Answered

Given the function [tex]f(x)=\sqrt{2x}+5x^2[/tex], analyze its behavior.

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Solve for [tex]\( x \)[/tex]:

[tex]\[ 3x = 6x - 2 \][/tex]

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Read the lines from "The Tide Rises, The Tide Falls":

"Darkness settles on roofs and walls,
But the sea, the sea in darkness calls;"

The imagery in these lines evokes a sense of:
A. laziness
B. fear
C. mystery
D. despair

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Which best explains why Irving sets "The Adventure of the Mysterious Stranger" in a land of "masks and gondolas"?

A. The setting is symbolic of the idea that a life of quiet study is the ideal pursuit.
B. The setting is symbolic of the idea that innocence cannot be outgrown.
C. The setting is symbolic of the idea that ease and affluence are available to all.
D. The setting is symbolic of the idea that appearances can be deceiving.

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An electric device delivers a current of [tex]15.0 \, \text{A}[/tex] for 30 seconds. How many electrons flow through it?



Answer :

Alright, let's delve into the given function [tex]\( f(x) \)[/tex] and understand its various components step-by-step.

The function in question is:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]

### Step-by-Step Solution:

1. Understand Each Term:

- The first term is [tex]\( \sqrt{2x} \)[/tex], which involves a square root of the product of 2 and [tex]\( x \)[/tex].
- The second term is [tex]\( 5x^2 \)[/tex], which is a basic polynomial term where [tex]\( x \)[/tex] is squared and then multiplied by 5.

2. Rewrite the Function:

Let's rewrite the function to clearly see its structure:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]


3. Handling the Square Root Term:

Consider the first term [tex]\( \sqrt{2x} \)[/tex]:
- The expression [tex]\( 2x \)[/tex] is inside the square root. To manipulate or simplify this, remember that:
[tex]\[ \sqrt{2x} = \sqrt{2} \cdot \sqrt{x} \][/tex]
Thus, we separate it into two distinct square root factors.

4. Handling the Polynomial Term:

The second term [tex]\( 5x^2 \)[/tex] is already in its simplest form:
- [tex]\( 5 \)[/tex] is the coefficient.
- [tex]\( x^2 \)[/tex] is [tex]\( x \)[/tex] raised to the power of 2.

So, combining both observations, we can rewrite the function as:
[tex]\[ f(x) = \sqrt{2} \cdot \sqrt{x} + 5x^2 \][/tex]

However, this expression:
[tex]\[ \sqrt{2}\sqrt{x} + 5x^2 \][/tex]

is more commonly written in a slightly more compact form:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]

### Conclusion

In summary, the function [tex]\( f(x) \)[/tex] combines a radical expression and a polynomial expression:
[tex]\[ f(x) = \sqrt{2} \cdot \sqrt{x} + 5x^2 \][/tex]

Given this function:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
we recognize it can also be written as:
[tex]\[ f(x) = \sqrt{2}\sqrt{x} + 5x^2 \][/tex]

stressing the separate nature of the constants and variables involved.