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real-numbers/44160: solve. approximate irrational roots to the nearest tenth.
Together Anna and Carla can spray- paint a van in 8 hours. Alone it takes Anna 2 hours less than Carla. Find the time it takes each of them to paint the van alone. Give your answers to the nearest tenth of an hour. (units optional)
1 solutions

Answer 29097 by fractalier(2101) on 2006-06-28 15:44:33 (Show Source):

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Let Carla's individual time be c. So Anna's time is c-2.
We set this one up like this
t/A + t/B = 1
8/c + 8/(c-2) = 1
now multiply by the LCD, c(c-2), and get
8(c-2) + 8c = c(c-2)
8c - 16 + 8c = c^2 - 2c
now collect like terms and solve...
c^2 - 18c + 16 = 0
This cannot be factored so let's try completing the square...
c^2 - 18c + 81 + 16 = 81
c^2 - 18c + 81 = 65
(c - 9)^2 = 65
c - 9 = ± √65
c = 9 ± √65
The negative root does not work since that would make Anna's time negative so Carla's time is
c = 9 + √65 or about 17.1 hours
Anna can do it in c-2 or about 15.1 hours

Polynomials-and-rational-expressions/44139: Write each expression in simplest form

4r2 - 25s2 / 2r2 + 3rs - 20s2
Thank you!!!
1 solutions

Answer 29094 by fractalier(2101) on 2006-06-28 15:36:42 (Show Source):

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The key technique in rational expressions is to FACTOR and CANCEL...that's what we do here...so from
4r^2 - 25s^2 / 2r^2 + 3rs - 20s^2 =
(2r+5s)(2r-5s) / (2r-5s)(r+4s) =
(2r+5s) / (r+4s)

real-numbers/44157: solve. approximate irrational roots to the nearest tenth.
The difference of the square of a number and the number is 12. find the number.
1 solutions

Answer 29093 by fractalier(2101) on 2006-06-28 15:33:51 (Show Source):

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Let the number be x...then we have
x^2 - x = 12
x^2 - x - 12 = 0
(x - 4)(x + 3) = 0
x = 4 or x = -3

real-numbers/44150: solve by any method you prefer.
u^2 - 15u = -1
1 solutions

Answer 29092 by fractalier(2101) on 2006-06-28 15:32:38 (Show Source):

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Let's use the quadratic this time...so from
u^2 - 15u = -1
u^2 - 15u + 1 = 0
u = (15 ± sqrt(225 - 4)) / 2
u = (15 ± √221) / 2

real-numbers/44152: solve by any method you prefer.
x^2 + 8x + 1 = 0
1 solutions

Answer 29091 by fractalier(2101) on 2006-06-28 15:30:43 (Show Source):

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Let complete the square on this one...thus from
x^2 + 8x + 1 = 0 we add 15 to both sides
x^2 + 8x + 16 = 15
(x + 4)^2 = 15
x + 4 = ± √15
x = -4 ± √15

real-numbers/44151: solve by any method you prefer.
3w^2 - 16 = 0
1 solutions

Answer 29089 by fractalier(2101) on 2006-06-28 15:28:42 (Show Source):

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From
3w^2 - 16 = 0
add 16, divide by three and take the root and get
3w^2 = 16
w^2 = 16/3
w = ± sqrt(16/3) now rationalize
w = ± 4√3 / 3

Numeric_Fractions/44137: Benny is traveling at a speed of 60 mi./h. What is his speed in feet per second.
1 solutions

Answer 29075 by fractalier(2101) on 2006-06-28 12:51:47 (Show Source):

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The direct conversion is 60 mi/hr = 88 ft/sec
but you would find that by multiplying 60 mi/hr
by 5280 ft / 1 mi and then 1 hr / 3600 sec...

Expressions-with-variables/44135: can someone please help me with i have tried it but i dont seem to be able to come up with an answer. thanks! solve the equation and check your solutions: sqaure root of 4x^2+5 = 3x
1 solutions

Answer 29071 by fractalier(2101) on 2006-06-28 12:37:13 (Show Source):

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√(4x^2 + 5) = 3x
we square both sides to begin and get
4x^2 + 5 = 9x^2
5 = 5x^2
x^2 = 1
x = ±1
Now check...
only positive one checks out...

Polynomials-and-rational-expressions/43813: This question is from textbook Algebra and trigonometry with analytic geometry
The polynomial f(x)divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3). my answer is -2, could that be right. thanks again.
1 solutions

Answer 29064 by fractalier(2101) on 2006-06-28 12:13:32 (Show Source):

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To find the original f(x) we need to multiply
(x^2 + 3x - 5) by (x - 3) and then adding 2...we get
f(x) = x^3 - 14x + 15 + 2
f(x) = x^3 - 14x + 17
so that
f(3) = 3^3 - 14(3) + 17
f(3) = 27 - 42 + 17
f(3) = 2
Close, but I get positive 2, not -2.

