Answer:
The equation of the parabola is 
.
Step-by-step explanation:
Since the directrix is of the form 
, the parabola is vertical. The vertex of the parabola (
) is the midpoint between the focus (
) and a point of the directrix (
), that is to say:
(1)
If we know that 
and 
, then the coordinates of the vertex of the parabola:
The vertex factor (
) is the distance of the focus with respect to the vertex:
![p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]}](https://tex.z-dn.net/?f=p%20%3D%20%5Csqrt%7B%5BF%28x%2Cy%29-V%28x%2Cy%29%5D%5C%2C%5Cbullet%20%5C%2C%5BF%28x%2Cy%29-V%28x%2Cy%29%5D%7D)
(2)
If we know that and , then the vertex factor is:
The equation of the parabola in the vertex form is described below:
(3)
Where:
- Independent variable.
- Dependent variable.
- Coordinates of the vertex.
If we know that 
and , then the equation of the parabola is .
Answer:
<u> 105</u> students could prefer kiwi if there are 357 total students.
Step-by-step explanation:
Given:
The ratio of students who prefer pineapple to students who prefer kiwi is 12 to 5.
Now, to find number of students prefer kiwi if there are 357 total students.
Let the students prefer pineapple be 
And the students prefer kiwi be 
Total students = 357.
So, we set an equation to get the number of students who prefer kiwi.
According to question:
<em>Dividing both sides by 17 we get:</em>
<em>Thus, students prefer kiwi are:</em>
Therefore, 105 students could prefer kiwi if there are 357 total students.
9514 1404 393
Answer:
C) 14 cm
Step-by-step explanation:
A triangle solver can quickly show you the third side is 14 cm.
__
The law of cosines can be used for this purpose. If the given sides are 'a' and 'b', and the third side is 'c', then that law tells you ...
c² = a² +b² -2ab·cos(C)
c² = 7² +11² -2·7·11·cos(100°) ≈ 196.74
c ≈ √196.74 ≈ 14.03
The length of the third side is about 14 cm.
Answer:
10. 23
11. -17
12. 0
13. -4
14. -6
15. 4
Explanation:
10. 8+15= 23
11. -8-9= -17
12. 8-8= 0
13. -8+4= -4 (same as 4-8)
14. -10+4= -6 (same as 4-10)
15. 12-8= 4
