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user_dude2008 answered: 1858 problems
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Numeric_Fractions/187511: find the cardinal number for each set
A={xlx is a letter in the word six}
1 solutions

Answer 140655 by user_dude2008(1861) on 2009-03-21 00:49:56 (Show Source):

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A={x | x is a letter in the word six} = {s, i, x}

3 elements ----> cardinal number is 3

Percentage-and-ratio-word-problems/187624: Mike invested $6000 for one year. He invested part of it at 9% and the rest at 11%. At the end of the year he earned $624 in interest. How much did he invest at each rate?
1 solutions

Answer 140654 by user_dude2008(1861) on 2009-03-21 00:47:32 (Show Source):

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"Mike invested $6000 for one year" ----> x+y=6000 ----> y=6000-x

"He invested part of it at 9% and the rest at 11%. At the end of the year he earned $624 in interest" ----> 0.09x+0.11y=624 ----> 9x+11y=62400

9x+11y=62400

9x+11(6000-x)=62400

9x+66000-11x=62400

-2x+66000=62400

-2x=62400-66000

-2x=-3600

x=1800

He invested $1,800 at 9%

y=6000-x

y=6000-1800

y=4200

He invested $4,200 at 11%

Complex_Numbers/187613: how do i simplify the properties of rational exponents?
1 solutions

Answer 140632 by user_dude2008(1861) on 2009-03-20 20:44:50 (Show Source):

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Post a problem so we can show you.

Linear-systems/187604: This question is from textbook saxon algebra 2
Factor the expression.
64x^6+y^6
(8x^2)^3+(y^2)^3
(8x^2+y^2)(8x^4-8x^2y^2+y^4)
Did I do this right?
1 solutions

Answer 140626 by user_dude2008(1861) on 2009-03-20 20:28:29 (Show Source):

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64x^6+y^6

(4x^2)^3+(y^2)^3

(4x^2+y^2)( (4x^2)^2 - (4x^2)(y^2) + (y^2)^2 )

(4x^2+y^2)( 16x^4 - 4x^2y^2 + y^4 )

Ans:
64x^6+y^6 factors to (4x^2+y^2)(16x^4-4x^2y^2+y^4)

Trigonometry-basics/187606: This question is from textbook saxon algebra 2
Graph the periodic function. Determine the Domain and Range. Identify the period and amplitude.
y=6sin(x)+1
amplitude=6
That's all I know. Please help!
1 solutions

Answer 140623 by user_dude2008(1861) on 2009-03-20 20:25:39 (Show Source):

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y=6sin(x)+1

---> y=6sin(1x+0)+1

in form of y=a*sin(bx+c)+d

amplitude: A=abs(a)=abs(6)=6

Amplitude is 6

Period: T=(2pi)/b=(2pi)/1=2pi

Period is 2pi (360 degrees). Graph repeats every 2pi radians/360 degrees

Graph:

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+6%2Asin%28x%29%2B1%29+

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+6%2Asin%28x%29%2B1%29+

Domain: all real numbers

Range: [-5,7] or

Exponents-negative-and-fractional/187451: This question is from textbook
5^2 5^3
over
5^3 5^2
=
5^_
1 solutions

Answer 140506 by user_dude2008(1861) on 2009-03-19 20:05:01 (Show Source):

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Ans:

Exponents-negative-and-fractional/187452: This question is from textbook
I need help with this problem.
Simplify each expression.
2^7
over
2^5
1 solutions

Answer 140505 by user_dude2008(1861) on 2009-03-19 20:02:39 (Show Source):

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Ans:

Rational-functions/187453: 5y^2=-40
1 solutions

Answer 140504 by user_dude2008(1861) on 2009-03-19 20:01:25 (Show Source):

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5y^2=-40

y^2=-40/5

y^2=-8

y=sqrt(-8) or y=-sqrt(-8)

Ans: y=2i*sqrt(2) or y=-2i*sqrt(2)

Quadratic-relations-and-conic-sections/187456: This question is from textbook
Find a parabola equation y-k=a(x-h)^2 if its Vertex(3,2) and it contains the point (1,3)
1 solutions

Answer 140503 by user_dude2008(1861) on 2009-03-19 20:00:03 (Show Source):

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y-k=a(x-h)^2

Vertex(3,2) ----> y-2=a(x-3)^2

contains the point (1,3)

----> 3-2=a(1-3)^2

----> 1=4a

----> a=1/4

Equation:

Rational-functions/187317: This question is from textbook Prentice Hall Mathematics Algebra 2
What are the steps in doing this problem? My algebra 2 teacher isn't very good at explaining
1 solutions

Answer 140414 by user_dude2008(1861) on 2009-03-18 20:44:24 (Show Source):

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You need to post the entire problem. We dont have your books.

