Answer:
Step-by-step explanation:
Consider triangles BKE and DKA. In this triangles:
as vertical angles;
as alternate interior angles (lines BC and AD are parallel and BC is a transversal);
as alternate interior angles (lines BC and AD are parallel and BE is a transversal).
Thus triangles BKE and DKA are similar by AA theorem. Similar triangles have proportional sides lengths:
Thus, 
Since AD=BC and BC=BE+CE, we have that 4BE=BE+EC, EC=3BE. Hence, the ratio BE to EC is
Answer:
Q matches to a and P matches to b
Step-by-step explanation:
This is a volume question so we can use the volume of a cylinder to see which one corresponds to what. Volume of a cylinder is 
h. We know that the heights of the cylinders are the same since the diagram says so. We also know pi is the same since thats a constant. The only thing thats different is the radius (as you can see radius of P is bigger than Q). If the radius of P is bigger than Q and all the other things are the same (height is the same and pi is the same), then that automatically means that P has more volume than Q. More volume means more time to fill up. Since Q has less volume, it will take less time to fill up. So now we look at the graph. A shows that the height of water increases at a faster rate than that of B. This is because there is less volume in that container (less volume=less time to fill up). Therefore a matches to Q and therefore b matches to P
Answer:
The players ran 150 meters
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
Since we have a rectangle with sides 90 and 120, we know if we split a diagonal across it, we will get a right triangle with legs 90 and 120. From there, we use Pythagorean Theorem to solve:
90² + 120² = c²
8100 + 14400 = c²
c² = 22500
√c² = √22500
c = 150
5+(-13)= -8,
-8 + 100 = 92!
I hope this helped!
Answer:
PO = 36
Step-by-step explanation:
Since both the chords are equal in length so they must be equidistant from the centre.
And
PG = GO
-x+10 = -3(x+2)
-x+10 = -3x-6
-x+3x = -6-10
2x = -16
Dividing both sides by 2
x = -8
Now
PO = PG + GO
PO = -(-8)+10+(-3)((-8)+2)
PO = 8+10+(-3)(-6)
PO = 18+18
PO = 36
