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Exponents/40283: 7a/15b-2b/5
1 solutions

Answer 25642 by fractalier(2101) on 2006-06-01 10:33:16 (Show Source):

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Let us convert the denominator of the second fraction to match the first one...then combine..so we have
7a/15b - 2b/5 =
7a/15b - (2b/5)(3b/3b) =
7a/15b - 6b^2/15b =
(7a - 6b^2) / 15b

Functions/34627: what is the domain of the square root 2x-1 divided by the square root 1-x.
1 solutions

Answer 25545 by fractalier(2101) on 2006-05-31 17:21:37 (Show Source):

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Since the denominator cannot be zero, and the radicand cannot be negative, we need to find x such that
1 - x > 0 and
x < 1
That is the domain.

Exponents/35325: Hi I am having trouble with this question. Can you help?
9^(4x-3)=4^(2x-4)
1 solutions

Answer 25543 by fractalier(2101) on 2006-05-31 17:15:38 (Show Source):

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This has to be solved using logarithms...so from
9^(4x-3) = 4^(2x-4)
take the log of both sides, apply the power rule and use your algebar tools to solve for x...here goes...
log 9^(4x-3) = log 4^(2x-4)
(4x-3)*log 9 = (2x-4)*log 4
4xlog9 - 3log9 = 2xlog4 - 4log4
4xlog9 - 2xlog4 = 3log9 - 4log4
x(4log9 - 2log4) = 3log9 - 4log4
x = (3log9 - 4log4) / (4log9 - 2log4)

percentage/40107: Can someone help me with this problem?

Fir the circumference of a circle. The radius is 12 ft. Use 3.14 for pi and round the answer to one decimal place.
Thank you,
Sher
1 solutions

Answer 25541 by fractalier(2101) on 2006-05-31 17:11:35 (Show Source):

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The circumference of a circle is found by
C = 2(pi)r now plug in
C = 2(3.14)(12)
C = 75.4 ft

Polynomials-and-rational-expressions/40104: A square has sides of length 3x - 2cm. Express the area of the square as a polynomial.
1 solutions

Answer 25537 by fractalier(2101) on 2006-05-31 16:47:28 (Show Source):

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The area of a square is the side squared...so
A = s^2
A = (3x - 2)^2 or
A = 9x^2 - 12x + 4 cm^2

Geometry_Word_Problems/39880: You are standing 8 feet from a circular swimming pool. The distance to a
point of tangency is 16 feet. What is the radius of the pool?
1 solutions

Answer 25536 by fractalier(2101) on 2006-05-31 16:45:10 (Show Source):

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Just posted this solution...12 feet

Polynomials-and-rational-expressions/40103: Let x represent the number and then write an expression for the product.
The square of 5 more than a number

Is this correct?
x + 5^2
1 solutions

Answer 25535 by fractalier(2101) on 2006-05-31 16:43:47 (Show Source):

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Almost. It's more precisely written as
(x + 5)^2

Geometry_Word_Problems/39881: You are standing 8 feet from a circular swimming pool. The distance to a
point of tangency is 16 feet. What is the radius of the pool?
1 solutions

Answer 25534 by fractalier(2101) on 2006-05-31 16:40:45 (Show Source):

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Make yourself a diagram such that the distance from the center of the pool to you is 8 + r and the distance to the tangent is 16. It should be a right triangle, since the radius meets a tangent at a right angle. Via the Pythagorean Theorem, we have
r^2 + 16^2 = (r + 8)^2
r^2 + 256 = r^2 + 16r + 64
256 = 16r + 64
16r = 192
r = 12 feet

Square-cubic-other-roots/39926: Rationalize the Denominator

"variable a" divided by the cubic root of 4.
1 solutions

Answer 25533 by fractalier(2101) on 2006-05-31 16:35:27 (Show Source):

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We rationalize by multiplying top and bottom by a cube root that will make the denominator a perfect cube...that would be cbrt(16)...so we have
a/cbrt(4) =
a*cbrt(16) / cbrt(64) =
a*cbrt(16) / 4

Polynomials-and-rational-expressions/39934: David helped his father stock the pond with fish. They put in baby catfish and bluegill. They put in a total of 75 fish. If the # of bluegill was doubled & the number of catfish was trippled there would be 175 fish in the pond. how many catfish were put in the pond?
Thank you
1 solutions

Answer 25532 by fractalier(2101) on 2006-05-31 16:32:14 (Show Source):

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Let b be the number of bluegill and c be the number of catfish.
Thus
b + c = 75 and
2b + 3c = 175
Now double the first equation and subtract it from the second...we get
2b + 3c = 175
-(2b + 2c = 150)
and we get
c = 25 catfish

absolute-value/40102: when do you cross multiply fractions and when do you just multiply the numerators and denominators
1 solutions

Answer 25531 by fractalier(2101) on 2006-05-31 16:28:43 (Show Source):

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You only "cross-multiply" when two fractions are set equal into a proportion...
Thus if you have A/B = C/D, you can cross-multiply and get
AD = BC
If the fractions are on the same side of an equal sign, you merely multiply numerators and denominators...

