The symbol ₁₂P₉ represents the permutations of 9 quantities out of 12.
By definition,

From the calculator,
12! = 479,001,600
3! = 6
Therefore
₁₂P₉ = 479001600/6 = 79,833,600
Answer: 79,833,600
Step-by-step explanation:
We want to find two things-- the speed of the boat in still water and the speed of the current. Each of these things will be represented by a different variable:
B = speed of the boat in still water
C = speed of the current
Since we have two variables, we will need to find a system of two equations to solve.
How do we find the two equations we need?
Rate problems are based on the relationship Distance = (Rate)(Time).
Fill in the chart with your data (chart attached)
The resulting speed of the boat (traveling upstream) is B-C miles per hour. On the other hand, if the boat is traveling downstream, the current will be pushing the boat faster, and the boat's speed will increase by C miles per hour. The resulting speed of the boat (traveling downstream) is B+C miles per hour. Put this info in the second column in the chart. Now plug it into a formula! <u>Distance=(Rate)(Time) </u>Now solve using the systems of equations!
Answer:
AD = 7
Step-by-step explanation:
Given that the two triangles are similar by the SSS (side side side) postulate, the triangles share the same ratios when it comes to their sides.
We know the values for lines DB, EB and CB, therefore we can solve for AB, and subtract DB to find AD
We can solve the problem by solving for x:

Cross multiply.

Simplify.

Subtract the value of DB to find AD.


Answer:
B or 31r-71
Step-by-step explanation:
First, use distributive property to expand the first term.
30r-66-(5-r)
Remove the parenthesis of the third term:
30r-66-5+r
Combine like terms
31r-71
Answer: -500
Step-by-step explanation:
-408 - 92 = -500