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Earlsdon answered: 4900 problems
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Exponential-and-logarithmic-functions/240900: how do you solve e^x+7=98?
1 solutions
Answer 176486 by Earlsdon(4900)   on 2009-11-19 19:26:09 (Show Source):
You can put this solution on YOUR website!Solve:
1)  or is it
2)  ?
If it's 1) then subtract 7 from both sides.
 Take the natural log of both sides.
 Apply the power rule to the left side.
 Substitute 
 Evaluate.
Check:
 =  almost 98.
If it's 2) then take the natural log of both sides.
 Apply the power rule to the left side.
 Substitute
 Evaluate the right side.
 Subtract 7 from both sides.
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Quadratic_Equations/240910: x^4+10x^2+9=0
solve as quadratic function?
my assumption is
x^2=-1 and x^2=-9
which there is no real solution but i dont think i am right
1 solutions
Answer 176467 by Earlsdon(4900) on 2009-11-19 19:00:08 (Show Source):
You can put this solution on YOUR website!Solve:
 Rewrite this as:
 Factor.
 Apply the zero product rule.
 or  so...
If then  so  or 
If then  so  or 
These answers can be written as: (Note:  )
You are correct in stating that there are no REAL solutions, the solutions are complex.
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Equations/238988: Subtract.
3x^4 + 4x^3 + 7
- (x^4 - 2x^3 - x^2 - 9x)
____________________
Very confused here, thank you
1 solutions
Answer 175565 by Earlsdon(4900) on 2009-11-15 11:02:06 (Show Source):
You can put this solution on YOUR website!Subtract:
 It would be helpful to group the like-terms together but first, remove the parentheses and be sure to change the sign of each term inside the parentheses:
 Now group the like-terms.
 Now add or subtract the terms as indicated:
The solution is:
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Equations/238989: Lee worked 22 hours this week and made $132. Off show work 15 hours next week ast the same pay rate, how many much she make?
1 solutions
Answer 175564 by Earlsdon(4900) on 2009-11-15 10:51:57 (Show Source):
You can put this solution on YOUR website!If Lee earned $132.00 for 22 hours of work, you can find her hourly rate by dividing the amount she earned by the number of hours she worked:
$132/22hrs. = $6/hr.
If she works for 15 hours at the same pay rate, she will earn:
($6)X(15hrs) = $90.00
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Pythagorean-theorem/238960: The sum of the squares of the lengths of the three sides of a right triangle is 300 cm2. How many cm are in the length of the hypotenuse? Express you answer in simplest radical form.
1 solutions
Answer 175563 by Earlsdon(4900) on 2009-11-15 10:44:53 (Show Source):
You can put this solution on YOUR website!You can start with the Pythagorean theorem:
1)  and ...
2)  "The sum of the squares of the lengths of the three sides of a right triangle is 300 sq.cm."
Solve equation 2) for 
2a)  Substitute 
2b)  Add to both sides.
2c)  Divide both sides by 2.
2d)  Take the square root of both sides.
2e)  Simplify, noting that  .
2f)  cm.
The length of the hypotenuse is  cm.
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Polynomials-and-rational-expressions/238957: An open rectangular gutter is made by turning up the sides of a piece of metal 20in. wide. The area of the cross-section of the gutter is 50in^2. Find the depth of the gutter.
1 solutions
Answer 175560 by Earlsdon(4900) on 2009-11-15 10:19:34 (Show Source):
You can put this solution on YOUR website!Let d = the depth of the gutter and w = its width.
The area of the cross-section can be expressed as:
 and this is given as 50 sq.in.
The cross-section however consists of only three sides, d+d+w and the sum of these dimensions is given as 20 in.
So we can write the following:
1)  and
2) 
Rewrite equation 1) as  and substitute into equation 2).
2a)  Simplify and solve for d, the depth.
2b)  Rewrite as a quadratic equation in standard form.
2c)  Solve by factoring.
2d)  Apply the zero product rule.
2e)  or  which means that...
The depth of the gutter is 5 inches.
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Polygons/238770: each interior of a regular polygon is 174 degrees what is each exterior angle?
how many sides does the polygon have?
1 solutions
Answer 175451 by Earlsdon(4900) on 2009-11-14 12:41:09 (Show Source):
You can put this solution on YOUR website!The measure of each interior angle  of a regular polygon of n sides can be expressed by:
In this problem,  degrees, so we substitute...
 Multiply both sides by n and simplify.
 Add 360 to both sides.
 Subtract 174n from both sides.
 Finally, divide both sides by 6.
The polygon has 60 sides.
The exterior angle  is supplement of the interior angle, so...
 degrees.
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Mixture_Word_Problems/238768: I getting stumped on this problem, please help. A merchant has coffee worth $20 a pound that she wishes to mix with 80 pounds of coffee worth $90 a pound to get a mixture that can be sold for $60 a pound. How many pounds of the $20 coffee should be used?
