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Good morning, have some question that I need to see if you…

Good morning, have some question...
Good morning, have some question that I need to see if you will do for me:
1) x/3 = 4/x+1
2) -3/x = x/ -3
reduce to lowest term-assume variable represent only number for which the denominators are nonzero:
3) a^2 -b^2 / a-b
4) -2x -8 /x^2 + 2x -8
5)3/a^2 +a * 2a + 2/6
6) w^2 -1/(w-1)^2 * w-1/w^2 +2w +1
7) -7yt/2at = ---/ 2ayz
8)find LCD for rational expression, convert rationa expression into equivalent reational expression with LCD as denominator 4/a-6 , 5/6-a
9)lowest terms
a+7/a-4 +9-5a/a

10)2/x-3 + 3/3-x
Simplify and reduce to lowest terms
11)1/9 + 1/3x/ x/9 - 1/x

12. ab + b^2/4ab^5
________________
a+b/6a^2 b^4
need these word out step by step:
Use a proportion to sove each problem:
13) Fast Food: If four out of five doctors perfer fast food, then at a convention of 445 doctors, how many prefer fast food?

14) The anciet Greeks thought that the most pleasing shape for a retangle was one for which the ratio of the length was approximately 8 to 5, the golden ratio. If the length of a rectangular painting is 2 foot longer than it width, then for what dimensions would the length and width have the golden ration?

15) To estimate the size of the bear population in the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the convervationists estimate of the size of the bear poplulation?
Would like to have these by Wednesday if possible.
Need anyting else just let me know.
Thanks
Nena
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Answered in 57 minutes by:
6/28/2010
Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Hi there,

 

Not sure if these were meant for me, but we've been working together recently...

 

1) x/3 = 4/x+1
Cross multiply:
x(x+1) = 12
x^2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 or 3


2) -3/x = x/ -3
Cross multiply:
x^2 = 9
x = +/- 3
x = 3 or -3

 

reduce to lowest term-assume variable represent only number for which the denominators are nonzero:
3) a^2 -b^2 / a-b
Factor the top:
(a-b)(a+b) / (a-b)
Cancel:
a+b

 

4) -2x -8 /x^2 + 2x -8
Factor:
-2(x+4) / (x+4)(x-2)
Cancel:
-2 / (x-2)


5)3/a^2 +a * 2a + 2/6
Multiply:
3(2a+2) / 6(a^2+a)
= 6(a+1) / 6a(a+1)
= 1/a


6) w^2 -1/(w-1)^2 * w-1/w^2 +2w +1
Factor:
(w-1)(w+1)/(w-1)^2 * (w-1)/(w+1)(w+1)
Cancel:
(w+1)/(w-1) * (w-1)/(w+1)(w+1)
1/(w-1) * (w-1)/(w+1)
= 1 / (w+1)

 

7) -7yt/2at = ---/ 2ayz
Cross multiply:
2at? = -14ay^2tz
Divide out:
? = -7y^2z


8)find LCD for rational expression, convert rationa expression into equivalent reational expression with LCD as denominator
4/a-6 , 5/6-a
LCD = a-6
Fractions:
4/(a-6) and -6/(a-6)


9)lowest terms a+7/a-4 +9-5a/a
Do you mean:
(a+7)/(a-4) +(9-5a)/a
(You can use () to show me what's on top and the bottom)
Common denominator:
(a^2+7a)/(a^2-4a) + (9-5a)(a-4)/(a^2-4a)
(a^2+7a)/(a^2-4a) + (-5a^2+29a-36)/(a^2-4a)
= (-4a^2 + 36a - 36)/(a^2-4a)
But please confirm this problem...


10)2/x-3 + 3/3-x Simplify and reduce to lowest terms
= 2 /(x-3) - 3/(x-3)
= -1/(x-3)


11)1/9 + 1/3x/ x/9 - 1/x
Is this:
(1/9 + 1/(3x))/((x/9) - (1/x))
If so:
(x/(9x) + 3/(9x))/((x^2/9x) - (9/9x))
= ((x+3)/(9x))/ ((x^2-9)/(9x))
= ((x+3)/(9x)) / ((x-3)(x+3)/(9x))
1/(x-3)

 

12. ab + b^2/4ab^5 ________________ a+b/6a^2 b^4
Is it:
((ab + b^2)/(4ab^5)) / ((a+b)/(6a^2 b^4))
= (ab + b^2)(6a^2b^4) / (a+b)(4ab^5)
Cancel:
= (ab + b^2)(6a) / (a+b)(4b)
Expand:
= (6a^2b + 6ab^2) / (4ab + 4b^2)
= (3a^2b + 3ab^2) / (2ab + 2b^2)
But check the problem itself, since it didn't come through properly...

