Answer:
k=32
Step-by-step explanation:
Given the points:
The first step is to find the <u>Centroid</u> of the triangle.
Centroid, X
Next, let P be a point (x,y)
Using the <u>distance formula, </u>
<u />
<u />
<u />
On Substitution into: 
![(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y-%28-1%29%29%5E2%2B%28x-6%29%5E2%2B%28y-2%29%5E2%2B%28x-%28-1%29%29%5E2%2B%28y-2%29%5E2%3D3%5B%28x-3%29%5E2%2B%28y-1%29%5E2%5D%2Bk)
Let us simplify the LHS first
Also, the Right Hand Side
![RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k](https://tex.z-dn.net/?f=RHS%3A3%5B%28x-3%29%5E2%2B%28y-1%29%5E2%5D%2Bk%5C%5C%3D3%5Bx%5E2-6x%2B9%2By%5E2-2y%2B1%5D%2Bk%5C%5C%3D3x%5E2-18x%2B27%2B3y%5E2-6y%2B3%2Bk%5C%5C%3D3x%5E2%2B3y%5E2-18x-6y%2B30%2Bk)
Therefore:
Hello!
Let's write this as an equation below.
310/3+d=295/d
As you can see, we can cross-multiply this proportion giving us the equation below.
310d=295(3+d)
310d= 295d+885
Now, we subtract 295d from both sides.
15d=885
Now we divide both sides of the equation by 15.
d=59
Therefore, Dana travels 59 mph.
I hope this helps!
They are same side interior angles and same side interior angles are supplementary (add up to 180 degrees).
So, 6x+12+4x+18=180
Combine like terms:
10x+30=180
Subtract 30 from both sides:
10x=150
Divide both sides by 10:
x=15.
Therefore, the angles are same-side interior angles and x=15.
Hi!
The point where the three altitudes of a triangle intersect is called the orthocenter.
Altitudes are lines which pass through the the vertex of a triangle, and bisect the other side.
There are three other points like an orthocenter; an incenter, a circumcenter, and a centroid. They're where the angle bisectors, the perpendicular bisectors, and the medians of a circle intersect, respectively.
Hope this helped!
Answer:
Possible base lengths are 1, 2, 3, 4, 5
Step-by-step explanation:
Area = base x height / 2
Let base be b
b x 8 / 2 < 24 (Area < 24)
4b < 24
b < 6