Polynomials-and-rational-expressions/44109: simplify the following expression. write your answers with positive exponents only.
(x^2)^-3(x^-2)/(x^2)^-4
1 solutions

Answer 29063 by fractalier(2101) on 2006-06-28 12:08:52 (Show Source):

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Assuming the problem is correct as written, we get
[(x^2)^-3 * (x^-2)] / (x^2)^-4 =
[(x^-6)(x^-2)] / x^-8 =
x^-8 / x^-8 =
1

Divisibility_and_Prime_Numbers/44113: How would I determine the maximum and minimum values of the following set of numbers:
3, -36/7, -1, -2/3, 5/4, 26/9
1 solutions

Answer 29062 by fractalier(2101) on 2006-06-28 12:05:43 (Show Source):

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We can express these as decimals (approximately)...that's one way...so we get
3, -36/7, -1, -2/3, 5/4, 26/9
becoming
3, -5.143, -1, -.667, 1.25, 2.889
From this list you can see which is the greatest negative, that is, the minimum value ==> -36/7 and then the maximum value ==> 26/9

Money_Word_Problems/44108: Can someone explain this to me?
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 29061 by fractalier(2101) on 2006-06-28 12:03:10 (Show Source):

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Posted this one a few days ago, here goes again...
Let us call the cost function
c(w) = .07w + 13.3
Now if the number of wing nuts, w, is 375, we substitute that in for w and get
c(375) = .07(375) + 13.3
c(375) = 26.25 + 13.3
c(375) = $39.55
To find the average cost, we divide that total cost by 375 wing nuts and get
$39.55 / 375 = $.1055 or 10.55 cents each

real-numbers/44127: Give an example of a number that is a real number, but not a rational number.
1 solutions

Answer 29060 by fractalier(2101) on 2006-06-28 11:59:29 (Show Source):

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√2 or square root of two is an example. It cannot be expressed as a fraction of two integers and so is not rational.

real-numbers/44128: Give an example of a number that is a rational number, but not an integer.
1 solutions

Answer 29059 by fractalier(2101) on 2006-06-28 11:58:27 (Show Source):

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3/5 is an example.

Polynomials-and-rational-expressions/44107: I am so confused with these problems....
What expression raised to the fouth power is 81x (12 to the power)y (8 to the power) z (16 to the power).
All number except the 81 are exponents.
1 solutions

Answer 29058 by fractalier(2101) on 2006-06-28 11:57:54 (Show Source):

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Let us write it this way...looking for n such that
n^4 = 81(x^12)(y^8)(z^16)
well we need to raise both sides to the 1/4 power, so that
n = ±3(x^3)(y^2)(z^4)

Polynomials-and-rational-expressions/44110: perform the indicated calculation. write your result in scientific notation.
(6*10^12)(3.2*10^8)/(1.6*10^7(3*10^2)
1 solutions

Answer 29057 by fractalier(2101) on 2006-06-28 11:55:10 (Show Source):

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Okay from
(6*10^12)(3.2*10^8) / (1.6*10^7)(3*10^2)
19.2 x 10^20 / 4.8 x 10^9 =
4 x 10^11

Divisibility_and_Prime_Numbers/44112: How do I write 116 2/3% as a fraction or mixed number.
1 solutions

Answer 29055 by fractalier(2101) on 2006-06-28 11:53:35 (Show Source):

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Posted this solution about an hour ago...7/6

Linear-equations/44117: 4 - (2x-9) = -19
1 solutions

Answer 29054 by fractalier(2101) on 2006-06-28 11:52:38 (Show Source):

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Let us distribute the negative sign, collect terms and solve...we get
4 - (2x-9) = -19
4 - 2x + 9 = -19
-2x + 13 = -19
-2x = -32
x = 16

Polynomials-and-rational-expressions/44120: add using the vertical method
5x^2+2x-4
x^2-2x-3
and
2x^2-4x-3
1 solutions

Answer 29053 by fractalier(2101) on 2006-06-28 11:50:56 (Show Source):

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5x^2 + 2x - 4
+
x^2 - 2x - 3
+
2x^2 - 4x - 3
_____________
8x^2 - 4x - 10

Numeric_Fractions/44122: How do you find the remainder from division for the numerator when converting improper fractions into proper fractions?
1 solutions

Answer 29052 by fractalier(2101) on 2006-06-28 11:49:37 (Show Source):

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Let me show you by example...
Let's say we wish to convert 35/8 to a mixed number...
So we divide 8 into 35 and get 4 with a remainder of 3...
We then state our answer as
4 3/8
Notice that the divisor (8) remains the denominator and our remainder from the division becomes our numerator...

