We know that
the equation of a line in <span>slope intercept form is--------------> y=mx+b
where
m-----------> is the slope
b-----------> is the y-intercept point when x=0
</span><span>y+7=-1/7(x+4)---------> y+7=(-1/7)x-4/7
</span>y+7=(-1/7)x-4/7------> y=(-1/7)x-4/7-7------> y=(-1/7)x-(53/7)
the answer is
y=(-1/7)x-(53/7)-------------> this is the equation of a line in slope intercept form
m=(-1/7)=-0.14
b=(-53/7)=-7.57
y=-0.14x-7.57see the attached figure
Given a quadratic equation
, we define the discriminant as

The number of real solutions of the equation depend on the sign of
:
- If
the equation has two solutions - If
the equation has one double solution - If
the equation has no real solutions
In this case, we have

And so this equation has no real solutions.
<span>3.19459 seconds
Since we've been given the equation for how high the ball is at t seconds, all we need to do is solve for a height of 0. So
h = 67 - 5t - 5t^2
0 = 67 - 5t - 5t^2
And you should immediately notice that we have a quadratic equation with A = -5, B = -5, and C=67. Use the quadratic formula to determine the roots of -4.19459 and 3.19459. Since we can't have negative seconds, that means that the ball will hit the ground 3.19459 seconds after it was thrown.</span>