The foci of the hyperbola with equation 5y^2-4x^2=20 will be given as follows:
divide each term by 20
(5y^2)/20-(4x^2)/20=20/20
simplifying gives us:
y^2/4-x^2/5=1
This follows the standard form of the hyperbola
(y-k)²/a²-(x-h)²/b²=1
thus
a=2, b=√5 , k=0, h=0
Next we find c, the distance from the center to a focus.
√(a²+b²)
=√(2²+(√5)²)
=√(4+5)
=√9
=3
the focus of the hyperbola is found using formula:
(h.h+k)
substituting our values we get:
(0,3)
The second focus of the hyperbola can be found by subtracting c from k
(h,k-c)
substituting our values we obtain:
(0,-3)
Thus we have two foci
(0,3) and (0,-3)
Answer:
Already in standard form
Step-by-step explanation:
-4y=10
-4y= by
10= c
And in this case ax=0x, so it will not show up in the equation
0x-4y=10, which is already in standward form
Answer:
True: B, C and D
Step-by-step explanation:
The graph of the function is shown in the attached diagram.
The vertex of the parabola (parabola is the graph of the function f(x)) is at (-3,-16), because
So, option A is false and option B is true.
As you can see from the graph, the function is increasing for all x>-3, thus option C is true.
The graph is positive for x<-7 and x>1 and negative for -7<x<1, so option D is true and option E is false.
Well, in order to first determine the slope or y-intercept, you must put change the equation to this format: y=mx+b.
m=slope and b=y-interceptI
in order to do that, you must change this equation.
x+3y=9
-x -x
----------
3y=9-x
Then, rewrite it as:
3y=-x+9
_______
3 3
simplify to
y=-x/3 +9
Answer:
D. 1,044 is the total amount of money Mrs. Smith collected
