Question 550677: I have a few problems with a worksheet I am doing, that do not understand can you please help me?
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#1# Find the LCD of the fractions in the equation 4.5x / 2x+5 = 2x / x^2
I keep getting the answer (2x+5)(x) But it does not seem correct to me.
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#2# Solve each equation if no real answer then select no real answer.
x / x-5 = -2x/x
I keep getting x=10 in every way I try to solve the problem and it is not listed as one of the possible answers, I marked no real solution.
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#3# For this problem I do not understand on how to attempt it.
Find the focal length of the magnifying glass if you can see the butterfly clearly when your eye is 5.5 cm away from the glass and the glass is 25 cm away from the butterfly. The formula is 1/s + 1/t = 1/f.
I do not understand on how to do it.
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#4# Simplify the rational equations.
x+5 / 3x+15
I think it is in the simplist form already but I know you can divide the 5 into the 15 but can't divide the 3x into 3 .
x+5/4 divided by (x^2+5x)
I got 1/4x but i do not think it is correct.
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#5#
Solve the rational equation
x^3 / 16 = x^6 / 2
I keep getting an answer that is not listed as a possible answer.
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I am using the symbol "/" as the fraction symbol not the division symbol.
And thank you for your help.
Found 2 solutions by Alan3354, JBarnum:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the LCD of the fractions in the equation 4.5x / 2x+5 = 2x / x^2
I keep getting the answer (2x+5)(x) But it does not seem correct to me.
On the RHS, 2x/x^2 = 2/x
The LCD is x(2x+5)
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Solve each equation if no real answer then select no real answer.
x / x-5 = -2x/x
x = 0
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3x = 10
x = 10/3
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I keep getting x=10 in every way I try to solve the problem and it is not listed as one of the possible answers, I marked no real solution.
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For this problem I do not understand on how to attempt it.
Find the focal length of the magnifying glass if you can see the butterfly clearly when your eye is 5.5 cm away from the glass and the glass is 25 cm away from the butterfly. The formula is 1/s + 1/t = 1/f.
I do not understand on how to do it.
What are s, t & f?
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Simplify the rational equations.
x+5 / 3x+15
= 
= 1/3
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I think it is in the simplist form already but I know you can divide the 5 into the 15 but can't divide the 3x into 3 .
x+5/4 divided by (x^2+5x)
I got 1/4x but i do not think it is correct.
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Solve the rational equation
x^3 / 16 = x^6 / 2
Multiply by 16
x = 0 (multiplicity 3)
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x = 1/2
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| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
The discriminant -12 is less than zero. That means that there are no solutions among real numbers.
If you are a student of advanced school algebra and are aware about imaginary numbers, read on.
In the field of imaginary numbers, the square root of -12 is + or -  .
The solution is  , or
Here's your graph:
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It's 6th order --> 6 solutions:
0,0,0,1/2, and the 2 complex numbers.
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I keep getting an answer that is not listed as a possible answer.
Answer by JBarnum(2146)  (Show Source):
You can put this solution on YOUR website! for #1# it cant be your answer as x^2 isnt divisiable of  an  could come out but not  The LCD is best found by multiplying the 2 denoms together with variables. 
.
for #2#
cross multiply
see quadratic equation solver at bottom
 or 
.
for #3#
im not going to take credit as i had to look this up, same question from 5 years ago. this is coppied from yahoo answers.
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Find the focal length of the magnifying glass?
if you can see the butterfly clearly when your eye is 5.5 cm away from the glass and the glass is 25 cm away from the butterfly. The formula is 1/s + 1/t ≈ 1/f.
a) focal length is about 30.5 cm
b) focal length is about 4.5 cm
c) focal length is about 4.2 cm
which option is a true answer ?
5 years ago
by DavidK93 Member since:
18 August 2006
Total points:
46,927 (Level 7)
Add Contact
Best Answer - Chosen by Voters
Your formula 1/s + 1/t = 1/f is correct in its form, although I haven't seen it with those particular variables; the object and image lengths are usually called R1 and R2 or s1 and s2, or sometimes s and s'. So I'm not sure which of s and t is supposed to be the object's location and which is the observer's position, but luckily it doesn't matter.
1/5.5 + 1/25 = 1/f ==> 0.18 + 0.04 = 1/f ==> 1/f = 0.22 ==> f = 1/0.22 = 4.51
The focal length is 4.51 cm, so choice b) about 4.5 cm is the correct answer.
Source(s):
http://en.wikipedia.org/wiki/Thin_lens
5 years ago
<<<
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#4#
#5#
cross multiply
= 
= 
= 
x=1/2 and no real solutions according to solver below
#5#
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
The discriminant -12 is less than zero. That means that there are no solutions among real numbers.
If you are a student of advanced school algebra and are aware about imaginary numbers, read on.
In the field of imaginary numbers, the square root of -12 is + or - .
The solution is 
Here's your graph:
|
#2#
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation (in our case  ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=100 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 3.33333333333333, 0.
Here's your graph:
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