Answer:
x=3, y=9
Step-by-step explanation:
5x-2y=-3
4x-2y=-6
Then:
solve for y:
-2y=-6-4x
y=3+2x
Substitute y into either equation:
4x-2(3+2x)=-6
4x-6-4x=-6
-6=-6, use other equation
5x-2(3+2x)=-3
5x-6-4x=-3
x-6=-3
x=3
then:
y=3+2(3)
y=9
5*3=15
15-4= 11
hope I helped:)
Answer:
- (1,3) is inside the triangle
Step-by-step explanation:
Orthocenter is the intersection of altitudes.
We'll calculate the slopes of the two sides and their altitudes ad find the intersection.
<h3>Side QR</h3>
- m = (3 - 5)/(4 - (-1)) = -2/5
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through S(-1, -2):</u>
- y - (-2) = 5/2(x - (-1)) ⇒ y = 5/2x + 1/2
<h3>Side RS</h3>
- m = (-2 - 3)/(-1 -4) = -5/-5 = 1
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through Q(-1, 5):</u>
- y - 5 = -(x - (-1)) ⇒ y = -x + 4
The intersection of the two lines is the orthocenter.
<u>Solve the system of equations to get the coordinates of the orthocenter:</u>
- 5/2x + 1/2 = x + 4
- 5x + 1 = -2x + 8
- 7x = 7
- x = 1
<u>Find y-coordinate:</u>
The orthocenter is (1, 3)
If we plot the points, we'll see it is inside the triangle
Step-by-step explanation:
Use tan relation :
tan85.7=h/80
h=tan85.7×80
h=1063.96ft