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3 years ago

How to find the perimeter of a right triangle

Mathematics

1 answer:

QveST [7]3 years ago

6 0

Answer:

There are three primary methods used to find the perimeter of a right triangle.

1. When side lengths are given, add them together.

2. Solve for a missing side using the Pythagorean theorem.

3. If we know side-angle-side information, solve for the missing side using the Law of Cosines.

Step-by-step explanation:

there i hope this helps!!!

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Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has

Aleksandr [31]

Answer:

Step-by-step explanation:

for the first gear

revolutions/teeth

1 / 24

2 / 48

3 / 72

4 / 96

5 / 120

6 / 144

for the second gear

revolutions/teeth

1 / 40

2 / 80

3 / 120

4 / 160

the two marks will meet after 120 teeth, 5 revolutions of the first gear and 3 revolutions of the second.

the way to get that amount of teeth is

$24 = 2 \times 2 \times 2 \times 3 = {2}^{3} \times 3$

$40 = 2 \times 2 \times 2 \times 5 = {2}^{3} \times 5$

the Least Common Multiple equals the product of all factors, but those factors who are repeted for both numbers should be only once.

${2}^{3} \times 5 \times 3 = 120$

120 teeth are 5 revolutions for gear1 and 3 por gear2

8 0

3 years ago

1. A boat is 18 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 68°

slega [8]

Answer:

19.4 feet

Step-by-step explanation:

When calculating distances using perpendicular angles, we use trig functions such as Sin, Cos, and Tan.

Sine is defined in a perpendicular triangle as the ratio of the opposite side to the angle over the hypotenuse.
Cosine is defined in a perpendicular triangle as the ratio of the adjacent side to the angle over the hypotenuse.
Tangent is defined in a perpendicular triangle as the ratio of the opposite side over the adjacent side.

Because our angle and know side value are across from each other and we need to know the hypotenuse, we chose to use Sine.

We set up the equation $sin (68) = \frac{18}{h}$ .

We isolate h by multiplying h across the equal sign and dividing sin (68) across as well. $sin (68) = \frac{18}{h}\\hsin (68) = \frac{18}{h}*h\\hsin (68) = 18\\\frac{hsin (68)}{sin (68)} =\frac{18}{sin (68)} \\$

And finally we have $h=\frac{18}{sin (68)}$ . We input to calculator.

$h=\frac{18}{0.92718} \\h=19.4 feet$

See the attached picture below showing the shore with the boat out at sea and the position of the person.

8 0

3 years ago

Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r

erastova [34]

Answer:

The probability is $\frac{56!}{64!}$

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, $64 \choose 8 .$

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function $f : A \rightarrow A ,$ with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

$\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}$

7 0

2 years ago

What is the greatest common factor of 40 and 27?

Olenka [21]

To find the greatest common factor of 40 and 27, we can first start by making a list of factors for each number.

The factors of 27 are: 1, 3, 9, 27

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

When looking at these numbers, we can see that 1 is the greatest common factor of both 40 and 27.

7 0

3 years ago

Solve the system of equations by graphing. x+y=3 y=2x−15

Stella [2.4K]

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x + y = 3

x = 3 - y

y = 2x - 15

y = 2(3 - y) - 15

y = 6 - 2y - 15

y = -2y - 9

3y = -9

y = -3

y = 2x - 15

-3 = 2x - 15

-2x = -12

x = 6

So...

The answer is: (6, -3)

4 0

3 years ago

Read 2 more answers