Answer:
Yes!
Step-by-step explanation:
We know that right triangles follow the Pythagorean Theorem, where
So we will put our side lengths into this formula, keeping in mind that c = the hypotenuse, which is the longest side. a and b are fairly arbitrary.
If this works, we know it's a right triangle.
1089 + 1936 = 3025
3025 = 3025
It worked! It's a right triangle!!
1. set up the equation which makes these shapes equal, 1/2(2(x+1)) = 1x
2. solve, x+1=x, 1=0
3. since this is impossible, there is no solution and zero answers
Answer:
680 games
Step-by-step explanation:
Suppose that 681 tennis players want to play an elimination tournament.
1st round:
One of 681 players, chosen at random, sits out that round and 680 players play. There will be 340 winners plus one player which sits - 341 players for the next round and 340 games
2nd round:
There will be 170 winners plus one player which sits - 171 players for the next round and 170 games
3rd round:
There will be 85 winners plus one player which sits - 86 players for the next round and 85 games
4th round:
There will be 43 winners - 43 players for the next round and 43 games
5th round:
There will be 21 winners plus one player which sits - 22 players for the next round and 21 games
6th round:
There will be 11 winners - 11 players for the next round and 11 games
7th round:
There will be 5 winners plus one player which sits - 6 players for the next round and 5 games
8th round:
There will be 3 winners - 3 players for the next round and 3 games
9th round:
There will be 1 winner plus one player which sits - 2 players for the next round and 1 game
10th round - final:
1 champion and 1 game.
In total,
340 + 170 + 85 + 43 + 21 + 11 + 5 + 3 + 1 + 1 = 680 games
Answer:
1595 ft^2
Step-by-step explanation:
The answer is obtained by adding the areas of sectors of several circles.
1. Think of the rope being vertical going up from the corner where it is tied. It goes up along the 10-ft side. Now think of the length of the rope being a radius of a circle, rotate it counterclockwise until it is horizontal and is on top of the bottom 20-ft side. That area is 3/4 of a circle of radius 24.5 ft.
2. With the rope in this position, along the bottom 20-ft side, 4.5 ft of the rope stick out the right side of the barn. That amount if rope allows for a 1/4 circle of 4.5-ft radius on the right side of the barn.
3. With the rope in the position of 1. above, vertical and along the 10-ft left side, 14.5 ft of rope extend past the barn's 10-ft left wall. That extra 14.5 ft of rope are now the radius of a 1/4 circle along the upper 20-ft wall.
The area is the sum of the areas described above in numbers 1., 2., and 3.
total area = area 1 + area 2 + area 3
area of circle = (pi)r^2
total area = 3/4 * (pi)(24.5 ft)^2 + 1/4 * (pi)(4.5 ft)^2 + 1/4 * (pi)(14.5 ft)^2
total area = 1414.31 ft^2 + 15.90 ft^2 + 165.13 ft^2
total area = 1595.34 ft^2
Answer:
The Answer is 25
Step-by-step explanation:
