Answer:
2.62 seconds
Step-by-step explanation:
Let
t ----> the time in seconds
h(t) ----> he height of the ball, in feet
we have

we know that
When the ball hits the ground, the height is equal to zero
so

The formula to solve a quadratic equation of the form
is equal to
in this problem we have

so
substitute in the formula
therefore
The solution is t=2.62 seconds
Answer: the system of equations are
3x + y = 14
y = 4x
Step-by-step explanation:
Let x represent the number of three point shots that Hailey made.
Let y represent the number of free throws(worth one point each) that Hailey made.
Hailey made some three point shots and some free throws and
scored a total of 14 points. This would be expressed as
3x + y = 14
Hailey made 4 times as many free throws as three point shots. This would be expressed as
y = 4x
Answer:
a. Vertex = (2.5,-12.25)
b. y-intercept = (0,-6)
c. x-intercept = (6,0) ; (-1,0)
Step-by-step explanation:
a.
Your equation is written as:

The easiest way to find the vertex is writing the equation this way:

Being the vertex (h,k)
So first complete the square

Vertex : (2.5,-12.25)
b.
To find the y-intercept you need to replace the equation when x = 0 and get y

c.
To find the x-intercept you need to replace the equation when y = 0 and get x

Answer & Step-by-step explanation:
Using the information given in the question we can form the following 3 equations (in the order of the first 3 sentences)
w = 2h (twice the price)
t = h - 4 ($4 less)
3w + 2h + 5t = 136 (total purchasing and cost)
We can solve all 3 equations for h first, by substituting the first two equations, into the third equations w and t
3(2h) + 2h + 5(h-4) = 136
Simplify
6h + 2h + 5h - 20 = 136
13h = 136 + 20
13h = 156
h = 156/13
h = $12
Using this information, we can solve for w and t
w = 2h
w = 2(12)
w = $24
And finally
t = h - 4
t = 12 - 4
t = $8