Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
Part 1) Find the measure of angle a
we know that
The formula to calculate the measure of the interior angle of a regular polygon is equal to
where
n is the number of sides of the regular polygon
For the regular pentagon in the figure
n=5
substitute in the formula
Part 2) Find the measure of angle b
Remember that a regular polygon has equal sides and equal interior angles
so
In the figure , the length of the side of the two smaller equilateral triangles is equal to the length of the side of the regular pentagon
therefore
The triangle in white of the figure is an isosceles triangle
The measure of the vertex angle of the isosceles triangle is equal to
Remember that
The sum of the interior angles of triangle must be equal to 180 degrees
so
solve for b
Answer: inverse of given function = log(x)/log(3)
Step-by-step explanation: how to find the inverse of any function?
in the complete function, replace y with "x" and x with "y"then, solve the obtained equation from step 2 for yand, then the value obtained for "y" is the inverse required i.e. = f^{-1}(x)
now, we solve the problem:
given : - y = 3^x
replacing the value of "y" with "x", we get,
x = 3^y
to solve for "y" we should take the "logarithm" for both sides
log (x) = y log(3)
or y = log(x)/log(3)
or f^(-1) (x) = log(x)/log(3)
( I hope this helped <3 )
On't want to be ripped off do you?/ That's why you want to have some interest. Just in a simple form this is a rush job right now.
Answer:
infinitely many
Step-by-step explanation:
You have the system
(1/2)x + 5y = 6
3x + 30y = 36
Multiplying the first equation by 6 results in 3x + 30y = 36, which is exactly the same as the second equation. The two graphs coincide, and so there are infinitely many solutions to this system
Step-by-step explanation:
a) 7!
If there are no restrictions, answer is 7! as it is the permutation of all animals.
b) 4! x 3!
As cats are 6 and Dogs are 5, thus 1st and last must be cats in order to have alternate arrangements. Therefore the only choices are the order of the cats among themselves and the order of the dogs among themselves. There
are 4! permutations of the cats and 3! permutations of the dogs,
so there are a total of 4! x 3! possible arrangements of the suites.
c) 3! x 5!
There are 3! possible arrangements of the dogs among themselves. Now, if we consider the dogs as one ”object” together, then we can think of arranging the 4 cats together with this 1 additional object. There are 5! such arrangements possible, so there are a total of 3! · 5! possible arrangements of the suites.
d) 2 x 4! x 3!
As required that all the cats must be together and all the dogs must be together, either the cats are all before the dogs or the dogs are all before the cats. There are two possible arrangements thus two times of both possibilities is the answer i.e. 2 x 4! x 3!
