There are 3x−2 trees planted in each row of a rectangular parcel of land. If there are a total of 24x−16 trees planted in the pa
1 answer:
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Answer:
- y = -2(x -3)² +24
- 16 feet
Step-by-step explanation:
We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...
y = a(x -3)² +b
Filling in the values from the first two table points, we get
For (x, y) = (0, 6):
6 = a(0 -3)² + b ⇒ 9a +b = 6
For (x, y) = (2, 22):
22 = a(2-3)² +b ⇒ a +b = 22
Subtracting the second equation from the first gives ...
(9a +b) -(a +b) = (6) -(22)
8a = -16 . . . . . . collect terms
a = -2 . . . . . . . . divide by 8
The second equation above tells us ...
b = 22 -a = 22 -(-2) = 24
So, our equation for y is ...
y = -2(x -3)² +24
__
The value of y for x=5 is ...
y = -2(5 -3)² +24 = 16
The height of the ball after 5 seconds is 16 feet.
Answer:
F is E reflected across the y-axis; only the signs of the x-coordinates of F and E are different.
Step-by-step explanation:
The question is incomplete. Here is the complete question.
" Points F and E on the coordinate grid below show the positions of two midfield players of a soccer team:
Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point E is 1.5 units to the left and 3 units up. From the origin, point F is 1.5 units to the right and 3 units up.
Which statement best describes the relationship between the positions of the two midfield players? (1 point)
Based on the coordinate of E;
The value on the x axis is -1.5 since the point is 1.5unitsTO THE LEFT from the origin(-ve x-axis acts towards the left in space). The value on the y-axis will be +3units since its 3units UP(+ve y axis acts upward).
The E coordinates will therefore be (-1.5, 3)
Similarly, for coordinate F:
If from the origin, point F is 1.5 units TO THE RIGHT, then the x-axis will be +1.5 (x-axis is positive towards the right) and +3 units up(+ve y axis acts upward).
The F coordinate will therefore be;
(1.5, 3).
From both coordinates, it can be seen that both x axis are of the same value but different signs. This means that the points E and F will act in the opposite side of the y-axis and a reflector of each other.
Based on the explanation above, it can be concluded that "F is E reflected across the y-axis; only the signs of the x-coordinates of F and E are different."
