Answer:
C. 30
Step-by-step explanation:
We have a list of names that need to be sorted in a specific order. For this, we will use a permutation. This can be found on a scientific calculator, however, I'll be using the equation.

n = total number of objects
r = number of objects selected
In this instance, n will equal 6 since we have 6 different names to choose from and r will equal 2 since we are picking two names. Enter the values into the equation and evaluate.

Therefore, there are 30 possible two-part names.
Answer:
The play started at 5:10 PM.
Step-by-step explanation:
We are given the following in the question:
Length of first act = 45 minutes
Length of intermission = 55 minutes
Length of second act = 1 hour and 10 minutes
1 hour = 60 minutes
Thus, length of second act =

The second part ended at 8:00 PM. We have to find the starting time of play.
Starting time of play =

Thus, the play started at 5:10 PM.
Answer:
-7/4
Step-by-step explanation:
Since the graph is moving down the slope has to be negative we need to write the answer in rise over run rise as in the y range and run as in x range
Answer:
x = 
Step-by-step explanation:
The absolute value always returns a positive value but the expression inside can be positive or negative, that is
x + 4 = 3x - 5 ( subtract 3x from both sides )
- 2x + 4 = - 5 (subtract 4 from both sides )
- 2x = - 9 ( divide both sides by - 2 )
x = 
OR
-(x + 4) = 3x - 5
- x - 4 = 3x - 5 ( subtract 3x from both sides )
- 4x - 4 = - 5 ( add 4 to both sides )
- 4x = - 1 ( divide both sides by - 4 )
x = 
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions
|
+ 4 | = |
| = 
right side =
- 5 = 
left side = right side , thus x =
is a solution
check second solution
|
+ 4 | = |
| = 
right side =
- 5 = - 
right side ≠ left sides, hence not a solution
Answer:
2nd option
Step-by-step explanation:
Using the identities
tan²θ + 1 = sec²θ
cotθ = 
Given
secθ = -
, then
tan²θ + 1 = (-
)² =
( subtract 1 from both sides )
tan²θ =
( take the square root of both sides )
Since
< θ < π and tanθ < 0 , then
tanθ = - 
Then
cotθ =
= - 