Find the vertices and foci of the hyperbola with equation.

quantity x minus 3 squared divided by 81 minus the quantity of y plus 5 squared divided by 144 equals 1

Vertices: (-5, 15), (-5, -9); Foci: (-5, -9), (-5, 15)
Vertices: (12, -5), (-6, -5); Foci: (-12, -5), (18, -5)
Vertices: (-5, 12), (-5, -6); Foci: (-5, -12), (-5, 18)
Vertices: (15, -5), (-9, -5); Foci: (-9, -5), (15, -5)

The vertices are (12 , -5) , (-6 , -5)

The foci are (18 , -5) and (-12 , -5) ⇒ 2nd answer

Step-by-step explanation:

The standard form of the equation of a hyperbola with  center (h , k) and transverse axis parallel to the x-axis is   , where

∵ The equation of the hyperbola is  

- Compare it with the form above

∴ h = 3 and k = -5

∴ a² = 81

- Take √  for both sides

∴ a = ± 9

∴ b² = 144

- Take √  for both sides

∴ b = ± 12

∵ Its vertices are (h + a , k) and (h - a , k)

∵ h + a = 3 + 9 = 12

∵ h - a = 3 - 9 = -6

∵ k = -5

∴ Its vertices are (12 , -5) , (-6 , -5)

∵ c² = a² + b²

∴ c² = 81 + 144

∴ c² = 225

- take √  for both sides

∴ c = ± 15

∵ Its foci are (h + c , k) and (h - c , k)

∵ h + c = 3 + 15 = 18

∵ h - c = 3 - 15 = -12

∵ k = -5

∴ Its foci are (18 , -5) and (-12 , -5)

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

at each of the parallel lines adjacent angles are supplementary. the angles have special names identifying their positions with respect to the parallel lines and transversal. they are corresponding angles, alternate interior angles, or alternate exterior angles. an angles is congruent to its matched angle.