Polynomials-and-rational-expressions/40084: The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut?
1 solutions

Answer 25530 by fractalier(2101) on 2006-05-31 16:25:28 (Show Source):

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Let C be the cost. So we have
C = .07w + 13.3
Now if w = 375, we just plug it in and calculate
C = .07*375 + 13.3
C = $39.55
We divide that by 375 to find the average cost...
Average = $39.55/375 = $.1055 or a little more than 10 1/2 cents each...

Quadratic_Equations/40101: help
which of the following are the factors of x%5E3%2B3x%5E2

?
a)

1 solutions

Answer 25529 by fractalier(2101) on 2006-05-31 16:21:44 (Show Source):

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Here both b and c qualify, yet c is a more complete factoring. You could always multiply out each choice and see which give you back the original polynomial...

Quadratic_Equations/40100: can you help?
what is the gratest common factor of the terms %2814c%5E2d%29+and+%2842c%5E3d%29

1 solutions

Answer 25528 by fractalier(2101) on 2006-05-31 16:18:42 (Show Source):

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What is the greatest quantity that goes into both evenly? That is your GCF...here it is
14c^2d

percentage/40099: Could you help me with this problem?
Find the area of the shaded part . It's a square with a circle in the middle.
The circle is not shaded, Use 3.14 for pi and round your answer to one decimal place.
Thank you,
Sher
1 solutions

Answer 25527 by fractalier(2101) on 2006-05-31 16:16:40 (Show Source):

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Well without providing the radius, I'll give you the general solution...if the circle is inside the square and has a radius of r, the side of the square is 2r.
Thus the square's area is 4r^2, and the area of the circle is (pi)r^2. Just subtract the two to find the shaded area of the square not contained in the circle...
(4-(pi))r^2
Just plug in whatever r you have and get the answer...

Probability-and-statistics/40093: What is the probability of getting two 5's in a row when rolling die?
What is the probability of selecting two Queeens in a row from a deck of cards?
1 solutions

Answer 25526 by fractalier(2101) on 2006-05-31 16:08:36 (Show Source):

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For two fives in a row, the probability is 1/6 * 1/6 = 1/36
For drawing two queens in a row (without replacing the first one), the probability would be 4/52 * 3/51 = 1/13 * 1/17 = 1/221

Quadratic_Equations/40096: can someone help me? Which of the following is the greatest common factor of the terms 48s%5E5t%5E3u%5E2+and+%2840s%5E3tu%5E4%29

48s%5E5t%5E3u%5E2+and+%2840s%5E3tu%5E4%29

?
a)

1 solutions

Answer 25525 by fractalier(2101) on 2006-05-31 16:06:01 (Show Source):

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The GCF of 48s^5t^3u^2 and 40s^3tu^4
must be the combination of the greatest common factors
of each of the pieces...
so it must be
8s^3tu^2
Choice d.

Probability-and-statistics/40094: A QDA instructor gave a class two tests. 25% of the class passed both tests and 42% passed the first test. What percentage of those who passed the first test also passed the second test?
1 solutions

Answer 25523 by fractalier(2101) on 2006-05-31 16:02:46 (Show Source):

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Just posted this solution...59.5%

Probability-and-statistics/40095: A QDA instructor gave a class two tests. 25% of the class passed both tests and 42% passed the first test. What percentage of those who passed the first test also passed the second test?
1 solutions

Answer 25522 by fractalier(2101) on 2006-05-31 16:01:28 (Show Source):

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To make this a bit easier to see, imagine there were 100 students in the class.
Thus 42 passed the first test, and 25 passed both. Thus 25 of the 42 who passed the first test also passed the second test...that percentage is
25/42 = 59.5%

Graphs/40092: please help me to find the value of "a" in the equation (5)/(a+3)=(3)/(a-2)
1 solutions

Answer 25521 by fractalier(2101) on 2006-05-31 15:57:09 (Show Source):

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Let us cross-multiply and solve...we have
(5)/(a+3)=(3)/(a-2)
and then
5(a-2) = 3(a+3) expand
5a - 10 = 3a + 9 subtract 3a
2a - 10 = 9 add 10
2a = 19 divide by 2
a = 19/2

Polynomials-and-rational-expressions/40088: Add the following
(5b^3 - 8b + 2b^2) + (3b^2 - 7b^3 + 5b)
1 solutions

Answer 25520 by fractalier(2101) on 2006-05-31 15:48:36 (Show Source):

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We combine like terms, no matter where they are present in the polynomial, so we have
(5b^3 - 8b + 2b^2) + (3b^2 - 7b^3 + 5b) =
-2b^3 + 5b^2 - 3b
sort of like three separate little problems all linked together...

Polynomials-and-rational-expressions/40090: A triangle has sides 3x + 7, 4x - 9 and 5x + 6. Find the polynomial that represents its perimeter.
1 solutions

Answer 25519 by fractalier(2101) on 2006-05-31 15:46:15 (Show Source):

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Perimeter is the sum of the lengths of the sides...therefore
P = 3x + 7 + 4x - 9 + 5x + 6 =
P = 12x + 4

Graphs/40089: help please find the lowest common denominator of %28p%2B3%29%2F%28p%5E2%2B7p%2B10%29

and

1 solutions

Answer 25518 by fractalier(2101) on 2006-05-31 15:44:20 (Show Source):

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Well
p^2+7p+10 factors into
(p+5)(p+2)
and
p^2+5p+6 factors into
(p+3)(p+2)
so our LCD is
(p+5)(p+2)(p+3)

Polynomials-and-rational-expressions/40086: If there are 6 x 10^9 people on the Earth and there is enough freshwater to provide each person with 8.79 x 10^5L, how much freshwater is on the Earth?
1 solutions

Answer 25517 by fractalier(2101) on 2006-05-31 15:38:55 (Show Source):

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We just multiply the two quantities being sure to express our answer in proper sci not...so we have
(6 x 10^9) * (8.79 x 10^5L) =
52.74 x 10^14 L =
5.274 x 10^15 L

Equations/38721:
Can you help me solve this problem?
Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24-hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?
Thanks!
1 solutions

Answer 25516 by fractalier(2101) on 2006-05-31 15:35:24 (Show Source):

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I posted this solution a few days ago...please scroll down thru my work to find it...I think he could allow two defective bottles at most before rejecting the whole lot...

Graphs/39889: simlify the fraction -(2x//xy) completely. would this be -2/y?
1 solutions

Answer 25513 by fractalier(2101) on 2006-05-31 15:16:21 (Show Source):

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Yes, -(2x/xy) = -2/y

Rational-functions/39970: using -1 as a factor (divide)
(x-4)^2
__________ =
(4-x)^2

thanx
1 solutions

Answer 25512 by fractalier(2101) on 2006-05-31 15:14:24 (Show Source):

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(x-4)^2 / (4-x)^2 =
(x-4)^2 / (4-x(4-x) =
(x-4)^2 / (-1)(x-4)(-1)(x-4) =
(x-4)^2 / (x-4)^2 =
1

Graphs/40067: Help please!!
Add the fractions q%2Fq%5E2%2B5q%2B6

and

1 solutions

Answer 25511 by fractalier(2101) on 2006-05-31 15:12:40 (Show Source):

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Well from
q/(q^2 + 5q + 6) + 1/(q^2 + 3q +2)
we factor the denominators and then look for the lowest common denominator to change each fraction into. Once we do that we can combine the fractions. Hopefuly something will simplify. So here goes...
q/(q^2 + 5q + 6) + 1/(q^2 + 3q +2) =
q/(q+2)(q+3) + 1/(q+2)(q+1) =
q(q+1)/(q+1)(q+2)(q+3) + (q+3)/(q+1)(q+2)(q+3) =
(q^2+q)/(q+1)(q+2)(q+3) + (q+3)/(q+1)(q+2)(q+3) =
(q^2+2q+3)/(q+1)(q+2)(q+3)
Nothing else simplifies...we are done...

Radicals/39890: Can you help me solve this equation?
sqrt 2y+7 + 4 = y
The 2y+7 is in the radical sign
Thanks
1 solutions

Answer 25510 by fractalier(2101) on 2006-05-31 15:06:36 (Show Source):

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First we isolate the radical and then square both sides...so from
sqrt(2y+7) + 4 = y
sqrt(2y+7) = y - 4
2y + 7 = (y - 4)^2
2y + 7 = y^2 - 8y + 16 now collect like terms and solve
y^2 - 10y + 9 = 0
(y-9)(y-1) = 0
y = 9 or y = 1
Yo have to check these, however, and only y = 9 checks out. y = 1 doesn't check. Thus,
y = 9

Graphs/40082: can you help me?
find the illegal values of c in the multiplcation statement %28c%5E2-3c-10%29%2F%28c%5E2%2B5c-14%29

1 solutions

Answer 25509 by fractalier(2101) on 2006-05-31 15:03:13 (Show Source):

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Once again, denominators cannot be zero, so we have to see what values of c make that so...those values are the "illegal" ones...so for
c^2 + 5c - 14 = 0
(c+7)(c-2) = 0
c = -7 or c = 2 and for
c^2 - 2c - 15 = 0
(c-5)(c+3) = 0
c = 5 or c = -3
Thus c is not allowed to be any of
-7, 2, 5, or -3

Linear-systems/40080: i do not know how to answer this and show my work
1 solutions

Answer 25508 by fractalier(2101) on 2006-05-31 15:00:38 (Show Source):

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If you post the problem, I will help you.

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Recent problems solved by 'fractalier'