Part 1: The general form for this matches y^2 = -4cx, which implies that this opens to the left. (Imagine assigning any value of y, whether positive or negative, which would result in a positive left-hand value. Then to match this sign, the value of x must be negative so that the right-hand side becomes positive as well.)
Part 2: The distance from the vertex to the directrix is given by c. This equation has its vertex at the origin (0, 0). If it opens to the left, the directrix is a vertical line to the right of the origin. This equation is y^2 = -4(1/2)x, so c = 1/2, and the directrix has the equation x = 1/2.
Part 3: The focus is inside the parabola, but it is the same distance from the vertex as the directrix. This distance is 1/2 units, and it will be to the left of the vertex. So the focus is at (-1/2, 0).
Answer:
$1.25 & $10.25
Step-by-step explanation:
Let c be the cost of renting one chair and t be the cost of renting table. We're given two equations:
#1. 5c + 3t = 37
#2. 2c + 6t =64
We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below:
- Chairs (c) cost $1.25
- Tables (t) cost $10.25
Answer:
c≥47
Step-by-step explanation:
120+20=140
140/3≈46.667
46.667≈47
Ther can be no less than 47 cupcakes
Answer:age of the man: 75 age of the woman:25
Step-by-step explanation:
First, We need to define the variables
x: age of the man
y: age of the woman
at the first time he has three times her age
x=3y (1)
in 25 years time
(x+25)=2(y+25) (2)
we clear the equation
X+25=2y+50
X=2y+25
we substitute in the (1) equation:
2y+25=3y
y=25
x=3*25=75
