12:21:56 (Show Source):
You can put this solution on YOUR website!We factor denominators first and get
2y/x^2+2x+1 + x/x^2-1 =
2y / (x+1)^2 + x / (x+1)(x-1)
The lowest common denominator is then
(x-1)(x+1)^2
We convert both fractions to that denominator and combine and get
2y / (x+1)^2 + x / (x+1)(x-1) =
2y(x-1) / (x-1)(x+1)^2 + x(x+1) / (x-1)(x+1)^2 =
[2y(x-1) + x(x+1)] / (x-1)(x+1)^2 =
No further significant simplification can be done...
|
Rational-functions/39541: The cost of producing a number of items x is given by C=mx+b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).
(a) if the fixed cost is $40 and the variable cost is $10, write the cost equation.
(b) Graph the cost equation
1 solutions
Answer 24991 by fractalier(2101) on 2006-05-26 12:17:15 (Show Source):
You can put this solution on YOUR website!To get the cost equation, just plug in for m and b to get
C = 10x + 40
To graph it, go to the point (0, 40) and plot a point.
From that point, we have a slope of 10. We go up 10 and over 1, and plot another point. Then draw a line thru the points.
|
logarithm/39444: Solve 2/3^2x = 12.
1 solutions
Answer 24977 by fractalier(2101) on 2006-05-26 10:28:06 (Show Source):
You can put this solution on YOUR website!It is not clear exactly what the problem is but I assume you mean
2 / (3^2x) = 12
I will show you this one...if you meant something else, please repost...
Okay, from
2 / (3^2x) = 12
we can rearrange the terms and get
3^2x = 2/12 = 1/6
take the log of both sides
log 3^2x = log 1/6
now use the power rule
2x log 3 = - log 6
and
x = (- log 6) / (2 log 3)
|
Equations/39470: Solve each equation. identify each equation as a conditional equation, an inconsistent equation, or an identity.
1/2b - 1/2=1/4b
1 solutions
Answer 24976 by fractalier(2101) on 2006-05-26 10:22:40 (Show Source):
You can put this solution on YOUR website!Let us multiply all by 4b to clear the fractions, so we get
1/2b - 1/2 = 1/4b
4b[1/2b - 1/2 = 1/4b]
2 - 2b = 1
now subtract 2, then divide by -2 and get
-2b = -1
b = 1/2
Must be a conditional equation, since an inconsistent equation has no solution, and an identity has an infinite number of solutions...
|
Sequences-and-series/39510: write out the term of the geometric sequence that satisfies the given conditions.
a1=-9,r=-9/10,n=5
1 solutions
Answer 24975 by fractalier(2101) on 2006-05-26 10:16:53 (Show Source):
You can put this solution on YOUR website!Okay, our first tern is -9. After that, we just multiply each term by the common ratio, which is in this case -9/10, until we get 5 terms...so we get
-9
81/10
-729/100
6561/1000
-59049/10000
|
absolute-value/39535: One of our sample problems is.. and i'm lost:
Identify the property that is used
5 (6+7)=5+ (7+6)
1 solutions
Answer 24973 by fractalier(2101) on 2006-05-26 10:10:44 (Show Source):
You can put this solution on YOUR website!I imagine that you meant to write
5 + (6 + 7) = 5 + (7 + 6)
If that is the case, then we are demonstrating the commutative property of addition, a property which states that order doesn't matter when we add numbers...
|
Geometric_formulas/39514: The quotient when 3 more than a number is divided by less than that same number
Write each of the following geometric expressions using the given symbols
If you can please help me.I got this problem wrong,and I would like to know how to do it correct. Thank you
1 solutions
Answer 24971 by fractalier(2101) on 2006-05-26 10:06:35 (Show Source):
|
Length-and-distance/39533: The quotient when 3 more than a number is divided by 3 less than that same number. Write each of the following geometric expressions using the given symbols
1 solutions
Answer 24969 by fractalier(2101) on 2006-05-26 10:03:41 (Show Source):
|
Equations/39515: It is estimated that the Earth is losing 4000 species of plants and animals per year. If S represents the number of species living last year year, how many species are on Earth this year..