 

need these word out step by step: Use a proportion to sove each problem: 13) Fast Food: If four out of five doctors perfer fast food, then at a convention of 445 doctors, how many prefer fast food?
Set up the proportion:
4/5 = x/445

Cross multiply:

5x = 4*445

Divide by 5:

x = 4*445/5

Simplify:

x = 356

 

 

14) The anciet Greeks thought that the most pleasing shape for a retangle was one for which the ratio of the length was approximately 8 to 5, the golden ratio. If the length of a rectangular painting is 2 foot longer than it width, then for what dimensions would the length and width have the golden ration?
width = x

length = x+2

ratio:

(x+2)/x = 8/5

Cross multiply:

5(x+2) = 8x

5x + 10 = 8x

3x = 10

x = 10/3

x+2 = 16/3

 

The dimensions are 10/3 ft and 16/3 ft.

 

15) To estimate the size of the bear population in the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the convervationists estimate of the size of the bear poplulation?

Set up a proportion:

2/100 = 50/x

 

Cross multiply:

2x = 100*50

2x = 5000

 

Divide by 2:

x = 2500

 

2500 bears

 

Let me know if you have any questions,
Scott

Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Scott and 87 other Math Homework Specialists are ready to help you
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Customer reply replied 8 years ago
Thanks ever so much, will you help me out some more later on Thursday evening. I will need for you to do as we did last week, I will send you the problem and you send it back. If that will be ok let me know. I appreciate you so very much.

Thanks,
Nena

Sure, but if you want to work with me, just write For Scott at the top.

Thanks,

Scott

Ask Your Own Math Homework Question
Customer reply replied 8 years ago
Sure, I will ask for you personally,

Thanks,
Nena

Thanks! Putting my name at the top is the only way to be sure to get me. If you use that "box" in my profile, anyone can post :)

 

-Scott

Ask Your Own Math Homework Question
Customer reply replied 8 years ago
Scott,

need to see if you can do these few problems for me today and then I will get back on line with you tomorrow evening. I just got home from the ER I fell at work and busted my left hand, the ring finger and pinky up. Had to have twelve stiches and I am kind of out of it right now. if you can do these for me tonight i would appreciate it greatly.
1) 2t -9 /t (t-3) - t-9 / t (t-3)

2) what numbers cannot be used for x in rational expression 8 / ( 3 + 2x)

3) multiply rational expression and simply ( x^2 -4x 4) * 3 / (x -2)

4) solve: x/2 + 5/ x+3
need each step of the solution described in detail

if you can do this for me it would help me out greatly. They gave me something for pain and I will not be up for long. Will post tomorrow and include this in it.

Thanks a bunch
Nena

Hi there,

 

I'm so sorry to hear about that!

 

Please rewrite these:

3) multiply rational expression and simply ( x^2 -4x 4) * 3 / (x -2)

What's before that 4?

 

4) solve: x/2 + 5/ x+3

Where is the = sign?

 

Let me know,

-Scott

Ask Your Own Math Homework Question
Customer reply replied 8 years ago
3) ( x^2 - 4x + 4)
( x-2)

so sorry I was not thing straight

4) x/2 = 5 / x + 3


Hi there,

 

1) 2t -9 /t (t-3) - t-9 / t (t-3)

There already is a common denominator: t(t-3) -- I'm assuming that's on the
bottom of both...

So subtract the numerators:

t/(t(t-3))

Cancel:

1/(t-3)

 

2) what numbers cannot be used for x in rational expression 8 / ( 3 + 2x)
Set the bottom to 0:

3 + 2x = 0

2x = -3

x = -3/2 cannot be used

 

3)
( x^2 - 4x + 4) / ( x-2)
factor the top:
(x-2)(x-2)/(x-2)
Cancel an x-2:
x-2

 

4) solve: x/2 = 5/ x+3
cross multiply:
x(x+3) = 10
x^2 + 3x = 10
x^2 + 3x - 10 = 0
factor:
(x+5)(x-2) = 0
x = -5 or 2

 


Let me know if you have any questions, and don't forget to put "For Scott" at the top of your new thread later today :) This evening will work well, maybe starting after dinner -- say 6:30 eastern time.

-Scott

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