What are the period, phase shift, and vertical shift of y = csc[3(x + 4)] + 6?

period: pi/3 ; phase shift: 4 units right; vertical shift: 6 units up
period: pi/3 ; phase shift: 4 units left; vertical shift: 6 units down
period: 2pi/3 ; phase shift: 4 units left; vertical shift: 6 units up
period: 2pi/3 ; phase shift: 4 units right; vertical shift: 6 units down

Step-by-step explanation:

Alright, lets get started.

The given equation is:

Period =

hence the period is =

Phase shift =

hence phase shift 4 units to the left

ertical shift is 6 units up

So, the answer is C, period 2pi/3, phase shift 4 units left and vertical shift 6 units up  :   Answer

Hope it will help :)

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.