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4 years ago

What is the value of x?

Mathematics

2 answers:

zheka24 [161]4 years ago

6 0

Answer:

x = 34

Step-by-step explanation:

It is given to us that when all the interior angles are added together, it will equal 360. Set all the angles equal to 360.

3x - 6 + 2x + 88 + 108 = 360

Simplify. Combine like terms.

(3x + 2x) + (88 + 108 - 6) = 360

(5x) + (190) = 360

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 190 from both sides.

5x + 190 (-190) = 360 (-190)

5x = 360 - 190

5x = 170

Isolate the variable x. Divide 5 from both sides.

(5x)/5 = (170)/5

x = 170/5

x = 34

34 is your answer for x.

Oliga [24]4 years ago

3 0

Answer:

x = 34

Step-by-step explanation:

The sum of the interior angles of a quadrilateral are 360

(3x-6) + 88 + 108 +2x = 360

Combine like terms

5x +190 = 360

Subtract 190 from each side

5x+190 - 190 = 360 - 190

5x = 170

Divide each side by 5

5x/5=170/5

x =34

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Answer:

After 1st year, the age distribution will be

$x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right]$

After 2nd year, the age distribution will be

$x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right]$

Step-by-step explanation:

A population has the following characteristics.

A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year.

The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.

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The population now consists of 144 members in each of the three age classes.

From the above information, we can construct the current age matrix.

$x = \left[\begin{array}{ccc}144\\144\\144\end{array}\right]$

How many members will there be in each age class in 1 year?

After 1st year, the age distribution will be

$x_1 = A \cdot x$

$x_1 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}144\\144\\144\end{array}\right]$

The matrix multiplication is possible since the number of columns of first matrix is equal to the number of rows of second matrix.

$x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right]$

After 2nd year, the age distribution will be

$x_2 = A \cdot x_1$

$x_2 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}1584\\36\\108\end{array}\right]$

$x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right]$

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