1 solutions
Answer 175449 by Earlsdon(4900) on 2009-11-14 12:29:30 (Show Source):
You can put this solution on YOUR website!Let x = the number of pounds of the $20-coffee. After mixing this amount with the 80 pounds of $90-coffee, the merchant will have (80+x) pounds of coffee worth $60 per pound.
Let's set up the algebraic equation to solve for x.
x($20)+80($90) = (80+x)($60) Simplify and solve for x.
20x+720 = 480+60x Subtract 20x from both sides.
720 = 480+40x Subtract 480 from both sides.
240 = 40x Finally, divide both sides by 40.
60 = x
The merchant will need to mix 60 pounds of the $20-coffee with 80 pounds of the $90-coffee to obtain (80+x = 140) pounds of $60-coffee.
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Polynomials-and-rational-expressions/237901: Please help with the following questions. I am really confused when it comes to rational expressions. Thanks
Find all numbers for which the rational expression is undefined.
n^3-2n
------
n^2-81
rationalize the denominator
 -  }
--------------------------------
 + }
1 solutions
Answer 174888 by Earlsdon(4900) on 2009-11-11 20:20:45 (Show Source):
You can put this solution on YOUR website!1)
For what value of n is  undefined?
The expression is undefined when the denominator is zero, so what value of n would make the denominator equal to zero?
Set the denominator equal to zeor and solve for n.
 Add 81 to both sides.
 Take the square root of both sides.
 or 
When n=9 or n=-9, the expression is undefined.
2)
Rationalize the denominator:
 Multiply the top and bottom of the fraction by the conjugate of the denominator  .
 Simplify.
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Quadratic_Equations/237680: 3x3x^2+7=0
3x^2+2x-7=0
x=-2+or-sqrt2^2-4(3)(-7)/2(3)
x=-2+or-sqrt4+84/6
x=-2+or-sqrt88/6
I am stuck at this point do I break the radicand 4*22?
Thank you,
Tina
1 solutions
Answer 174779 by Earlsdon(4900) on 2009-11-11 12:05:24 (Show Source):
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Geometry_Word_Problems/236860: the height of an object projected upward from ground level is given by h+-16t^2+128t where h is in feet and t is time in seconds. when will the object be 240 feet above ground level ...
please help i dont understand
1 solutions
Answer 174236 by Earlsdon(4900) on 2009-11-09 11:19:06 (Show Source):
You can put this solution on YOUR website!Starting with the given function:
 you are being asked..."at what time, t, will h(t) = 240 ft."
So you set h(t) = 240 and solve for t.
 Subtract 240 from both sides and rearrange a bit.
 Now you have a quadratic equation that can be solved by various methods.
I would factor -16 first just to simplify the calculations a bit.
 Notice the change of signs when we factored the -16!
Now, from the zero product rule, you get:
 This can be solved by factoring.
 Apply the zero product rule again.
 or  so that...
 or 
Why are there two answers?
On the way up, the object will reach 240 feet in 3 seconds (t = 3).
On the way down, the object will again pass the 240-foot level in 5 seconds (t = 5).
Does this all make sense to you?
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Radicals/236495: I am just checking if I am doing this right, I am multiplying radicals
(3 sqrt 5 - 9 sqrt 3)(4 sqrt 5 + 12 sqrt 3).
I did foil and I came up with the answer -264. Is that right?
Thank you
1 solutions
Answer 174072 by Earlsdon(4900) on 2009-11-08 15:11:13 (Show Source):
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logarithm/236392: For this problem I must write the logarithmic equation in exponential form. For example the exponential form of "log5 25 = 2" is "5^2 = 25"
log3 27 = 3
1 solutions
Answer 174024 by Earlsdon(4900) on 2009-11-08 11:12:59 (Show Source):
You can put this solution on YOUR website!Recall the definition of a logarithm: " The logarithm of a number is the power to which the base of the logarithm must be raised to equal that number."
Write in exponential form:
 The base is 3, so...
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Exponential-and-logarithmic-functions/236404: How do I do these?
Solve the equation 9^x-1=(1/3)^2x
Solve the equation 4^3x-1=1.5625x10^-2
1 solutions
Answer 174022 by Earlsdon(4900) on 2009-11-08 11:07:58 (Show Source):
You can put this solution on YOUR website!Solve for x:
 Substitute 
 Multiply the exponents on the left side.
 Invert the right side and change the sign of the exponent.
 Now since the bases (3) are equal, the exponents must be equal, so...
 Add 2x to both sides.
 Add 2 to both sides.
 Divide both sides by 4.
 Simplify.
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Equations/235912: I'm trying to remember how do to this particular problem:
-11 less than equal to 3x - 4 less than equal to -3
Do I start out by adding 4 to both sides
so it would be -11 -4 < x -4 -4 ? am I on the right track?
Thanks for your help!!
1 solutions
Answer 173684 by Earlsdon(4900) on 2009-11-06 11:33:23 (Show Source):
You can put this solution on YOUR website!You have the right idea but your last line is not correct!
Solve for x:
 Add 4 to all three "sides".
 Now divide all three sides by 3.
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