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Earlsdon answered: 6281 problems
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4^x+1=64 Where appropriate, include approximations to the nearest thousandth.
1 solutions
Answer 11146 by Earlsdon(6287)   on 2005-12-15 21:11:14 (Show Source):
You can put this solution on YOUR website!I assume that the use of logarithms is expected.
 Subtract 1 from both sides of the equation.
 Take the log of both sides.
 Divide both sides by 
 You can do this on your calculator or use a table of logarithms.
 to the nearest thousandth.
Check:
 = 64.031
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Numeric_Fractions/22793: I am trying to explain an answer to my son but I am having a hard time rememberng this from high school. The problem is:
.13 where the 3 goes on for infinity
He is to put the number in a fraction form
I thought it would be just 13/100 but I recall in his book last night (he didn't bring the book home tonight) that you multiply by 100 then subtract one so the answer would be something like 13/99?
Help....
1 solutions
Answer 11145 by Earlsdon(6287) on 2005-12-15 20:58:57 (Show Source):
You can put this solution on YOUR website!Here's how you do these: To convert repeating decimals to an equivalent fraction, isolate the repeating group as an integer, in this case, the repeating group is .13, using the following technique:
Let:
n = 0.131313...Now multiply n by 100 to isolate the repeating group of .13
100n = 13.131313... Subtract n from 100n = 99n.
99n = 13.131313 -0.131313 = 13
So, 99n = 13 Divide both sides by 99
n = 13/99 but n is 0.131313...
So, 0.131313... = 13/99 Check this out on your calculator.
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Linear_Equations_And_Systems_Word_Problems/22761: I ran into this in an old math textbook. Any solvers?
. One man and two boys can do in 12 days certain work that could be done in 6 days by three men and one boy. How long would it take one man to do it?
1 solutions
Answer 11144 by Earlsdon(6287) on 2005-12-15 20:48:53 (Show Source):
You can put this solution on YOUR website!Let M = one man and B = 1 boy.
If one man plus two boys can do the work in 12 days, then they can do 1/12 of the work in 1 day.
If three men and a boy can do the work in 6 days, then they can do 1/6 of the work in 1 day.
So we can write, for one day's work:
 and
To find out how much of the work can be done in 1 day by 1 man (M), solve this system of equations for M:
Rewrite the second equation as  and substitute into the first equation.
 Simplify and solve for M.
 Subtract 1/3 (= 4/12) from both sides of the equation.
 Divide both sides by -5.
 Simplify.
 This means that 1 man can do 1/20 of the work in 1 day. Therefore, it will take 1 man 20 days to do the entire job.
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logarithm/22747: I need help figuring out which way to proceed to solve this problem.
log2(x-2) +5 = 8- log2 4. The 2 is the base of the log. I think I should rewrite as log2(x-2) + log2 4 = 3 What is the correct way. I think answer is
4(x-2) =2^3 x=4
Thanks
1 solutions
Answer 11136 by Earlsdon(6287) on 2005-12-15 17:50:23 (Show Source):
You can put this solution on YOUR website!Your first step is flawless!
 Now apply the Product Rule for logarithms: 
 = 3 Simplify.
 Rewrite this in exponential form:  means 
 Simplify and solve for x.
 Add 8 to both sides.
 Divide both sides by 4.
Check: You could use your calculator but most likely it doesn't have logs to base 2. So, you can change the base of logs from 2 to base 10, which your calculator most-likely can handle.
Change of base from 2 to 10:  Apply this to your problem:
 Substitute x = 4.
 Use your calculator.
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Human-and-algebraic-language/22620: I cannot find a place that explains how to do this problem,any help would be appreciated.
Angles A and B are supplementary angles because their sum is 180 degrees. The measure of angle A is ten less than 4 times the measure of angle B. Find the measure of angle B?
1. 45 degrees
2. 38 degrees
3. 142 degrees
4. 36 degrees
1 solutions
Answer 11124 by Earlsdon(6287) on 2005-12-15 12:12:03 (Show Source):
You can put this solution on YOUR website!Start with A + B = 180 degrees (A means...the measure of angle A)
A = 4B-10 "The measure of angle A is (=) 4 times the measure of angle B (4B) less 10 degrees (-10)". Substitute this equation for A into the above equation for A + B = 180.
