The permutation illustrates that if no one has been cast yet, the different ways that are there to cast Jean Valjean from the 22 men is 22.
<h3>How to compute the value?</h3>
The ways to cast Jean will be:
= 22!/(22 - 1)!
= 22!/21!
= 22
When Jean Valjean has already been cast, the different ways that are there to cast Inspector Javert from the remaining men will be:
= 21!/(21 - 1)!
= 21!/20!
= 21
When Jean Valjean and Inspector Javert have already been cast, the different ways that are there to cast Marius from the remaining men will be:
= 20!/(20 - 1)!
= 20!/19!
= 20
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Answer:
I will answer in English.
We can prove that the angle APS is a triangle rectangle.
Remember that for a triangle rectangle of catheti A and B, and hypotenuse H, the Pythagorean's theorem says that:
A^2 + B^2 = H^2
In this case, we can assume that the hypotenuse is the longer side, AS, and the other two sides are the catheti.
Then we have:
H = 5x + 10
A = 3x + 6
B = 4x + 8
Now let's write the equation from the theorem, and let's see if its true.
A^2 + B^2 = H^2
( 3x + 6 )^2 + (4x + 8)^2 = (5x + 10)^2
So we can start with:
( 3x + 6 )^2 + (4x + 8)^2
And try to "transform" this into:
(5x + 10)^2
First, let's expand it:
((3x)^2 + 2*(3x)*6 + 6^2) + ( (4x)^2 + 2*(4x)*8 + 8^2)
9x^2 + 24x + 36 + 16x^2 + 64x + 64
25x^2 + 40x + 100
Now we can complete squares on the left side, by writing:
(5x)^2 + 2*10*(5x) + 10^2
(5x + 10)^2
Then we saw that the equation is true for every value of x, then we just prove that the triangle fulfills the theorem, thus, the triangle is a triangle rectangle.
Answer:
188
Step-by-step explanation:
3(8^2)-4
3(64)-4
192-4
188
Answer:
- The angle ∠2 = 4x = 4(36°) = 144°
Step-by-step explanation:
We know that when two lines meet or intersect, we get a linear pair of angles.
Linear pairs are basically two adjacent angles that form a line.
The measure of two adjacent angles forming a straight line is 180, meaning they are supplementary.
We are given that <1 and <2 forms a linear pair, and
m∠1 = 4m∠2
It means the angle ∠1 is 4 times the measure of angle ∠2.
Let the angle ∠1 be = x
As the angle 1 is 4 times the measure of angle ∠2, so
The angle 2 will be = 4x
As <1 and <2 forms a linear pair, thus the measure of the sum of <1 and <2 will be 180°, so
x + 4x = 180
5x = 180
divide both sides by 5
5x/5 = 180/5
x = 36°
Therefore,
- The angle ∠2 = 4x = 4(36°) = 144°
Answer: (141/4)pi
This looks like it matches up with choice D
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Work Shown:
Let's complete the square for the x and y terms like so
4x^2 + 4y^2 - 40x + 24y - 5 = 0
4x^2 - 40x + 4y^2 + 24y = 5
4(x^2 - 10x + y^2 + 6y) = 5
x^2 - 10x + y^2 + 6y = 5/4
x^2 - 10x + 25 + y^2 + 6y = 5/4 + 25
(x^2 - 10x + 25) + y^2 + 6y = 5/4 + 100/4
(x-5)^2 + y^2 + 6y = 105/4
(x-5)^2 + y^2 + 6y + 9 = 105/4 + 9
(x-5)^2 + (y^2 + 6y + 9) = 105/4 + 36/4
(x-5)^2 + (y + 3)^2 = 141/4
The last equation is in the form (x-h)^2 + (y-k)^2 = r^2 where (h,k) = (5,-3) is the center and r^2 = 141/4 leads to r = sqrt(141)/2 which is the radius.
The area of the circle is therefore,
A = pi*r^2
A = pi*141/4
A = (141/4)pi