For any graph of a hyperbola, which of the following statements describes the locations of the foci, vertices, and center with respect to one another ? Select all that apply .A- the foci are closer to the center than vertices

B- the foci are further from the center than the vertices

C- the center is located at the midpoint of the two foci

D- the center is located at the midpoint of the two vertices

Answer:

(x+3)(x-3)

Step-by-step explanation:

x²-b² = (x+b)(x-b)

x²-9 = x²-3² = (x+3)(x-3)

Answer:

Center is at (-4, -2) and the radius = 5.

Step-by-step explanation:

Convert to Standard form:

x^2 + 8x + y2 + 4y - 5= 0  

Completing the square:

(x + 4)^2 - 16 + (y + 2)^2 - 4 = 5

(x + 4)^2 + (y + 2)^2  = 5 + 16 + 4

(x + 4)^2 + (y + 2)^2  = 25

(x - h)^2 + (y - k)^2 = r^2     Comparing:-

The center is at (-4, -2) and the radius = 5.

Answer:

Amount = Initial value × (1 + rate of interest)^years and 374

Step-by-step explanation:

The formula to determine the student population and the estimated student population is given below:

As we know that

Amount = Initial value × (1 + rate of interest)^years

= 284 × (1 + 0.04)^7

= 284 × 1.04^7

= 373.72

= 374

Answer:

First find the slope of the straight line, m=(Y2-Y1)/(X2-X1)=(17–7)/(-5–0)=-2.

Using the standard equation of a straight line, y=mx+b, we know that m=-2.

Thus, so far we know that y=-2x+b.

Now plug in the coordinates of either of the above points, that we know do lie on the straight line, into our equation, y=-2x+b, and solve for b.

I will use the first point, (0,7), to get 7=(-2)(0)+b.

Solving for b, we see that b=7.

Therefore, the equation of the straight line is y=-2x+7.

It is a good idea to check your answer on a graphing calculator.