1 solutions
Answer 24966 by fractalier(2101) on 2006-05-26 10:00:49 (Show Source):
|
Functions/39517: It is estimated that the Earth is losing 4000 species of plants and animals per year. If S represents the number of species living last year year, how many species are on Earth this year..
1 solutions
Answer 24965 by fractalier(2101) on 2006-05-26 09:57:57 (Show Source):
You can put this solution on YOUR website!Look at it this way...
No matter how many species there were last year, you would be subtracting 4000 to get this year's number...if there were 90,000 last year, you'd have 86,000 this year...
Thus if there were S species last year, there would be S - 4000 this year...
|
Travel_Word_Problems/39529: Suppose that the tempature outside is dropping at a constant rate.At noon, the tempature is 70 F,and it drops to 58F at 5pm ..How much did the tempature change each hour?
I thought it was half hour ,but i was wrong.Sorry the 5 did not come up in my other post.
1 solutions
Answer 24963 by fractalier(2101) on 2006-05-26 09:55:13 (Show Source):
You can put this solution on YOUR website!Well, we can logic it out...
If the temperature drops from 70 to 58, it dropped 12 degrees.
If it took 5 hours, then we divide 12 degress by 5 hours, and get
12 / 5 = 2.4 degrees per hour
We can look at it another way too...
(70 - 58) / (5 - 0) = 2.4
|
Inequalities/39527: This question is from textbook
Fill in the chart given this linear equation:
2x + y = 42.
x y
-2
-1
0
1
2
1 solutions
Answer 24962 by fractalier(2101) on 2006-05-26 09:51:53 (Show Source):
You can put this solution on YOUR website!To fill in these values, merely substitute the various x's into the equation and determine the y's...
2x + y = 42
x_____y
-2____46
-1____44
0_____42
1_____40
2_____38
See the pattern? Linear equations are always like this...
|
Rational-functions/39438: what's the answer to this problem? 10y2+15y divded by 35y2-5y
(the 2's beside the y's mean the y's are squared)
1 solutions
Answer 24881 by fractalier(2101) on 2006-05-25 17:59:42 (Show Source):
You can put this solution on YOUR website!(10y^2 + 15y) / (35y^2 - 5y)
we can factor both and get
(10y^2 + 15y) / (35y^2 - 5y) =
5y(2y + 3) / 5y(7y - 1)
now notice the 5y's cancel, leaving us
(2y + 3) / (7y - 1)
|
Polynomials-and-rational-expressions/39451: how do you rationalize(sqrt x+5)-3/ x-4?
1 solutions
Answer 24880 by fractalier(2101) on 2006-05-25 17:57:36 (Show Source):
You can put this solution on YOUR website!Normally when we use the term rationalize, it usually refers to a denominator that is irrational or complex, but the way you have given the expression,
(sqrt x+5)-3/ x-4
it appears that the numerator is irrational. This is acceptable the way it is.
If we try to rationalize it, the denominator will become irrational and unacceptable.
|
Travel_Word_Problems/39410: A cyclist rode 1 mile in 3 minutes with the wind and returned in 4 minutes against the wind. Find his speed without the wind.
1 solutions
Answer 24867 by fractalier(2101) on 2006-05-25 13:39:59 (Show Source):
You can put this solution on YOUR website!The equation we use in these problems is D = RT, distance = rate times time.
With the wind, D = 1, T = 3 and his rate is R + w, w being the wind.
Against it, D = 1, T = 4, and his rate is R - w.
So we have
3(R + w) = 1
4(R - w) = 1
from which we get
(R + w) = 1/3
(R - w) = 1/4
adding equations we get
2R = 7/12
and
R = 7/24 miles per minute = 60(7/24) = 17.5 miles per hour
|
|
