Answer:
See explanation
Step-by-step explanation:
Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).
Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.
We apply the 90 degrees clockwise rotation rule.
We apply the 90 degrees clockwise rotation rule again on the resulting points:
Let us now apply 90 degrees counterclockwise rotation about the origin twice to obtain 180 degrees counterclockwise rotation.
We apply the 90 degrees counterclockwise rotation rule.
We apply the 90 degrees counterclockwise rotation rule again on the resulting points:
We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.
Answer:
a) TO = OP = 13
b) Height = 12
Step-by-step explanation:
a) Isosceles triangle TOP with base TP = 10 cm, side TO = OP = x cm.
Perimeter of triangle TOP = 36 cm
=> TO + OP + TP = 36
=> x + x + 10 = 36
=> 2x = 26
=> x = 13
=> TO = OP = 13 cm.
b) Apply Pythagorean theorem:
height^2 + (base/2)^2 = side^2 (height^2 + (TP/2)^2 = TO^2)
or
height^2 + (10/2)^2 = 13^2
or
height^2 + 25 = 169
or
height^2 = 144
or
height = 12
Hope this helps!
Solving for the midpoint:
x - coordinate: (7.6 + 4.6)/2 = 6.1
y - coordinate: (10.1 + 3.1)/2 = 6.6
Midpoint: (6.1 , 6.6)
Solving for the distance:
Distance formula: sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
D = sqrt( (7.6 - 4.6)^2 + (10.1 - 3.1)^2 <span>)
D = sqrt( 3^2 + 7^2)
D = sqrt(58)
D = 7.62 units
Distance = 7.62 units</span>
After the 3rd pick we have: 4 white, 3 red and 8 black marbles.
The probability that the 4th marble is black is:
P ( Black ) = 8 / 15 = 0.5333
After the 4th pick we have: 4 white, 3 red and 7 black marbles.
P ( Red or Black ) = 10 / 14 = 5 / 7 = 0.7143
The answer would be 89.90558242
If u round it off, the answer will be 90
