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
Answer:
D
Step-by-step explanation:
If you look at the centerand radius of a circle (those are the two most important things when defining a circle), you will see, they shrank by a factor of two, so since it affected both x and y, it had to be from the origin.
-4.4(s - 2) + 6.9s = 14.8
Distribute -4.4 into the parenthesis:
-4.4s + 8.8 + 6.9s = 14.8
Combine like terms:
2.5s + 8.8 = 14.8
Subtract 8.8 from both sides of the equation:
2.5s + 8.8 - 8.8 = 14.8 - 8.8
2.5s = 6
Divide both sides by 2.5:
2.5s/2.5 = 6/2,5
s = 2.4
s =
Answer:
53/36
Step-by-step explanation:
56/36 is already in it's simplest form
Answer:
x^3+9x^2-3x^2-3
Step-by-step explanation:
You can use a various of methods but when you use the box method you multiply each separately.
Like you would multiply x² by x, 8x by x, -3 by x (thats the first row)
x² by 1, 8x by 1, -3 by 1 ( for the second row)
Then you get those final variables and combine like terms getting the answer above
