Given the line 2x-3=9 and the point (4,-1) find the lines through the point that are (a) parallel to the given line and (b) perpendicular to it

I must assume that you meant 2x - 3y = 9.

A line parallel to this line has exactly the same format, but a different constant on the right: 2x - 3y = c. Substituting the given values of x and y, we get:

2(4) - 3(-1) = 8+3 = 11. Thus, c = 11, and the equation of the new parallel line is

11 - 2x

2x - 3y = 11. Solving for y, -3y = 11 - 2x, or y =

-3

so the slope of the parallel lilnes is 2/3.

A line perpendicular to the given line has a slope which is the negative reciprocal of 2/3: -3/2.

This perpendicular line has the equation

y + 1 = (-3/2)(x-4) (point-slope form), or

2y + 2 = -3(x-4) = -3x + 12. Then 2y = -3x + 12, and y = (-3/2)x + 6 (the perpendicular line's equation)

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

your answer is a

step-by-step explanation:

4*4*4*4=256