Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y plus five squared divided by nine = 1.
a. vertices: (-5, 3), (-5, -5); foci: (-5, -6), (-5, 4)
b. vertices: (2, -5), (-4, -5); foci: (-4, -5), (2, -5)
c. vertices: (3, -5), (-5, -5); foci: (-6, -5), (4, -5)
d. vertices: (-5, 2), (-5, -4); foci: (-5, -4), (-5, 2)

C

Step-by-step explanation:

This hyperbola is a horizontal hyperbola of the standard form:

Since our equation is

,

a = 4 and b = 3.

The coordinates for the vertices are (±a, 0) and

the coordinates for the foci are (±c, 0).

We have a, but we need c.  To find c, we use Pythagorean's Theorem:

or

giving us that

c = 5.

But these a and c values have to be figured from the center of the hyperbola which is located at (-1, -5).  

For the vertices, then, we add the a value of 4 and -4 to the x value of the center, which is -1.  The -5 remains, since the vertices and the foci are on the same transcersal axis which is the line y = -5.

For the foci, then, we add the c value of 5 to -1, and again the -5 remains in the y position.

Vertices: (-1+4, -5)-->(3, -5) and (-1-4, -5)-->(-5, -5)

Foci: (-1+5, -5)-->(4, -5) and (-1-5, -5)-->(-6, -5)

Choice C

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer