Nate tosses a ball up a hill for his dog to chase. The path of the ball is modeled by the function y=- 1 4 x^ 2 + 33 5 x. , where x is the ball's horizontal distance from Nate in feet and y is the ball's height in feet. The hill is modeled by the line y = 1/5 * x . How far does the ball travel horizontally before it hits the ground? (in feet, round to tenth place if necessary )

The ball's horizontal distance from Nate in feet when the ball hits the ground is 25.6 feet

Step-by-step explanation:

The given equation that represents the path of the ball is y = -1/4·x² + 33/5·x

The equation of the that models the hill is y = 1/5 × x  = 1/5·x

Where, x represents the ball's horizontal distance from Nate in feet and y represents the ball's height in feet

To find the point of contact, we equate both equations to find the common solutions as follows;

-1/4·x² + 33/5·x = 1/5·x

-1/4·x² + 33/5·x - 1/5·x = -1/4·x² + 32/5·x = 0

-1/4·x² + 32/5·x = 0

0 = 1/4·x² - 32/5·x

1/4·x² - 32/5·x = 0

x·(1/4·x - 32/5) = 0

x = 0 or 1/4·x - 32/5, and x = 32/5 × 4 = 128/5 = 25.6

The ball's horizontal distance from Nate in feet = x = 25.6 feet

The ball's horizontal distance from Nate in feet when the ball hits the ground is 25.6 feet.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

the answer is su.k.my? ? co.kc