<span>(3.5, 3) is the circumcenter of triangle ABC.
The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors.
Line segment AB:
Slope
(4-2)/(1-1) = 2/0 = infinity.
This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3).
So the equation for this perpendicular bisector is y = 3.
Line segment BC
(2-2)/(6-1) = 0/5 = 0
This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2)
So the equation for this perpendicular bisector is x=3.5
So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC.
Now let's do a cross check to make sure that's correct.
Line segment AC
Slope = (4-2)/(1-6) = 2/-5 = -2/5
The perpendicular will have slope 5/2 = 2.5. So the equation is of the form
y = 2.5*x + b
And will pass through the point
((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3)
Plug in those coordinates and calculate b.
y = 2.5x + b
3 = 2.5*3.5 + b
3 = 8.75 + b
-5.75 = b
So the equation for the 3rd bisector is
y = 2.5x - 5.75
Now let's check if the intersection with this line against the other 2 works.
Determining intersection between bisector of AC and AB
y = 2.5x - 5.75
y = 3
3 = 2.5x - 5.75
8.75 = 2.5x
3.5 = x
And we get the correct value. Now to check AC and BC
y = 2.5x - 5.75
x = 3.5
y = 2.5*3.5 - 5.75
y = 8.75 - 5.75
y = 3
And we still get the correct intersection.</span>
Answer:
(3, 0) and (5, 0)
Step-by-step explanation:
we have
we know that
The x-intercepts are the values of x when the value of y is equal to zero
so
For y=0
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
so
x=3, x=5
therefore
The x-intercepts are (3,0) and (5,0)
You know that there are 25 people and each person had 36 carrots. To find how many carrots everyone has in total, you have to multiply 25 by 36.
25 times 36 is 900.
There are 900 carrots altogether.
Answer:
This is trigonomentry
Use SOHCAHTOA
where :
s is sin
c is cos
t is tan
o is opposite (side)
h is hypotenuse (opposite of 90 degree angle)
and a is adjacent (side)
Sin = o/h
cos = a/h
tan = o/a
in this case we are looking for side BC which is the hypotenuse(h)
and we have the side adjacent(a) to angle 71
since we have a and h determine what to use SIN, COS, OR TAN?
we should use Cos
they‘ve given the angle so we should do this...
Cos71 = 
Cos71 = 
now apply algebra...
6.3/cos71= BC
BC= 19.3507869666
BC = 19.4 (3SF)