Polynomials-and-rational-expressions/44121: Subract usin gthe vertical method
7x^2+6x from 9x^2-3
1 solutions

Answer 29048 by fractalier(2101) on 2006-06-28 11:36:16 (Show Source):

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Okay, vertically
9x^2 - 3
-(7x^2 + 6x)
_____________
2x^2 - 6x - 3

Polynomials-and-rational-expressions/44065: I am not sure of this problem, can someone help me with this one?
Use the five properties of exponents to simplify each of the following expressions.
(y5)3(y3)2
_____________________
(y4)4
(all the numbers are suppose to be exponents)

1 solutions

Answer 29042 by fractalier(2101) on 2006-06-28 10:38:38 (Show Source):

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[(y^5)^3 * (y^3)^2] / (y^4)^4 =
[(y^15) * (y^6)] / (y^16) =
(y^21) / (y^16) =
y^5

Linear-equations/38919: 4. Find values for m and b in the following system so that the solution to the system is (-3,4).
5x + 7y = b
mx + y = 22

1 solutions

Answer 29041 by fractalier(2101) on 2006-06-28 10:36:42 (Show Source):

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We have to plug in -3 for x and 4 for y...we get
5(-3) + 7(4) = -15 + 28 = 13 = b
and then
-3m + 4 = 22
-3m = 18
m = -6

Miscellaneous_Word_Problems/44034: Columbian Earthquake of 1906 At 8.6 on the richter scale, the Colombian earthquake of January 31, 1906, was one of the strongest earthquakes on record. Use the formula log(I)-log(Io) to write I as a mulitple of Io for this earthquake.
1 solutions

Answer 29040 by fractalier(2101) on 2006-06-28 10:31:53 (Show Source):

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We have log(I) - log(Io) = 8.6
and then by the laws of logarithms we have
log (I/Io) = 8.6
I/Io = 10^8.6
I = (Io)(10^8.6) or about 400000000 * Io

Equations/44041: graph the inequality y is less than or equal to -4
1 solutions

Answer 29039 by fractalier(2101) on 2006-06-28 10:28:37 (Show Source):

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Draw a solid horizontal line thru the point (0, -4) and then shade the half-plane below the line (since it is less than or equal to -4)

logarithm/44101: Solve log a (8x+5)=log a (4x+29). Thank you for any help you can provide.
1 solutions

Answer 29038 by fractalier(2101) on 2006-06-28 10:26:09 (Show Source):

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Well if logarithmic expressions are equal, their arguments are too, so that if
log_a (8x+5) = log_a (4x+29)
then
8x + 5 = 4x + 29
4x = 24
x = 6

logarithm/44103: Write the expression log a(y+5)+2log a (x+1) as one logarithm. Thank you for your help on this:)
1 solutions

Answer 29037 by fractalier(2101) on 2006-06-28 10:23:59 (Show Source):

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The log of a product equals the sum of the logs...if we apply that and the power rule, we get
log_a (y+5) + 2log_a (x+1) = log_a [(y+5)(x+1)^2]

logarithm/44102: Given that log a (x)=3.58 and log a (y)=4.79, find log a (y/x). Thank you for any help.
1 solutions

Answer 29036 by fractalier(2101) on 2006-06-28 10:21:41 (Show Source):

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One of the basic laws of logarithms says that the log of a quotient is equal to the difference of the logs...so that
log_a (y/x) = log_a (y) - log_a (x) = 4.79 - 3.58 = 1.21

Equations/44053: Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?
1 solutions

Answer 29035 by fractalier(2101) on 2006-06-28 10:19:44 (Show Source):

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Let N be the number of nickels and D be dimes, so that
N + D = 50
Their values are 5N and 10D respectively, so that
5N + 10D = 350
Now let's multiply the first equation by 5 and subtract it from the second...we get
5N + 10D = 350
-(5N + 5D = 250)
so we have
5D = 100
D = 20
N = 30

Numeric_Fractions/44085: I need some help on this problem.
I need to arrange the following numbers from smallest to largest:
3.07, 37/10, 3.0712, 3.078, 371/100, 3.0717, 3.072, 3.071
Thanks!
1 solutions

Answer 29034 by fractalier(2101) on 2006-06-28 10:13:57 (Show Source):

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In ascending order (smallest to largest)
3.07, 37/10, 3.0712, 3.078, 371/100, 3.0717, 3.072, 3.071
becomes
3.07, 3.071, 3.0712, 3.0717, 3.072, 3.078, 37/10, 371/100

Numeric_Fractions/44084: Can someone help me on this?
I need to add the following in the lowest terms:
2/7 + 2/7 + 6/7
Thanks, Lyn
1 solutions

Answer 29033 by fractalier(2101) on 2006-06-28 10:11:11 (Show Source):

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Since all of these are like denominators, we can add numerators directly and get
2/7 + 2/7 + 6/7 = 10/7 = 1 3/7

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Recent problems solved by 'fractalier'