Solve the proportion:
4/x = (radical sign over 11, not -1) 11 - 1/3
Please solve and explain. My answer does not match any of my choices.
4/x= sqrt11 -1/3
x= 4/(sqrt11-1/3)
Now some would rationalize the denominator, but multiplying the right side by sqrt11+1/3
x=4(sqrt11+1/3)/(11-1/9)
are you certain you copied this correctly? This is a little complicated for an Algebra I student.
It is copied correctly. My choices are:
6/5 sqrt11 + 6/5
5/6 sqrt11 + 6/5
6/5 sqrt11 - 6/5
5/6 sqrt11 - 6/5
To solve the proportion "4/x = (√11 - 1)/3", we can cross multiply.
Cross multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction, and then multiplying the denominator of the first fraction by the numerator of the second fraction. This gives:
4 * 3 = x * (√11 - 1)
We simplify the right side of the equation:
12 = x(√11 - 1)
Next, we isolate x by dividing both sides of the equation by (√11 - 1):
12 / (√11 - 1) = x
To simplify the denominator, we rationalize it by multiplying both the numerator and the denominator by the conjugate of (√11 - 1), which is (√11 + 1):
12 / (√11 - 1) * (√11 + 1) / (√11 + 1) = x
This gives us:
x = 12(√11 + 1) / ((√11)^2 - (1)^2)
Simplifying further:
x = 12(√11 + 1) / (11 - 1)
x = 12(√11 + 1) / 10
x = 6(√11 + 1) / 5
Therefore, the solution to the proportion "4/x = (√11 - 1)/3" is x = 6(√11 + 1) / 5.
If your answer does not match any of the given choices, please double-check your calculations and ensure that you accurately substituted the values.