Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 81 minus the quantity of y minus 3 squared divided by 144 = 1.

a). vertices: (4, 3), (-14, 3); foci: (-20, 3), (10, 3)
b). vertices: (3, 7), (3, -17); foci: (3, -17), (3, 7)
c). vertices: (7, 3), (-17, 3); foci: (-17, 3), (7, 3)
d). vertices: (3, 4), (3, -14); foci: (3, -20), (3, 10)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$15.40 per mile

step-by-step explanation:

you have to round up to 4 because 6 is over 5 so you have to round the 3 up to 4