Average/187318: Solve. (x – 2)^ = 10
1 solutions

Answer 140413 by user_dude2008(1861) on 2009-03-18 20:43:36 (Show Source):

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Ans:

which really means:

Exponential-and-logarithmic-functions/187263: we are doing solving equations by using logarithms. im stuck.
8^x=10

1 solutions

Answer 140371 by user_dude2008(1861) on 2009-03-18 15:55:00 (Show Source):

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Numeric_Fractions/187185: x/2+(1-x)/3=1
1 solutions

Answer 140351 by user_dude2008(1861) on 2009-03-18 13:37:42 (Show Source):

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x/2+(1-x)/3=1

3x+2(1-x)=6

3x+2-2x=6

x+2=6

x=6-2

Ans: x=4

Linear-equations/187137: The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 34 cm, what are its dimensions?
1 solutions

Answer 140350 by user_dude2008(1861) on 2009-03-18 13:35:16 (Show Source):

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"length of a rectangle is 2 cm more than four times the width" ---> L=4W+2

"the perimeter of the rectangle is 34 cm" ---> P=2L+2W ---> 34=2L+2W

34=2L+2W

34=2(4W+2)+2W

34=8W+4+2W

34-4=8W+2W

30=10W

W=3

L=4W+2

L=4(3)+2

L=12+2

L=14

Ans: length = 14 cm, width = 3 cm

Square-cubic-other-roots/187233: i dont know how to multiply squarroots and i have homework due tomorow and i will get a week of detention if it is not dont i need some one to explain it to me so i can do it.!!!????
1 solutions

Answer 140348 by user_dude2008(1861) on 2009-03-18 13:08:10 (Show Source):

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You need to post the problem or problems.

logarithm/187163: e^x+1 = 20
1 solutions

Answer 140298 by user_dude2008(1861) on 2009-03-17 23:38:01 (Show Source):

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e^x+1 = 20

e^x = 20 - 1

e^x = 19

Ans: x = ln(19)

logarithm/187165: log(x^2+19) = 2
1 solutions

Answer 140297 by user_dude2008(1861) on 2009-03-17 23:36:32 (Show Source):

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log is assumed to be base 10

log(x^2+19) = 2

x^2+19 = 10^2

x^2+19 = 100

x^2 = 100 - 19

x^2 = 81

x=-9 or x=9

logarithm/187166: log(2x^2+3x) = log(10x+30)
1 solutions

Answer 140296 by user_dude2008(1861) on 2009-03-17 23:33:53 (Show Source):

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log(2x^2+3x) = log(10x+30)

2x^2+3x = 10x+30

2x^2+3x - 10x - 30 = 0

2x^2-7x-30 = 0

(x-6)(2x+5) = 0

x-6=0 or 2x+5=0

Ans: x=6 or x=-5/2

logarithm/187167: log(x^3) = (log x)^2
1 solutions

Answer 140295 by user_dude2008(1861) on 2009-03-17 23:29:56 (Show Source):

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log(x) assumed base 10

log(x^3) = (log x)^2

3*log(x) = (log x)^2

Let z=log(x)

3*z = z^2

0 = z^2-3z

0 = z(z-3)

z = 0 or z = 3

log(x) = 0 or log(x) = 3

x=1 or x=1000

Ans: x=1 or x=1000

real-numbers/187168: sum of three consecutive numbers is 18.what are these numbers?
1 solutions

Answer 140294 by user_dude2008(1861) on 2009-03-17 23:26:35 (Show Source):

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"sum of three consecutive numbers is 18." ----> x+(x+1)+(x+2)=18

x+(x+1)+(x+2)=18

x+x+1+x+2=18

3x+3=18

3x=15

x=5

--> x+1=6, x+2=7

Ans: nums are 5, 6, and 7

Check: 5+6+7=18

Square-cubic-other-roots/187078: square root of 4q-3 =3
1 solutions

Answer 140228 by user_dude2008(1861) on 2009-03-17 16:23:52 (Show Source):

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sqrt( 4q-3 ) = 3

4q-3 = 3^2

4q-3 = 9

4q = 9+3

4q = 12

q = 12/4

q = 3

Ans: q = 3

Linear_Algebra/187019: I have tried to get some of these but I have a problem of being just a little off and then blowing the whole deal. Please help.
Write standard form and identify a, b, and c.
4x² + 4 = 2x + 3
I need to solve this equation.
x(x-3) = 40 Would it be -5,-8?

Find the x-intercepts
Y = x² +4
And yet another one.
Y = x² -4x -32
Find the ordered pair for the vortex.
Y = 2x² -4x +6 Could it be (4,1)?
Solve the specified variable.
a/(l-r) for r Could it be r = a/s ?

1 solutions

Answer 140227 by user_dude2008(1861) on 2009-03-17 16:22:12 (Show Source):

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"Write standard form and identify a, b, and c.
4x² + 4 = 2x + 3 "

4x² + 4 = 2x + 3

4x² + 4 - 3 = 2x

4x² + 4 - 3 - 2x = 0

4x² - 2x + 1 = 0

Now in standard form: ax^2+bx+c = 0 ---> a = 4, b = -2x, and c = 1

----------------------------------------------------------

x(x-3) = 40

x^2-3x=40

x^2-3x-40=0

(x-8)(x+5)=0

x = 8 or x = -5

close...off by a sign

----------------------------------

x-intercepts:

