ChowMein

A horizontal asymptote is the line that a function approaches as x goes to infinity or negative infinity. So although the function crosses the x axis at (-1, 0), it's not what the function approaches as x goes to infinity or negative infinity. It's why something like this could happen. 

125 electrons gained.

I tried to make it as neat as possible. 

Part 1: Find the coordinates of point Q in terms of a, b, and c

Part 2: Use the coordinates to verify that SQ and PR bisect each other.

For inscribed quadrilaterals, opposite angles are supplementary. 
By setting the measures of B plus D equal to 180, we solve for x.
\(x+24+x+10=180\\ x=73\) 
You use this x value to plug into x+15 (measure of angle A).
Opposite angles are supplementary so you subtract the measure of angle A you just calculated from 180 to get the measure of angle C. 

\(x+15\\ 73+15=88\\ 180-88=92\)

\(2x^2-3=6x\\ \text{Make sure it's in}\,ax^2+bx=c\;\text{form}\\ 2x^2-6x=3\\ \text{Leading coefficient must be 1}\\ x^2-3x=\frac{3}{2}\\ x^2-3x+(\frac{3}{2})^2=\frac{3}{2}+(\frac{3}{2})^2\\ (x-\frac{3}{2})^2=\frac{15}{4}\\ \text{Take the square root of both sides}\\ x-\frac{3}{2}=\pm\frac{\sqrt{15}}{2}\\ x=\frac{3\pm\sqrt{15}}{2}\\ x=\frac{3+\sqrt{15}}{2},\;x=\frac{3\pm\sqrt{15}}{2}\)

\(R^3=\sqrt{4hp}\\ \text{Square both sides to remove square root}\\ (R^3)^2=(\sqrt{4hp})^2\\ R^6=4hp\\ \text{Divide 4h to isolate p}\\ \frac{R^6}{4h}=p \)

For line 3, one of the law of exponents state:
\((x^a)^b=x^{ab}\)

\(15*9=135\)

What percent of 75 is 15?

Translates to:

\(75\,*\,x\,=15\\ x\%=\frac{15}{75}\\ x=0.2\\ 0.2 = 20\% \)

Tips:

I'll use the same numbers for each example. 

Three variants

What percent of 100 is 40?

oldnum * {percent} = newnum

(What percent of the original number [100] gives you the new number [40]?)

100 * ? = 40

? = 40/100

? = 0.4

0.4 --> 40%

What is 40% of 100?

oldnum * percent = {newnum}

([40] percent of the original number [100] results in what number?)

100 * 40% = ?

40% --> 0.4

100 * 0.4 = 40

40% of what is 40?

{oldnum} * percent = newnum

([40] percent of what number gives you the new number [40])?

? * 40% = 40 

40% --> 0.4

? * 0.4 = 40

? = 40/0.4

? = 100

*this was hard for me at first, but with practice, you'll get used to the wording of the questions

\(\frac{51800000000}{133900000000}=0.387\)

\(0.387=0.00387\%\)

We need to find the base first.

b=l*w

b=6*6

b=36

Next, we need to find the slant height.

Find s using the pythagorean theorem,

s^2=6^2-3^2

s=√36-9

s=√27=3√3

Great, now we have s. The only thing that's left is h, for the formula for the volume of a pyramid.

V=bh/3

We need h. To help you better visualize the picture above, take a look at this one.

Since the sides are 6, r is side/2 = 3.

Use pythagorean theorem for h.

h=√(3√3)²-3²

h=√27-9

h=√18

Alright, lets plug everything into the volume formula.

V=bh/3

V=36√18/3

V=36√9*2/3

V=108√2/3

V=36√2=50.9 units^3