Because the focus is (-2,-2) and the directrix is y = -4, the vertex is (-2,-3).
Consider an arbitrary point (x,y) on the parabola.
The square of the distance between the focus and P is
(y+2)² + (x+2)²
The square of the distance from the point to the directrix is
(y+4)²
Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3
Answer:
The system of equations can be used to find the cost of a night's stay and the cost of a meal is:
2n + 5m = $395
5n + 11m = $959
<h3>
Simultaneous equations</h3>
Simultaneous equations are two or more groups of equations. These equations have to be solved together at the same time in order to determined the required valued. The two above equations have to be solved in order to determine the cost of a night's stay and the cost of a meal.
The methods of determining the required values are:
- Elimination method
- Graph method
- Substitution method
To learn more about simultaneous equations, please check: brainly.com/question/25875552
Answer:
Step-by-step explanation:
Since point B is located between A and C
then
AB + BC = AC
or, 3x-16 + 4x-8 = 60
or, 7x = 60 + 24
or, 7x = 84
x = 12
This is not an actual equation,
Answer:
7
Step-by-step explanation:
first, we would set up an equation. let 3x-4 represent "four less than a number tripled". "a number" would be represented by x. let x+10 represent "the same number increased by 10".
set 3x-4 and x+10 equal to each other:
3x-4=x+10
next, we would solve this equation for x. first we would get the x together on one side of the equation. we would do this by subtracting x from both sides to remove it from the right side of the equation:
2x-4=10
then, we would get the 2x by itself. we would do this by adding 4 to both sides:
2x=14
finally, we would divide each side of the equation by 2 to find x:
x=7.
The number is 7.
