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Alik [6]
3 years ago
9

The right triangle shown has one leg of length 5 centimeters and a hypotenuse of length 13 centimeters a) find the length of the

other leg b) what is the perimeter of the triangle c) what is the area of the triangle
Mathematics
1 answer:
melisa1 [442]3 years ago
8 0
A) By Pythagoras' Theorem  x^2 = 13^2 - 5^2    where x = length of the other leg.  x^2 = 169 - 25 = 144 so x = 12. cms.

b) perimeter = 5 + 12 + 13 = 30 cms

c) Area of triangle = product of the 2 legs  = 5*12 = 60 cm^2.
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HELP!!
leonid [27]

Answer:

The focus point is (2 , 0) ⇒ answer D

Step-by-step explanation:

* Lets revise the equation of the parabola in standard form

- The standard form is (x - h)² = 4p(y - k)

- The focus is (h, k + p)

- The directrix is y = k - p

- If the parabola is rotated so that its vertex is (h , k) and its axis of

 symmetry is parallel to the x-axis, it has an equation of

 (y - k)² = 4p(x - h)

- The focus is (h + p, k)

- The directrix is x = h - p

* Lets solve the problem

∵ The equation of the parabola is y = 1/8(x² - 4x - 12)

- Lets make x² - 4x completing square

∵ √x² = x  

∴ The 1st term in the bracket is x

∵ 4x ÷ 2 = 2x

∴ The product of the 1st term and the 2nd term is 2x

∵ The 1st term is x

∴ the second term = 2x ÷ x = 2

∴ The bracket is (x - 2)²

∵  (x - 2)² = (x² - 4x + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out  

  the bracket to keep the equation as it

∴ (x² - 4x + 4) - 4 = (x - 2)² - 4

- Lets put the equation after making the completing square

∴ y = 1/8 [(x - 2)² - 4 - 12]

∴ y = 1/8 [(x - 2)² - 16] ⇒ multiply both sides by 8

∴ 8y = (x - 2)² - 16 ⇒ add 16 to both sides

∴ 8y + 16 = (x - 2)² ⇒ take from the left side 8 as a common factor

∴ 8(y + 2) = (x - 2)²

∴ The standard form of the equation of the parabola is

   (x - 2)² = 8(y + 2)

∵ The standard form of the equation is (x - h)² = 4p(y - k)

∴ h = 2 , k = -2 , 4p = 8

∵ The focus is (h , k + p)

∵ h = 2

∵ 4p = 8 ⇒ divide both sides by 4

∴ p = 2

∴ The focus = (2 , -2 + 2) = (2 , 0)

* The focus point is (2 , 0)

6 0
3 years ago
Select the correct answer.
nydimaria [60]

Answer:

It is CD

Step-by-step explanation:

because 300+200=500, juts times it by 3 and divide

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2 years ago
How many solutions does the following equation have ?
bija089 [108]
There is only one solution
8 0
3 years ago
Read 2 more answers
Please help quickly, will give brainliest to the correct answers for these problems :)
Veseljchak [2.6K]

Answer:

Step-by-step explanation:

7 0
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The end of the cave is 380 meters below surface of the earth generate an integer to reoresent this profit
RSB [31]

The question says that the end of the cave is 380 meters below.

Lets say  the sea level or the surface is at 0 meters or we can say that  it is the reference level for us.

Now if we go up the height will be measured with positive integer but if we go down the depth will be represented by  a negative integer.

Negative integer also represents the depth or the distance below the surface level.

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