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2 years ago

Match the pairs of equations that represent concentric circles.

Mathematics

2 answers:

posledela2 years ago

6 0

if the answer is correct it should look like this =) you welcome.

lesantik [10]2 years ago

4 0

3x^2 + 3y^2 + 12x − 6y − 21 = 0 => x^2 + y^2 + 4x - 2y - 7 = 0 => x^2 + 4x + 4 + y^2 - 2y + 1 = 12 => (x + 2)^2 + (y - 1)^2 = 12 => centre is (-2, 1)

5x^2 + 5y^2 − 10x + 40y − 75 = 0 => x^2 + y^2 - 2x + 8y - 15 = 0 => x^2 - 2x + 1 + y^2 + 8y + 16 = 32 => (x - 1)^2 + (y + 4)^2 = 32 => centre is (1, -4)

5x^2 + 5y^2 − 30x + 20y − 10 = 0 => x^2 + y^2 - 6x + 4y - 2 = 0 => x^2 - 6x + 9 + y^2 + 4y + 4 = 15 => (x - 3)^2 + (y + 2)^2 = 15 => centre is (3, -2)

4x^2 + 4y^2 + 16x − 8y − 308 = 0 => x^2 + y^2 + 4x - 2y - 77 = 0 => x^2 + 4x + 4 + y^2 - 2y + 1 = 82 => (x + 2)^2 + (y - 1)^2 = 82 => centre is (-2, 1)

x^2 + y^2 − 12x − 8y − 100 = 0 => x^2 - 12x + 36 + y^2 - 8y + 16 = 152 => (x - 6)^2 + (y - 4)^2 = 152 => centre is (6, 4)

2x^2 + 2y^2 − 8x + 12y − 40 = 0 => x^2 + y^2 - 4x + 6y - 20 = 0 => x^2 - 4x + 4 + y^2 + 6y + 9 = 33 => (x - 2)^2 + (y + 3)^2 = 33 => centre is (2, -3)

4x^2 + 4y^2 − 16x + 24y − 28 = 0 => x^2 + y^2 - 4x + 6y - 7 = 0 => x^2 - 4x + 4 + y^2 + 6y + 9 = 20 => (x - 2)^2 + (y + 3)^2 = 20 => centre is (2, -3)

3x^2 + 3y^2 − 18x + 12y − 81 = 0 => x^2 + y^2 - 6x + 4y - 27 = 0 => x^2 - 6x + 9 + y^2 + 4y + 4 = 40 => (x - 3)^2 + (y + 2)^2 = 40 => centre is (3, -2)

x^2 + y^2 − 2x + 8y − 13 = 0 => x^2 - 2x + 1 + y^2 + 8y + 16 = 30 => (x - 1)^2 + (y + 4)^2 = 30 => centre = (1, -4)

x^2 + y^2 + 24x + 30y + 17 = 0 => x^2 + 24x + 144 + y^2 + 30y + 225 = 352 => (x + 12)^2 + (y + 15)^2 = 352 => center is (-12, -15)

Therefore, 3x^2 + 3y^2 + 12x − 6y − 21 = 0 and 4x^2 + 4y^2 + 16x − 8y − 308 = 0 are concentric.
5x^2 + 5y^2 − 10x + 40y − 75 = 0 and x^2 + y^2 − 2x + 8y − 13 = 0 are concentric.
5x^2 + 5y^2 − 30x + 20y − 10 = 0 and 3x^2 + 3y^2 − 18x + 12y − 81 = 0 are concentric.
2x^2 + 2y^2 − 8x + 12y − 40 = 0 and 4x^2 + 4y^2 − 16x + 24y − 28 = 0 are concentric.

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9966 [12]

Answer:

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Step-by-step explanation:

Given:

Total number of bracelet = 3

Y is chosen first

Find:

Number of ways to chose bracelet

Computation:

Y is chosen first so remain number of bracelet is 2

So,

Number of ways to chose bracelet = !2

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Number of ways to chose bracelet = 2 ways

8 0

2 years ago

A coat at a store is originally priced at 54.99.The store marks the price down to 32.99.To the nearest percent ,what is the perc

AnnZ [28]

For this case what we can do is the following rule of three:
54.99 ------> 100%
32.99 ------> x
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x = (32.99 / 54.99) * (100)
x = 59.99272595
Therefore, the discount percentage is:
100-59.99272595 = 40.00727405%
To the nearest percent;
40%
Answer:
The percent markdown of the coat is:
40%

7 0

2 years ago

The cost function for a certain company is C = 20x + 700 and the revenue is given by R = 100x − 0.5x2. Recall that profit is rev

Brilliant_brown [7]

Answer:

x = 20

x = 140

Step-by-step explanation:

Find the equation for profit P

P = R - C

Substitute the equations for R and C then simplify.

P = 100x − 0.5x² - (20x + 700)

P = -0.5x² + 80x - 700

Find the values of x when profit is $700

P = -0.5x² + 80x - 700

700 = -0.5x² + 80x - 700

0 = -0.5x² + 80x - 1400

This is in the standard form 0 = ax² + bx + c

Use the quadratic formula to find values of x

$x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}$

(Ignore Â)

Substitute a b and c.

a = -0.5

b = 80

c = -1400

$x = \frac{-(80)±\sqrt{80^{2}-4(-0.5)(-1400)} }{2(-0.5)}$

$x = \frac{-80±60}{-1}$

Split the formula at the ± so that there are two to get the two x values.

$x = \frac{-80+60}{-1}$

$x = \frac{-80-60}{-1}$

x = 20

x = 140

The profit will be $700 when x is 20 or when x is 140.

5 0

2 years ago

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and the

Lera25 [3.4K]

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

The population is $\mu = 6.6$

The level of significance is $\alpha = 5\% = 0.05$

The sample data is 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds

The Null hypothesis is $H_o : \mu = 6.6$

The Alternative hypothesis is $H_a : \mu > 6.6$

The critical value of the level of significance obtained from the normal distribution table is

$Z_{\alpha } = Z_{0.05 } = 1.645$

Generally the sample mean is mathematically evaluated as

$\=x = \frac{\sum x_i }{n}$

substituting values

$\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}$

$\=x = 7.5571$

The standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }$

substituting values

$\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }$ $\sigma = 1.1774$