First we have to find the vertex (h,k) h is also x and it also is the a xis symmetry
1st: group the number
(X2+6x)-9
2nd: use b/2
6/2 = 3 , 3^2= 9
(X2+6x+9)-9-9
(X2 + 3)-18
Vertex is 3,-18 so the symmetry is 3
The height is 9.875 feet from which the goalkeeper catches the ball.
The player kicks soccer from a height of 2 feet
x = 0 and y = 2
Maximum height of 20 feet after traveling 40 feet
x = 40, y = 20
So let y = a(x - 40)² + 20 ( the path of parabola)
Since x = 0 , y = 2
So, 2 = a(0 - 40)² + 20
2 = 1600a + 20
-18 = 1600a
a = - 9/800
Thus, y = -9/800(x - 40)² + 20
Since the soccer is caught by the goalkeeper 70 feet from where it was kicked
x = 70
So at this time,
y = -9/800 ( 70 - 40)² + 20
= -9/800 × 900 + 20
= - 81/8 + 20
= 79/ 8
= 9.875 feet
Therefore the height at which the goalkeeper catches the ball is 9.875 feet.
To know more about the height refer to the link given below:
brainly.com/question/27030273
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Answer:
B
Step-by-step explanation:
The volume (V) of a rectangular prism is calculated as
V = length × width × height
Calculate the volume of each prism
Q → V = 8 × 4 × 5 = 60 ft³
R → V = 6 × 7 × 12 = 504 ft³
S → V = 4 × 10 × 12 = 480 ft³
T → V = 2 × 13 × 5 = 130 ft³
Prism R has the greatest volume → B
B.The two figures are similar
