Quadrilateral lmno has diagonals that intersect at point p. if lp=np, mp = y + 25, and op = 5y + 29, find the length of mo such that lmno is a parallelogram.. a.24. b.48. c.61. d.122

The correct option is B.

Step-by-step explanation:

Given information: LMNO is a parallelogram, LMNO has diagonals that intersect at point P, LP=NP, MP = y + 25, and OP = 5y + 29.

Diagonals of parallelogram bisects each other.

Since P is the intersection point of diagonal and MO is a diagonal, so

Subtract y from both the sides.

Subtract 29 from both the sides.

Divide both sides by 4.

The value of y is -1.

The length of MO is

Substitute y=-1 in the above equation.

The length of MO is 48. Therefore the correct option is B.

When the ball hit the ground, the height of the ball will be zero. So using the value of h(x) as zero in the given equation, we can find the time in which the ball will hit the ground.

0 = -(x-2)^2 + 16

(x-2)^2 = 16

x-2 = 16

x-2 = 4

x = 6

This means the ball will hit the ground 6 seconds after Amir threw it.