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3 years ago

Find the equation of the circle in standard form for the given center (h, k) and radius r: (h, k) = (5, 4), r = 2

1 answer:

7 0

If cente ris (h,k) and radius is r then
equatn is (x-h)^2+(y-k)^2=r^2

so

center (5,4)
r=2
h=5
k=4

(x-5)^2+(y-4)^2=2^2
(x-5)^2+(y-4)^2=4

first option

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ANSWER ASAP!! Find the area of a triangle with legs that are: 12 m, 15 m, and 9 m.

Setler79 [48]

Answer:

Step-by-step explanation:

<h3>METHOD 1:</h3>

You can use the Heron's formula:

$A=\sqrt{p(p-a)(p-b)(p-c)}$

where

<em>p</em><em> - half of perimeter</em>

<em>a, b, c</em><em> - lengths of sides</em>

We have

$a=12m;\ b=15m;\ c=9m$

Calculate:

$p=\dfrac{12+15+9}{2}=\dfrac{36}{2}=18\ (m)\\\\A=\sqrt{18(18-12)+(18-15)(18-9)}\\\\A=\sqrt{(18)(6)(3)(9)}\\\\A=\sqrt{2916}\\\\A=54\ (m^2)$

<h3>METHOD 2:</h3>

Let's check that it is not a right triangle.

If the sum of the squares of the two shorter sides is equal to the square of the longest side, then this triangle is rectangular.

We have

$9m < 12m$

Check:

$9^2+12^2=81+144=225\\15^2=225$

This is a right trianglr wherew 9m and 12m are legs and 15m is a hypotenuse.

The formula of an area of a right triangle is:

$A=\dfrac{ab}{2}$

Substitute:

$A=\dfrac{(9)(12)}{2}=\dfrac{108}{2}=54\ (m^2)$

6 0

3 years ago

The length of the hypotenuse of the right triangle is 25 cm, the length of one of the legs is 10 cm. What is the length of the s

Anna007 [38]

Answer:

21 cm

Step-by-step explanation:

Call the triangle ABC, with the right angle at B, the hypotenuse AC=25, and the given leg AB=10. The altitude to the hypotenuse can be BD. Since the "other leg" is BC, we believe the question is asking for the length of DC.

The right triangles formed by the altitude are all similar to the original. That means ...

AD/AB = AB/AC . . . . . . ratio of short side to hypotenuse is a constant

Multiplying by AB and substituting the given numbers, we get ...

AD = AB²/AC = 10²/25

AD = 4

Then the segment DC is ...

DC = AC -AD = 25 -4

DC = 21 . . . . . centimeters

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3 years ago

What is the slope of the line on the graph?

Lelechka [254]

Answer:

5,-1,-7

Step-by-step explanation:

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3 years ago

The complement of an angle is 25 less than 3 times the angles itself. Find the measure of each

Semenov [28]

Answer: 28.75° and 61.25°

Step-by-step explanation:

A complementary angle equals 90°.

Let the measure of the angle be a

Therefore, its complement will be:

= 90-a.

The complement of an angle is 25 less than 3 times the angles itself can be written as:

90-a = 3a - 25

90 + 25 = 3a + a

115 = 4a

a = 115/4

a= 28.75

Since the angle is 28.75°, the complement will be:

= 90° - 28.75°

= 61.25°

The angles are 28.75° and 61.25°

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3 years ago

A. What is the vertex of the equation y = (x - 4)??

Contact [7]

Good morning,

Answer:

(4 , 0)

Step-by-step explanation:

THe vertex of y = (x - 4)² is (4,0).

Look at the photo below for the graph.

8 0

3 years ago