(4B-10) + B = 180 Simplify and solve for B
5B - 10 = 180 Add 10 to both sides.
5B = 190 Divide both sides by 5.
B = 38 degrees.
Check:
A = 4(38)-10 = 152 - 10 = 142 degrees.
A + B = 142 + 38 = 180 degrees.
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Functions/22731: I need to see if I got this answer correct. -3xtothe 1/4power (y1/2power) (-2x1/2power y1/3 power) i got x5power y2power x0.49? help me
1 solutions
Answer 11122 by Earlsdon(6287) on 2005-12-15 11:58:37 (Show Source):
You can put this solution on YOUR website!Let's see if I have this right!
Evaluate:
 Simplify.
 Remember: Add the exponents of x and add the exponents of y.
 It's a little hard to read but this is:
6(x to the 3/4 power)(y to the 5/6 power)
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Miscellaneous_Word_Problems/22738: PLease Help!
Larry can destroy a room in 30 minutes, moe can destroy the same room in 40 minutes, but curly can destrot the room in 20 minutes. "working" together how long will it take them to destroy the poor room?
1 solutions
Answer 11120 by Earlsdon(6287) on 2005-12-15 11:45:06 (Show Source):
You can put this solution on YOUR website!Try this:
If Larry can destroy the room in 30 minutes, he can destroy 1/30 of the room in 1 minute.
If Moe can destroy the room in 40 minutes, he can destroy 1/40 of the room in 1 minute.
If Curly can destroy the room in 20 minutes, he can destroy 1/20 of the room in 1 minute.
So, together, they can destroy  of the room in 1 minute.
Therefore, it will take them  minutes to destroy the room working together.
minutes = 9 minutes and 13.8 seconds.
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Polynomials-and-rational-expressions/22734: it says to calculate the problem
and i have no idea what to do. please help!
-8 - (-2) =
1 solutions
Answer 11118 by Earlsdon(6287) on 2005-12-15 11:36:44 (Show Source):
You can put this solution on YOUR website!Evalute  :
Remember, to subtract (-) an integer (-2), you add (+) its additive inverse (that's 2).
And to add two integers with different signs (-8 + 2), you subtract the smaller absolute value from the larger absolute value (|-8| - |+2| = 8 - 2 = 6) and the result takes the sign of the larger absolute value (-8 = negative}.
 = -6
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Square-cubic-other-roots/22740: SOlve by completing the square
x^2 - 6 - 5 = 0
1 solutions
Answer 11117 by Earlsdon(6287) on 2005-12-15 11:24:02 (Show Source):
You can put this solution on YOUR website!Solve by completing the square: I think you have a typo here: -6 should be -6x
 Add 5 to both sides.
 Add the square of half the x-coefficient, that's  to both sides.
 Factor the left side of the equation.
 Take the square root of both sides then add 3 to both sides.
The roots are:
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Coordinate-system/22741: What is the formula for finding the length of the segment represented by two vertices on a cooordinate plane?
1 solutions
Answer 11116 by Earlsdon(6287) on 2005-12-15 11:13:14 (Show Source):
You can put this solution on YOUR website!Given two points on a Cartesian coordinate plane with coordiates of (x1, y1) and (x2, y2), the distance between them is given by: 
You can easily see this by constructing a right triangle in which the hypotenuse is the line between the two points, then using the Pythagorean theorem to find the length of the hypotenuse (the distance between the two points).
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Mixture_Word_Problems/22706: How many 80% alcohol solution must be mixed with 40 gallons of a 13% solution to obtain a solution that is 70% alcohol?
1 solutions
Answer 11092 by Earlsdon(6287) on 2005-12-14 21:25:45 (Show Source):
You can put this solution on YOUR website!Let x = the number of gallons of 80% alcohol solution that are required to be mixed with 40 gallons of a 13% alcohol solution to obtain 40+x gallons of 70% alcohol solurtion. You can write the equation, after changing the percentages to their decimal equivalents:
 Simplify and solve for x.
 Subtract 0.7x from both sides of the equation.
 Subtract 5.2 from both sides.
 Finally, divide boths sides by 0.1
 gallons.
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Mixture_Word_Problems/22542: I really need help for this problem!
The capacity of an automobile cooling system is 16 quarts. It is half full of a 15% antifreeze solution. The owner is adding 2 gallons (another 8 qts.) of a 90% solution. When he is finished, what will the solution's percentage be?
