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nirvana33 [79]
3 years ago
15

Write the standard form of the equation of the circle with center (-5,-7) that passes through the point (7,5).

Mathematics
1 answer:
shutvik [7]3 years ago
4 0

Answer:

(x + 5)² + (y + 7)² = 288

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)

r = \sqrt{(7+5)^2+(5+7)^2} = \sqrt{12^2+12^2} = \sqrt{288}

Hence

(x - (- 5))² + (y - (- 7))² = (\sqrt{288})², that is

(x + 5)² + (y + 7)² = 288

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. Quantas senhas com 4 algarismos diferentes podemos escrever com os algarismos 1, 2, 3, 4, 5, 6?
ruslelena [56]

Answer:

We can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.

Step-by-step explanation:

We have to find how many passwords with 4 different digits can we write with the numbers 1, 2, 3, 4, 5, and 6.

Firstly, it must be known here that to calculate the above situation we have to use Permutation and not combination because here the order of the numbers in a password matter.

Since we are given six numbers (1, 2, 3, 4, 5, and 6) and have to make 4 different digits passwords.

  • Now, for first digit of the password, we have 6 possibilities (numbers from 1 to 6).
  • Similarly, for second digit of the password, we have 5 possibilities (because one number from 1 to 6 has been used above and it can't be repeated).
  • Similarly, for the third digit of the password, we have 4 possibilities (because two numbers from 1 to 6 have been used above and they can't be repeated).
  • Similarly, for the fourth digit of the password, we have 3 possibilities (because three numbers from 1 to 6 have been used above and they can't be repeated).

So, the number of passwords with 4 different digits we can write = 6 \times 5 \times 4 \times 3  = 360 possibilities.

Hence, we can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.

4 0
2 years ago
Is 8.27 rational or irrational?
vladimir1956 [14]

Answer:

Rational

Step-by-step explanation:

8.27 is rational

6 0
3 years ago
Read 2 more answers
Cuál es el resultado de |-15| x (-5)​
notka56 [123]

Answer:

\frac{15}{x^5}

Step-by-step explanation:

\left|-15\right|x^{-5}

Step 1: Apply exponent rule: \:a^{-b}=\frac{1}{a^b}

=\left|-15\right|\frac{1}{x^5}

Step 2: Multiply fractions: a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

=\frac{1\cdot \left|-15\right|}{x^5}

Step 3: Simplify

=\frac{15}{x^5}

The result is =\frac{15}{x^5}

<u>Spanish/Espanól</u>

Respuesta:

\frac{15}{x^5}

Explicación paso a paso:

\left|-15\right|x^{-5}

Paso 1: aplique la regla del exponente: \:a^{-b}=\frac{1}{a^b}

=\left|-15\right|\frac{1}{x^5}

Paso 2: multiplica fracciones: a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

=\frac{1\cdot \left|-15\right|}{x^5}

Paso 3: simplifica

=\frac{15}{x^5}

El resultado es =\frac{15}{x^5}

7 0
3 years ago
Which trinomials are perfect square trinomials?
taurus [48]
You can know a perfect square trinomial:

i) if the coefficient of a² = 1.

ii) If you divide the middle number coefficient by 2 and you square it you get the last term.

Take for example the first option: 

For all the options, the coefficient of a² = 1

a² + 4a + 16.

Coefficient of a = 4.
4/2 = 2
2² = 4, this does not equal the last term so it is not a perfect square trinomial.


a² + 14a + 49.

Coefficient of a = 14.
14/2 = 7
7² = 49, this is equal the last term so it is a perfect square trinomial.
And the perfect square is (a +7)²


Similarly if you test the last option.

a² + 26a + 169.

Coefficient of a = 26.
26/2 = 13
13² = 169, this is equal the last term so it is a perfect square trinomial.
And the perfect square is (a +13)²

So the only two options are: a² + 14a + 49 and a² + 26a + 169.

Other options do not pass this test.
3 0
3 years ago
Read 2 more answers
Please help with this pls.
allochka39001 [22]

Answer:

x = 9

(5x9) - 1° = 45 - 1 or 44°

Step-by-step explanation:

the little square indicates the angle is a right angle, measuring 90°

therefore, you can solve for 'x' by creating this equation:

46 + 5x-1 = 90

45 + 5x = 90

5x = 45

x = 9

5 0
2 years ago
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