Y = x² +4

0 = x² +4

x^2 = -4

x = sqrt(-4)

x = 2i or x = -2i

--------------------------------

x-intercepts:
Y = x² -4x -32

0= x² -4x -32

(x-8)(x+4)=0

x=8 or x=-4

------------------------------------------------

2x² -4x +6 ---> a=2, b=-4, c=6

x = -b/2a

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

x=4/4

x=1

y=2(1)^2-4(1)+6

y=2(1)-4(1)+6

y=2-4+6

y=4

Vertex: (1,4) ... mixed up coordinates

---------------------------------------------------

can't solve a/(l-r) since it is not equation

Percentage-and-ratio-word-problems/187051: Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1?
What is the size of the population at the end of year 2?
What is the size of the population at the end of year 3?
What is the size of the population at the end of year n (for any integer n)?
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200? Use a calculator to solve to x.
I am truly not even sure how to get started on this problem, any and all help would be greatly appreciated. Thanks
1 solutions

Answer 140202 by user_dude2008(1861) on 2009-03-17 13:45:51 (Show Source):

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" initial size 100 grows at the rate of 8% per year forever" --->

What is the size of the population at the end of year 1?

Ans: 108 people at end of yr 1

------------------------------------------------------

What is the size of the population at the end of year 2?

Ans: 116 people at end of yr 2

------------------------------------------------------

What is the size of the population at the end of year 3?

Ans: 125 people at end of yr 3

------------------------------------------------------

What is the size of the population at the end of year n?

------------------------------------------------------
find the number of years x that it would take for our population to reach 200?

Ans: takes about 9 yrs for pop. to reach 200 people

Rate-of-work-word-problems/187008: raphael can load a large shipping truck in 15 hours. working together, raphael and jana can load the same truck in 6 hours. how long would it take to load the truck by herself?

1 solutions

Answer 140169 by user_dude2008(1861) on 2009-03-17 00:13:12 (Show Source):

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Use equation

t(1/rate1 + 1/rate2) = 1

rate1 = raphael's rate = 15 hrs, rate2 = janas rate = x

t(1/15+1/x)=1

t is given as t=6

----> 6(1/15+1/x)=1

1/15+1/x=1/6

2x+30=5x

30=3x

x=10

Ans: jana can load the truck in 10 hrs

Expressions-with-variables/186988: (A squared + A + b)(A squared-A-B)
1 solutions

Answer 140163 by user_dude2008(1861) on 2009-03-16 23:46:50 (Show Source):

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(A^2 + A + B)(A^2-A-B)

(A^2 + A + B)(A^2-(A+B))

Let X=A+B

(A^2 + X)(A^2-X)

A^4-X^2

A^4-(A+B)^2

A^4-(A^2+2AB+B^2)

A^4-A^2-2AB-B^2

Ans: (A^2 + A + B)(A^2-A-B) = A^4-A^2-2AB-B^2

Exponential-and-logarithmic-functions/187005: 8^3t=32^4t-1
1 solutions

Answer 140162 by user_dude2008(1861) on 2009-03-16 23:44:03 (Show Source):

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8^(3t)=32^(4t-1)

2^(3(3t))=2^(5(4t-1))

2^(9t)=2^(20t-5)

9t=20t-5

-11t=-5

t=5/11

Ans: t=5/11

Exponential-and-logarithmic-functions/187004: 3^2-8x= 9^3x+1
1 solutions

Answer 140161 by user_dude2008(1861) on 2009-03-16 23:42:23 (Show Source):

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3^(2-8x)= 9^(3x+1)

3^(2-8x)= 3^(2(3x+1))

3^(2-8x)= 3^(6x+2)

---> 2-8x=6x+2 ---> x=0

Ans: x=0

Quadratic_Equations/186995: A = 3 pie a^2
solve for a
1 solutions

Answer 140160 by user_dude2008(1861) on 2009-03-16 23:40:31 (Show Source):

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A = 3pi*a^2

A/(3pi) = a^2

Ans: a = sqrt( A/(3pi) ) or a = -sqrt( A/(3pi) )

Angles/187001: A diagonal walk through a small rectangular garden 9 meters by 12 meters can be built at $10 per linear meter. How much will the walk cost
1 solutions

Answer 140159 by user_dude2008(1861) on 2009-03-16 23:39:16 (Show Source):

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9^2+12^2=x^2

81+144=x^2

225=x^2

x=sqrt(225)

x=15 .... diagonal walk is 15 meters

15 (meters) * ($10/meter) = $150

Ans: $150

Quadratic_Equations/187002: please solve by factoring.

y^2-4y=45
1 solutions

Answer 140158 by user_dude2008(1861) on 2009-03-16 23:37:21 (Show Source):

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y^2-4y=45

y^2-4y-45=0

(y-9)(y+5)=0

y-9=0 or y+5=0

Ans: y=9 or y=-5

Quadratic_Equations/187003: please help me factor and solve

x^2-21x-100=0

thank you...please show work
1 solutions

Answer 140157 by user_dude2008(1861) on 2009-03-16 23:36:00 (Show Source):

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x^2-21x-100=0

(x-25)(x+4)=0

x-25=0 or x+4=0

Ans: x=25 or x=-4

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Recent problems solved by 'user_dude2008'