Using the identity :
Cos (2a) = 1-2 Sin^2(a)
Therefore :<span>1−2 sin ^2 (22.5∘) = Cos(2a)
= Cos (2 * 22.5) = Cos 45</span>
The name of this property is symetric property of equality
Hi friend,
If you flipped the graph y=x^2+2x-2 vertically, you would get the graph y=-(x^2+2x-2) TRUE.
Hope this helps you!
Answer:

Step-by-step explanation:
Notice that we can get from the x-coordinate of A, 1, to the x-coordinte of A', -2, by subtracting 3 from the x-coordinate of A. More formaly:



Similarly, we can get from the y-coordinate of A, 5, to the y-coordinate of A', 3, by subtracting 2 from the y-coordinte of A. More formaly:



Now we now that to get to A' from A, we need to subtract 3 to the x-coordinate of A and subtract 2 to the y-coordinate. Knowing this, we can create the expression to translate any point of the polygon ABCD to create the polygon A'B'C'D':

Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters