Okay to find the perpendicular bisector of a segment you first need to find the slope of the reference segment.
m=(y2-y1)/(x2-x1) in this case:
m=(-5-1)/(2-4)
m=-6/-2
m=3
Now for the the bisector line to be perpendicular its slope must be the negative reciprocal of the reference segment, mathematically:
m1*m2=-1 in this case:
3m=-1
m=-1/3
So now we know that the slope is -1/3 we need to find the midpoint of the line segment that we are bisecting. The midpoint is simply the average of the coordinates of the endpoints, mathematically:
mp=((x1+x2)/2, (y1+y2)/2), in this case:
mp=((4+2)/2, (1-5)/2)
mp=(6/2, -4/2)
mp=(3,-2)
So our bisector must pass through the midpoint, or (3,-2) and have a slope of -1/3 so we can say:
y=mx+b, where m=slope and b=y-intercept, and given what we know:
-2=(-1/3)3+b
-2=-3/3+b
-2=-1+b
-1=b
So now we have the complete equation of the perpendicular bisector...
y=-x/3-1 or more neatly in my opinion :P
y=(-x-3)/3
A is correct because f(1)=3^1+1 so f(1)=4 and g(x)=4 so f(x)=g(x)
B is also correct because the ordered pair we get is (1,4) and this is in quadrant 1
C is incorrect
D is incorrect
E is incorrect
Ans: A and B are correct
It is a 45-45 - 90 triangle (as the right angle is split in half for the outer one)
In this case, x is in the hypotenuse. The side lengths follow the 1, 1, √2 formula.
If 1 = 3, then:
3 x √2 = Answer
Answer = 3√2
hope this helps
Nancy's rate=27 mph
Greg's rate=45 mph
t=Greg's time
t+2=Nancy's time
Since they both traveled same distance then:
27(t+2)=45t
27t+54=45t
18t=54
t=3 hours
Greg will pass Nancy after 3 hours
