Just did a specific one of these; let's do the general case.
The point nearest the origin is (a,b).
The line from the origin through the point is
The line we seek is perpendicular to this one. We swap the coefficients on x and y, negating one, to get the perpendicular family of lines. We set the constant by plugging in the point (a,b):
That's standard form; let's plug in the numbers:
Answer:
y+1=3(x-4)
Step-by-step explanation:
Hi there!
We are given a slope of 3 and a point (4,-1).
We need to find the equation of the line in point-slope form
Point-slope form is given as y-y1=m(x-x1), where m is the slope, and (x1,y1) is a point
We have all of the needed information to substitute into the formula
First, let's label the values of everything to avoid any confusion
m=3
x1=4
y1=-1
now substitute into the formula *remember, the formula has SUBTRACTION, and we have a NEGATIVE number, so we'll end up subtracting a negative*
y--1=3(x-4)
simplify
y+1=3(x-4)
That's it!
Hope this helps :)
The area of a rectangle is the product of its length and width.
Well this is a more complicated question than it may seem.
The laws of probability are based on observations whose number is very large or actually as the number of observations approaches infinity.
So on the one hand, you should be concerned that you get 0/8 to land on 3.
However, 42/500 land on 3 so your ratio has improved.
It's not near 125 but it's also not 0.
If it remained at 0, you would begin to be concerned and rightly so.
Perhaps if you did 5000, you would be less concerned as the ratio improved and got closer to 1/4 of the observations.
So at this point I don't think you have enough information to determine that the spinner is unfair.
