The ball will hit the ground at 2 seconds.
Step-by-step explanation:
Given that,
The path of the ball = h(x)=−2x2+1x+6
Here,
x is the time while h is the height of ball.
When the ball will hit the ground, the height will become zero. Therefore,
h(x)=−2x2+1x+6
0 =−2x2+1x+6
or
2x2 -1x - 6 = 0
This is a quadratic equation, hence by applying quadratic equation formula:
here,
a = 2
b = -1
c = -6
Putting these values in formula, we get
x = 2, -3/2
As the time cannot be negative. Therefore, the ball will hit the ground at 2 seconds.
Answer:
The expression for the perimeter of the rectangle is: 
Step-by-step explanation:
Perimeter of a rectangle:
A rectangle has length l and width w. It's perimeter is given by:
In this question:
So
The expression for the perimeter of the rectangle is:
Answer:
3) (2,-9)
4) (0,-5)
5) (1,-8)
Step-by-step explanation:
3)
The vertex will occur between you x-intercepts.
You already found that happens at x=2.
To find the corresponding y-coordinate, replace x in
f(x)=(x+1)(x-5) with 2:
f(2)=(2+1)(2-5)
f(2)=(3)(-3)
f(2)=-9
So the vertex is (2,-9).
4)
The y-intercept is when x=0.
So in f(x)=(x+1)(x-5) replace x with 0:
f(0)=(0+1)(0-5)
f(0)=(1)(-5)
f(0)=-5
So the y-intercept is (0,-5).
5)
To find another point just plug in anything besides any x already used.
We preferably want to use a value of x that will keep us on their grid however far up,down,left, or right their grid goes out. So I'm going to choose something close to the vertex which is at x=2. Let's go with x=1.
So replace x in f(x)=(x+1)(x-5) with x=1:
f(1)=(1+1)(1-5)
f(1)=(2)(-4)
f(1)=-8
So another point to graph is (1,-8).
We know the y intercept is -6 and we know the slope is positive 4 (rise over run) so the equation is y=4x-6 if we plug in a shaded point (I would choose 0,0 for convenience reasons) 0=-6 since -6 is less than 0, the expression would be y≥4x-6
Answer:
Step-by-step explanation:
- -1/9 × -5/4: 9 × 4 = 36, -1 × -5 = 5
- Put them together: 5/36