Any help would be greatly appreciated!
1 solutions
Answer 11017 by Earlsdon(6287) on 2005-12-13 23:06:32 (Show Source):
You can put this solution on YOUR website!Let x = the percentage of antifreeze in the 16 qts of coolant after the addition of the 8 qts of 90% solution. You can write the following equation after changing the percentages to their equvalent decimal values:
 Simplify and solve for x.
 Divide both sides by 16.
 Now change the decimal to a percent.
 %
The final solution will be 52.5% antifreeze.
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Polynomials-and-rational-expressions/22569: My homework is on factoring trinommials and i dont understand it. one problem i have is (the 2 after the b is squared like i dont know how to square it on here): b2+20b+36=0 and i dont know what to do.
1 solutions
Answer 11015 by Earlsdon(6287) on 2005-12-13 22:34:11 (Show Source):
You can put this solution on YOUR website!Factoring trinomials.
N.B. You can indicate a square by using the caret (^), thus...x^2 = x-squared.
Example, factor:
When you factor a trinomial such as the one above, you are looking for two binomials that will look like this: (b + m)(b + n) and when you multiply these binomial factors, you will get back the trinomial you started with.
 So, what are m and n and how do you find them?
Let's multiply the two binomials (b + m)(b + n) and compare the result with the original trinomial.
 Simplify.
 compare this with:
You can see that for these two trinomials to be equal, then (m+n) = 20 and mn = 36. That is, you are looking for two integers whose sum is 20 and whose product is 36. Let's try some examples:
4 X 9 = 36 and 4 + 9 = 13 No good!
6 X 6 = 36 and 6 + 6 = 12 No good!
2 X 18 = 36 and 2 + 18 = 20 Bingo! So, m = 2 and n = 18
So, mn = 2(18) = 36 and m+n = 2+18 = 20
Now you can write your two binomial factors (b + m)(b + n) as:
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Functions/22507: Find the slope of the graph of the linear function of f
f(6) = -1, F(3)=8 I know the answer (-3) I just don't know how to get it.
1 solutions
Answer 10958 by Earlsdon(6287) on 2005-12-13 11:00:10 (Show Source):
You can put this solution on YOUR website!Try this:
Start with the slope-intercept form.
f(x) = mx+b Now write two equations using the given data.
f(6) = m(6)+b = -1
f(3) = m(3)+b = 8 Solve this system of equations by subtracting one from the other to find the slope, m.
6m + b = -1
-(3m + b = 8)
----------
3m = -9 Divide both sides by 3
m = -3
The slope is -3.
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Equations/22349: My son needs your help in solving this problem.
Find the solution set for the system of equations
3X + 2Y = 3
-5X + Y = 8
Thanks
1 solutions
Answer 10835 by Earlsdon(6287) on 2005-12-11 22:36:03 (Show Source):
You can put this solution on YOUR website!Solve the system of equations:
1) 3x + 2y = 3
2) -5x + y = 8 Multiply equation 2) by 2 then subtract equation 1) from the result and solve for x.
2) -10y + 2y = 16
1) -(3x + 2y = 3)
-----------------
3) -13x = 13 Divide both sides by -13
x = -1 Now substitute this into equation 1) and solve for y.
1) 3(-1) + 2y = 3
-3 + 2y = 3 Add 3 to both sides.
2y = 6 Divide both sides by 2.
y = 3
Solution: (-1, 3)
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Polynomials-and-rational-expressions/22131: Factor the polynomial as the product of factors that are irreducible over the real numbers. Then write the polynomial in completely factored form involving complex nonreal, or imaginary numbers.
x to the 4th power + 7x to the second power - 18
1 solutions
Answer 10811 by Earlsdon(6287) on 2005-12-11 13:11:54 (Show Source):
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Graphs/22293: I do not know if this is in the right category but...
the question is- Find the equation of the line that has a y-intercept of 3 and a slope of 0
{thanks alot}
1 solutions
Answer 10808 by Earlsdon(6287) on 2005-12-11 12:56:30 (Show Source):
You can put this solution on YOUR website!First, a slope of 0 means that the line is horizontal.
The slope-intercept form of the equation is:  where m is the slope and b is the y-intercept.
Since m = 0 and b = 3, just substitute these values into the general form.
 or
See the graph of this line below:
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