If the square root of 1 over 2 x - 10 added by 3, which inequality can be used to find

From the description, we have the function [tex]f(x)= \sqrt{ \frac{1}{2x-10}+3 }[/tex]
Since the square root cannot be a negative number, the only thing need to do to find the domain of the function [tex]f(x)[/tex] is take the expression inside the square rot and set it greater or equal than zero:
[tex]\frac{1}{2x-10}+3 \geq 0[/tex]
[tex]\frac{6x-29}{2x-10} \geq 0[/tex]
[tex]\frac{6x-29}{2(x-5)} \geq 0[/tex]
[tex]x \leq \frac{29}{6}[/tex] or [tex]x\ \textgreater \ 5[/tex]

We can conclude that we can use the inequality [tex]\frac{1}{2x-10}+3 \geq 0[/tex] to find the domain of [tex]f(x)[/tex]. Also, the domain of [tex]f(x)[/tex] is (∞,[tex]\frac{29}{6}[/tex]]U(5,∞).

[tex]\frac{i}{(3 \: + \: 8i) \: - \: (2 \: + \: 5i)} \: = \: \frac{i}{1 \: + \: 3i} \: = \: \frac{i}{1 \: + \: 3 i} \: \times \: \frac{1 \: - \: 3i}{1 \: - \: 3i} \: = \: \frac{i \: + \: 3}{1 \: + \: 9} \: = \: \frac{3 \: + \: i}{10}[/tex]A) (3 + i)/10

Comment
I'm taking this to mean
[tex]\frac{ \sqrt{-1} }{(3 + 8i) - (2 + 5i)}[/tex]

Step One
Simplify the denominator
3 + 8i - 2 - 5i
1 + 3i

Step Two
rewrite the numerator in terms of i.
sqrt(-1) = i

Step 3
rewrite the fraction
[tex]\frac{i}{1 + 3i}[/tex]

Step 4
Rationalize the denominator. Multiply top and bottom by (1 - 3i)
[tex]\frac{i * (1 - 3i)}{(1 - 3i)(1 + 3i)}[/tex]

Step 5
Simplify the denominator.

[tex]\frac{i*(1 - 3i)}{(1 - 9i^2)}[/tex]
[tex]\frac{i* (1 - 3i)}{1 + 9} = \frac{i*(1 - 3i)}{10}[/tex]

Step Six
Remove the brackets in the numerator.
[tex]\frac{i + 4}{10}\text{ I'll leave you to figure out the numerator}[/tex]

Remember
[tex]\sqrt{ \frac{x}{y} } = \frac{ \sqrt{x} }{ \sqrt{y} }[/tex]
so

[tex]\sqrt{ \frac{1}{49} } = \frac{ \sqrt{1} }{ \sqrt{49} } = \frac{1 }{7 }[/tex]

answer is 1/7

This is easier than it may appear.
To find the square root of a fraction, you simply have to find the square root of the numerator and denominator separately.
In this problem, that just means finding the square root of 1 and the square root of 25.
√1 = 1 since 1•1=1
√25 = 5 since 5•5=25.
So the square root of 1/25 is 1/5.
Checking your work you can multiply 1/5 by 1/5 to be sure.
1/5 • 1/5 = 1/25 so that confirms this is the correct answer.

You can divide it for 2 different square roots, what will give you: sqrt(1)/sqrt(49)=1/7

If you need an equation, it would be y=2x+8, y would be how long it grew, x being weeks.if you need how long he was asleep, it would be 4 weeks if he started with no beard, the equation would be x=8÷2if he did have a beard before hand, the equation would be 2w+x=8

A