A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft.

Mathematics

2 answers:

SOVA2 [1]3 years ago

8 0

The answer is A. x-1,n,3x+5

brilliants [131]3 years ago

4 0

Answer:

The correct option is A. x – 1 < n < 3x + 5

Step-by-step explanation:

In a triangle sum of any two sides is always greater than the third side.

Now, the sides of the triangle are given to be :

2x + 2, x + 3 , n

Now, first take 2x + 2 and x + 3 as two sides and the side of length n as third side.

By using the property that sum of two sides is always greater than the third side in a triangle.

⇒ 2x + 2 + x + 3 > n

⇒ 3x + 5 > n ......(1)

Now, take n and x + 3 as two sides and the side of length 2x + 2 as the third side of triangle.

So, by the property, we have :

n + x + 3 > 2x + 2

⇒ n > x - 1 ...........(2)

From both the equations (1) and (2) , We get :

x – 1 < n < 3x + 5

Therefore, The correct option is A. x – 1 < n < 3x + 5

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The board of directors of a corporation must select a president, a secretary, and a treasurer. In how many possible ways can thi

pentagon [3]

Answer:

9,240 ways possible in which this can be accomplished if there are 22 members on the board of directors.

Step-by-step explanation:

Total number of available members in the board = 22

The number of posts chosen are a president, a secretary, and a treasurer.

For the Post of President:

The number of available options to choose a president = 22 options

For the Post of Secretary:

As we can not repeat the members because one person CANNOT hold two positions simultaneously.

The number of available options to choose a secretary = 21 options

For the Post of Treasurer:

As we can not repeat the members because two person CANNOT hold three positions simultaneously.

The number of available options to choose a treasure = 20 options

Now, the possible ways can this whole election be accomplished is the product of all possible options

= 22 option x 21 option x 20 option

= 9,240 ways

Hence, there are 9,240 ways possible in which this can be accomplished if there are 22 members on the board of directors.

4 0

3 years ago

Solve for x. (e^x-e^-x)/((e^x+e^-x)=t

Sergio [31]

$\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\\\\
\dfrac{e^{2x}-1}{e^{2x}+1}=t\\\\
e^{2x}-1=t(e^{2x}+1)\\\\
e^{2x}-1=e^{2x}t+t\\\\
e^{2x}-e^{2x}t=t+1\\\\
e^{2x}(1-t)=t+1\\\\
e^{2x}=\dfrac{t+1}{1-t}\\\\
e^{2x}=-\dfrac{t+1}{t-1}\\\\
2x=\ln\left(-\dfrac{t+1}{t-1}\right)\\\\
x=\dfrac{\ln\left(-\dfrac{t+1}{t-1}\right)}{2}\qquad t\in(-1,1)



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