Basic maths

I'll suck your balls, please tell me how.

Consider the equation of the line [math]y= mx + b[/math] in [math]\mathbb{R}^2[/math]

By picking two points in the line, [math]y_1 = m x_1+b[/math] and [math]y_2 = m x_2 +b[/math], we can solve one of the equations for b and substitute it into the other, for example, solve the second for b and substitute into the first.

[math]b = y_2 - m x_2 \Rightarrow y_1 = m x_1 + y_2 - m x_2 \Rightarrow m x_2 - m x_1 = y_2 - y_1[/math]
[math]\displaystyle \Rightarrow m(x_2 - x_1) = y_2 - y_1 \Rightarrow m = \frac{y_2 - y_1}{x_2 - x_1}[/math]

We can see if the slope is negative of positive by comparing [math]y_2,y_1,x_2,x_1[/math] given.
Since [math]y_2 > y_1[/math] and [math]x_2 > x_1[/math] it follows that [math]\displaystyle \frac{y_2 - y_1}{x_2 - x_1} > 0 \Rightarrow m > 0[/math]

We also know that [math]\displaystyle |m| = \frac{|y_2 - y_1|}{|x_2 - x_1|}[/math].

Where [math]|y_2 - y_1| = d(y_2,y_1)[/math] the distance from [math]y_2[/math] to [math]y_1[/math] and [math]|x_2 - x_1| = d(x_2,x_1)[/math], the distance from [math]x_2[/math] to [math]x_1[/math], and we also know that [math]m>0[/math], so [math]|m| = m[/math].

So we can write the our equation as [math]\displaystyle m = \frac{d(y_2,y_1)}{d(x_2,x_1)}[/math]

Now, to simplify things a bit, we take [math]\tau = \mathbb{P}(\mathbb{R}^2)[/math], so [math]\displaystyle m = \frac{d(y_2,y_1)}{d(x_2,x_1)} = \frac{d(5/6,\,0)}{d(3⅓,0)} = \frac{1}{1} = 1[/math]

So [math] m = 1 [/math]

answer is 1/4 try again plz dont fucken know how to get 1/4 from d(y2,y1)d(x2,x1)=d(5/6,0)d(3⅓,0)

found it !!!!

(5/6,0)
_____
(3⅓,0)

(3⅓,0) = 3/1 + 1/3 = 9/3 + 1/3 = 10/3

(5/6,0)
_____
(10/3,0) = 1/4

thx for youre help guys

That simply comes from our simplification of [math]\tau = \mathbb{P}(\mathbb{R}^2)[/math]

So d becomes [math]d(a,b) = 0[/math] if [math] a = b[/math] and [math]d(a,b) = 1[/math] if [math]a \neq b[/math]

I'm looking for HP and I don't know how to do it.

The m formula is to calculate the slope of a linear function.
Just plug in the values and do it:

3 and 1/3 is 10/3

m = 5/6-0 / 10/3 - 0
= (5/6)/(10/3)
= 5*3/6*10
=15/60
=1/4

Not that hard OP

Just apply as many side-angle rules as you can until the answer shakes out.

Find the length of HS

JH moves through a distance SH in 49 degrees
JH must then move through a distance SP in 59 degrees
Set up a ratio to find the length of PS then subtract HS to find HP

the answer is 26.0