Substitute this into the parabolic equation,
We're told the line 
intersects 
twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know
We can tell from the quadratic equation that has its vertex at the point (3, 6). Also, note that
and
so the furthest to the right that extends is the point (5, 2). The line passes through this point for 
. For any value of 
, the line passes through either only once, or not at all.
So 
; in set notation,
Do the division
(5.685 * 10^26) / (3.302*10^23)
= 1.722 * 10^3
or 1722 times greater
Base on the question and the given coordinates, I would say that the ordered pair among the choices that has a value of 7 in the x coordinate is (7,10). I hope you are satisfied with my answer and feel free to ask for more if you have questions and further clarification about the said question
Answer:
<h3>3 secs</h3>
Step-by-step explanation:
Given the height of the object as it drops from the observation deck expressed as;
h= -16t^2+152
To determine the the time it will take the object to be 8 feet above the valley floor, we will substitute h = 8 into the equation and calculate t as shown;
8 = -16t^2+152
subtract 8 from both sides
8-8 = -16t^2+152-8
0 = -16t^2+144
0-144 = -16t^2
-144 = -16t^2
16t^2 = 144
Divide both sides by 16;
16t^2/16 = 144/16
t^2 = 9
t = √9
t = 3seconds
Hence it will take 3 seconds for the object to be 8 feet above the valley floor
64000 x 0.12 = 7680
she was given a $7,680 bonus
