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just olya [345]
3 years ago
6

Polygon ABCD is a parallelogram, and m of abc =127°. The length of bc is 19 units, and an is 5 units. What is the perimeter of t

he parallelogram?
Mathematics
1 answer:
hjlf3 years ago
6 0
The perimeter of a parallelgram is the sum of the lengths of its four sides.

Parallelogram ABCD has sides AB, BC, CD, and AB.

Sides AB and CD are parallel and of equal length = 19 units.

Sides BC and CD are parallel and of equal length. Assuming thi is the length of 5 units given in the statement, the perimeter of the parallelogram ABCD is: 19  units + 19 units + 5 units + 5 units = 48 units.

Please, inform if the length of 5 units corresponds to other distance, but even in that case, with this explanation you should be able to calculate the perimeter of this and other parallelograms.

Answer: 48 untis.
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Determine the exact value of sin 13pi/12
ohaa [14]
To answer the problem above, convert the given angle to an equivalent angle with the unit of degrees.
                               (13π / 12 rad) x (360° / 2π) = 195°
We can solve this by directly inputting the value in our scientific calculators. The answer is approximately -0.2588.
6 0
3 years ago
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
Oksana_A [137]

Answer:

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

 In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

{n \choose 5 } = \frac{n!}{5!(n-5)!}

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 {n \choose 4} .

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is 4 * {n \choose 4} .

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is {n \choose 3} .

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have {3 \choose 2 } = 3  possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of 6 * {n \choose 3}

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of {n \choose 2}  possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

4 * {n \choose 2}

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

I hope that works for you!

4 0
3 years ago
What is 10÷5/8 in a math order.
Sedbober [7]
If you would like to calculate <span>10÷5/8, you can do this using the following steps:

</span><span>10÷5/8 = (10/5)/8 = 2/8 = 1/4 = 0.25

The correct result would be 1/4 or 0.25.</span>
3 0
3 years ago
DODOL
ZanzabumX [31]

For this case we have that the point-slope equation of a line is given by:

y-y_ {0} = m (x-x_ {0})

Where:

m: It is the slope of the line

(x_ {0}, y_ {0}): It is a point through which the line passes

In this case we have to:

(x_ {0}, y_ {0}) :( 3,2)

Substituting in the equation we have:

y-2 = m (x-3)

Answer:

y-2 = m (x-3)

We just need to replace the value of the slope

3 0
3 years ago
Tamara owns 595 shares of stock in a home appliance company. The value of the stocks is $12.75 per share. The company offers a 5
emmainna [20.7K]

Answer:

she would get 12.75 per eache 63.75 that the company gets hope this helps

Step-by-step explanation:

7 0
3 years ago
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