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3 years ago

Identify the center and radius for the equation x ^ 2 + (y - 3) ^ 2 = 4

Mathematics

1 answer:

marissa [1.9K]3 years ago

6 0

Answer:

r = 2. The center is at (0, 3).

Step-by-step explanation:

Compare the given x ^ 2 + (y - 3) ^ 2 = 4 to the standard equation

(x - h)^2 + (y - k)^2 = r^2.

It becomes obvious that h = 0, k = 3 and r = 2. The center is at (0, 3).

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Three equations have the same solution. Identify the equation that does not have the same solution as the others, 7.25 -15 10 +

german

Answer:

The second equation does not have the same solution, or -15 = -10 + z

Step-by-step explanation:

Every other equation is = to -2, while the one shown above is -5.

4 0

3 years ago

Evaluate the following pic

GREYUIT [131]

Answer:

1) $\sqrt{1225}+\sqrt{1024}=67$

2) $\sqrt[3]{-1331}=-11$

3) Evaluating $2:p :: p:8$ we get $p=\pm 4$

4) $x^3+y^2+z \ when \ x=3, y=-2, x=-6 \ we \ get \ \mathbf{25}$

5) $\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}=-6$

Step-by-step explanation:

1) $\sqrt{1225}+\sqrt{1024}$

Prime factors of 1225 : 5x5x7x7

Prime factors of 1024: 2x2x2x2x2x2x2x2x2x2

$\sqrt{1225}+\sqrt{1024}\\=\sqrt{5\times5\times7\times7}+\sqrt{2\times2\times2\times2\times2\times2\times2\times2\times2\times2}\\=\sqrt{5^2\times7^2}+\sqrt{2^2\times2^2\times2^2\times2^2\times2^2}\\=5\times7+(2\times2\times2\times2\times2)\\=35+32\\=67$

$\sqrt{1225}+\sqrt{1024}=67$

2) $\sqrt[3]{-1331}$

We know that $\sqrt[n]{-x}=-\sqrt[n]{x} \ ( \ if \ n \ is \ odd)$

Applying radical rule:

$\sqrt[3]{-1331}\\=-\sqrt[3]{1331} \\=-\sqrt[3]{11\times\11\times11}\\=-\sqrt[3]{11^3} \\Using \ \sqrt[n]{x^n}=x \\=-11$

So, $\sqrt[3]{-1331}=-11$

3) $2:p :: p:8$

It can be written as:

$p*p=2*8\\p^2=16\\Taking \ square \ root \ on \ both \ sides\\\sqrt{p^2}=\sqrt{16}\\p=\pm 4$

Evaluating $2:p :: p:8$ we get $p=\pm 4$

4) $x^3+y^2+z \ when \ x=3, y=-2, x=-6$

Put value of x, y and z in equation and solve:

$x^3+y^2+z \\=(3)^3+(-2)^2+(-6)\\=27+4-6\\=25$

So, $x^3+y^2+z \ when \ x=3, y=-2, x=-6 \ we \ get \ \mathbf{25}$

5) $\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}$

We know (-a)^n = (a)^n when n is even and (-a)^n = (-a)^n when n is odd

$\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}\\\\=\frac{1296\times-8\times 27}{46656}\\\\=\frac{-279936}{46656} \\\\=-6$

So, $\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}=-6$

8 0

3 years ago

I need help with this problem

Maru [420]

Answer:

Step-by-step explanation:

5^2-3^2=?

25-9=16

sqrt 16 = 4

6×4=24

6 0

3 years ago

The costs of 2 sound systems were decreased by $10. The original costs of the systems were $90 and $60. Without calculating, whi

bezimeni [28]

The 60$ system had a greater percentage decrease because it was a lower number to begin with. Taking the same portion out of two different numbers will always be a greater decrease for the lower number.

4 0

3 years ago

Perform the indicated operations.Express the answer in its lowest terms.

Marat540 [252]

Answer:

BlueSky06

2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10

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7 0

2 years ago

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