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Savatey [412]
3 years ago
14

Which equation represents the circle described?

Mathematics
2 answers:
bazaltina [42]3 years ago
6 0

We have the equation:

x^2+y^2-8x-6y+24=0


By arranging this equation in terms of x and y, we have:


x^2-8x+y^2-6y=-24 \\ \\


By using the method of completing the square, we have:

x^2-8x+\mathbf{\left(\frac{8}{2}\right)^2}+y^2-6y+\mathbf{\left(\frac{6}{2}\right)^2}=-24+\mathbf{\left(\frac{8}{2}\right)^2}+\mathbf{\left(\frac{6}{2}\right)^2} \\ \\ x^2-8x+\mathbf{16}+y^2-6y+\mathbf{9}=-24+\mathbf{16}+\mathbf{9} \\ \\ \boxed{(x-4)^2+(x-3)^2=1}


The center of this circle is:

(h,k)=(4,3)


So the equation that fulfills the statement is:

(x-4)^2+(y-3)^2=2^2


Finally, the right answer is c)

Reika [66]3 years ago
3 0

Answer:

The correct option is c.

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+(y-k)^2=r^2          .... (1)

Where, r is the radius and (h,k) is the center of the circle.

The given equation is

x^2+y^2-8x-6y+24=0

(x^2-8x)+(y^2-6y)+24=0

To make a perfect square add and subtract (-\frac{b}{2a})^2 in the parenthesis. where, b is coefficient of middle term and a is leading coefficient.

(x^2-8x+4^2-4^2)+(y^2-6y+3^2-3^2)+24=0

(x^2-8x+4^2)-16+(y^2-6y+3^2)-9+24=0

(x-4)^2+(y-3)^2-1=0

Add 1 both sides.

(x-4)^2+(y-3)^2=1        . ... (2)

On comparing (1) and (2), we can say that the center of the circle is (4,3).

The equation of circle having center (4,3) with radius 2 is

(x-4)^2+(y-3)^2=2^2

Therefore option c is correct.

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3 years ago
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cluponka [151]

Answer:

1 ⇒ D

2 ⇒ H

3 ⇒ B

4 ⇒ G

5 ⇒ A

6 ⇒ F

7 ⇒ E

8 ⇒ C

Step-by-step explanation:

* Lets explain how to solve the problem

- The left column has expressions and the right column has the

  equivalent expressions

- We must find the equivalent letter for each number

1.

# 7(12)

∵ 12 can be a sum of two numbers

∴ The equivalent expression to 7(12) is 7(8 + 4)

∴ 1 ⇒ D

2.

# 3(15)

∵ 3 can be a sum of two numbers

∴ The equivalent expression to 3(15) is (2 + 1)(15)

∴ 2 ⇒ H

3.

# 3a + 9

∵ 3 and 9 have a common factor 3

∵ 3a + 9 ⇒ divide them by 3

∵ 3a ÷ 3 = a and 9 ÷ 3 = 3

∴ 3a + 9 = 3(a + 3)

∴ The equivalent expression to 3a + 9 is 3(a + 3)

∴ 3 ⇒ B

4.

# 9a + 3

∵ 9 and 3 have a common factor 3

∵ 9a + 3 ⇒ divide them by 3

∵ 9a ÷ 3 = 3a and 3 ÷ 3 = 1

∴ 9a + 3 = 3(3a + 1)

∴ The equivalent expression to 9a + 3 is 3(3a + 1)

∴ 4 ⇒ G

5.

# 5 + 15a

∵ 5 and 15 have a common factor 5

∵ 5 + 15a ⇒ divide them by 5

∵ 5 ÷ 5 = 1 and 15a ÷ 5 = 3a

∴ 5 + 15a = 5(1 + 3a)

∴ The equivalent expression to 5 + 15a is 5(1 + 3a)

∴ 5 ⇒ A

6.

# 10 + 5a

∵ 10 and 5 have a common factor 5

∵ 10 + 5a ⇒ divide them by 5

∵ 10 ÷ 5 = 2 and 5a ÷ 5 = a

∴ 10 + 5a = 5(2 + aa)

∴ The equivalent expression to 10 + 5a is 5(2 + a)

∴ 6 ⇒ F

7.

# 3x + 6y + 9z

∵ The coefficient of x , y , z have a common factor 3

∵ 3x ÷ 3 = x

∵ 6y ÷ 3 = 2y

∵ 9z ÷ 3 = 3z

∴ 3x + 6y + 9z = 3(x + 2y + 3z)

∴ The equivalent expression to 3x + 6y + 9z is 3(x + 2y + 3z)

∴ 7 ⇒ E

8.

# 3x + 3y + 3z

∵ The coefficient of x , y , z have a common factor 3

∵ 3x ÷ 3 = x

∵ 3y ÷ 3 = y

∵ 3z ÷ 3 = z

∴ 3x + 3y + 3z = 3(x + y + z)

∴ The equivalent expression to 3x + 3y + 3z is 3(x + y + z)

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marysya [2.9K]

Answer:

see explanation

Step-by-step explanation:

(5)

Since ∠EBA = 90° then ∠ABD = 90° ( straight angle ) and

∠ABC + ∠CBD = ∠ABD, that is

2x + 3x - 10 = 90, simplifying

5x - 10 = 90 ( add 10 to both sides )

5x = 100 ( divide both sides by 5 )

x = 20, thus

∠ABC = 2x = 2 × 20 = 40°

∠CBD = 3x - 10 = (3 × 20) - 10 = 60 - 10 = 50°

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4x - 18 = 3x + 7 ( vertical angles are congruent )

Subtract 3x from both sides

x - 18 = 7 ( add 18 to both sides )

x = 25

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Kruka [31]
By the definition for the absolute value,

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|x+1|=\begin{cases}x+1&\text{for }x\ge-1\\-(x+1)&\text{for }x

So for the compound function f(x)=1-|x-1|+|x+1|, there are three intervals to consider. What happens when x? when -1\le x? when x\ge1?

You have

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8 0
3 years ago
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Nat2105 [25]

Answer:

See below.

Step-by-step explanation:

Lets take √72:

Factoring 72 to find perfect squares:

72 = 2*2*2*3*3

The largest perfect square in the above = 2*2*3*3 = 36.

So we can write 72 as 36*2.

√72 = √(36 * 2)

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= 6√2.

One more example:

√18  = √(2*3*3)

= √9*√2

= 3√2.

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