Step-by-step explanation:
I'm not sure about my answer
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
To find the correct fraction, multiply 6 by 3.
This gives you 18. Therefore the fraction is 18/3
Hope this helps!
LCM:
10: 0,10,20,30,40,50
4: 0,4,8,12,16,20
ANSWER IS 20
LCM:
10: see above numbers
6: 0,6,12,18,24,30
ANSWER IS 30
So, 10 and 8 would be 40
The 13 stripes alternate red and white: 7 red and 6 white.
Each of 13 stripes is (39 in. / 13) = 3 in. wide.
4 of the 7 red stripes are 39 in. long. The other 3 are 65 in. long.
The total area (l*w) of the flag is (65 in.)*(39 in.)=2535 sq. in.
The red stripes make up an area (l*w) that is:
4*(area of short stripes) + 3*(area of long stripes)
Red area is 4*(39*3) + 3*(65*3) = 1053 sq in.
The fraction of the flag that is red is:
1053 sq. in. / 2535 sq. in.