TheXSquaredFactor

\(\sqrt{52}=\sqrt{4*13}=\sqrt{4}\sqrt{13}=2\sqrt{13}\approx7.2111\)

\(\sqrt{33+\sqrt{8}}*\sqrt{6+\sqrt{3+\sqrt{8}}}*\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{8}}}}*\sqrt{3-\sqrt{3+\sqrt{3+\sqrt{8}}}}\approx32.87856\)

YIPPEE! I have 1111 hearts now!

Cartography and astronomy rely heavily on trigonometry. 

With trigonometry one can accurately represent the locations of the landmasses of the Earth or calculate the distance in between two stars.

An irrational number is a real number that cannot be represented as a ratio of \(\frac{a}{b}\)such that a and b are both integers.

Another way to know if a number is irrational is to notice if the decimal expansion does not terminate or repeat indefinitely. If it is, that number is irrational.

\(\pi\), for example, is irrational. \(\sqrt{2}\) is also irrational. \(\phi\) (known as the golden ratio) is irrational, too.

\(\frac{1}{3}\) is not irrational because it is a ratio of \(\frac{a}{b}\) where a=1 and b=3.

\(2.7551\) is not irrational because the decimal terminates.

\(1.3\overline{949494}\) is not irrational because the decimal repeats indefinitely. 

Well, I am going to answer anyway.

Absolute value inequalities are not that simple! You can't simply just ignore them.

This is your answer. Since the greater than symbol will cause an "or" statement, we know that solutions are the following:

\(x>\frac{17}{7}\hspace{1mm}\text{or}\hspace{1mm} x<-\frac{117}{7}\)

Here's another solution!

\(4^{2+3-5}-1=0\)

\(4^2-5*3-1=0\)

\(\frac{4*3}{2}-5-1=0\)

\(\frac{4+1}{5}-3+2=0\)

These are a few possibilities that I came up with.

We can use the Euclidean algorithm for this:
 

To find the equation that passes through \((-4,0)\) and is parallel to the line \(y=\frac{3}{4}x-2\), we must understand a few properties. 

1) Parallel lines have the same slope.

This fact, alone, can help us do half the problem. The slope of the line \(y=\frac{3}{4}x-2\) is \(\frac{3}{4}\). As I stated above, parallel lines have the same slope, so the equation of this unknown line is \(\frac{3}{4}\).

We have deduced already that this unknown line is in the form of \(y=\frac{3}{4}x+b \). The only thing to find now is the b:
 

We have found both of the mystery values to construct the proper equation of a line. It is \(y=\frac{3}{4}x+3\)

1)

If \((2x+3y)(3y+2x)=z\), according to the given information, and \(x=3.2\) and \(z=457.96\), just plug those values in to solve for y:
 

2)

This is a system of equations. I usually refrain from using the elimination method here because it is difficult to showcase. Therefore, I will use the substitution method. 

I will solve for y in equation 2:
 

Plug this value for y into equation 1 and then solve for x.

Now, plug x=-4 into either equation and solve for y. I'll choose equation 2 because it look easier to do:

Therefore, the coordinate where both lines intersect is \((-4,2)\).