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damaskus [11]
3 years ago
5

Find the equation of the circle with center at (3,-2) and radius of 3.

Mathematics
1 answer:
AURORKA [14]3 years ago
3 0

Answer:

The equation of the circle is (x - 3)² + (y + 2)² = 9

Step-by-step explanation:

The form of the equation of a circle is (x - h)² + (y - k)² = r², where

  • h is the x-coordinate center of the circle
  • k is the y-coordinate of the center of the circle
  • r is the radius of the circle

∵ The center of a circle is (3, -2)

∴ x-coordinate of the center is 3

∴ y-coordinate of the center is -2

∴ h = 3 and k = -2

∵ The radius of the circle is 3

∴ r = 3

→ Substitute them in the form of the equation above

∵ (x - 3)² + (y - -2)² = (3)²

∴ (x - 3)² + (y + 2)² = 9

∴ The equation of the circle is (x - 3)² + (y + 2)² = 9

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Mrac [35]

A. \frac{27}{19}

To find greater than or smaller than relation, we multiply the terms like (numerator of L.H.S with denominator of R.H.S and put the value on the left side. Then multiply the denominator of L.H.S with numerator of R.H.S and put the value on right side. Now compare the digits.)

So, solving A,  we get 810<209  ... This is false

B. \frac{17}{31}>\frac{19}{14}

= 238>589   ..... This is false

C. \frac{16}{26}>\frac{30}{31}

= 496>780    .... This is false

D. \frac{35}{30}

= 420<660   ..... This is true

Hence, option D is true.

6 0
3 years ago
Bonnie planted a garden in her backyard. Both the garden and the backyard are right triangles. The garden is proportional to the
Mandarinka [93]
You can find the area of Bonnue's backyard by comparing the hypotenuse of the garden to the hypotenuse of the back yard.  If the hypotenuse of the garden is 10 (with the side lengths being 6, 8 and 10 - the longest is always the hypotenuse) and the hypotenuse of the back yard is 30, this is a scale factor of 3 (3 times longer).

This means the other two sides would also be 3 times longer.

6 yards x 3 = 18
8 yards x 3 = 24

To find the area using these dimensions, you will use the formula for finding the area of a triangle.

A = 1/2bh
A = 1/2 x 18 x 24
A = 216 square yards

The area of the backyard is 216 square yards.
8 0
3 years ago
The value of x for which 3 (x-2) = 2 (x+1)​
netineya [11]

Answer:

x = 8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

3(x - 2) = 2(x + 1)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                     3x - 6 = 2x + 2
  2. Subtract 2x on both sides:          x - 6 = 2
  3. Add 6 to both sides:                    x = 8

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    3(8 - 2) = 2(8 + 1)
  2. Subtract/Add:                      3(6) = 2(9)
  3. Multiply:                               18 = 18

Here we see that 18 does indeed equal 18.

∴ x = 8 is a solution to the equation.

7 0
3 years ago
Maria’s phone bills were $95, $67, $43, and $115. What was the mean, or average, of her phone bills?
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The answer is 80$.........
6 0
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Anna007 [38]

Answer:

19/30

Step-by-step explanation:

30 students

12 have cat , 19 have dog , 6 no cat or dog

P dog = 19 have dogs/30 students total = .633333...

7 0
3 years ago
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