What we know:
line P endpoints (4,1) and (2,-5) (made up a line name for the this line)
perpendicular lines' slope are opposite in sign and reciprocals of each other
slope=m=(y2-y1)/(x2-x1)
slope intercept for is y=mx+b
What we need to find:
line Q (made this name up for this line) , a perpendicular bisector of the line p with given endpoints of (4,1) and (2,-5)
find slope of line P using (4,1) and (2,-5)
m=(-5-1)/(2-4)=-6/-2=3
Line P has a slope of 3 that means Line Q has a slope of -1/3.
Now, since we are looking for a perpendicular bisector, I need to find the midpoint of line P to use to create line Q. I will use the midpoint formula using line P's endpoints (4,1) and (2,-5).
midpoint formula: [(x1+x2)/2, (y1+y2)/2)]
midpoint=[(4+2)/2, (1+-5)/2]
=[6/2, -4/2]
=(3, -2)
y=mx=b when m=-1/3 slope of line Q and using point (3,-2) the midpoint of line P where line Q will be a perpendicular bisector
(-2)=-1/3(3)+b substitution
-2=-1+b simplified
-2+1=-1+1+b additive inverse
-1=b
Finally, we will use m=-1/3 slope of line Q and y-intercept=b=-1 of line Q
y=-1/3x-1
Your wording amounts to the equation
4*sqrt(x)+2=-16
4*sqrt(x)=-18
sqrt(x)=-9
but square roots are nonnegative so no solution exists.
There are four quarts in a gallon
There are four cups in one quart
so four times four would give you your answer...
16
I don't have a calculator near me... but you probably do. So just plug in those values for t.
Y = 4(-3) ^2 + 5
(Actually.. I might be able to do these in my head...) Y = 41
Y = 4(-1.5) ^2 + 5
Y = 14
Y = 4(0) ^2 + 5
Y = 5
Y = 4(1) ^2 + 5
Y = 9
Y = 4(4) ^2 + 5
Y = 69
The range is all the Y values. So it would be {41, 14, 5, 9, 69}
and the second one 2 will work!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
