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3 years ago

What is the radius for this given equation? (x^2+10x) + (y^2-8y)=59

Mathematics

1 answer:

Eva8 [605]3 years ago

5 0

Answer:

The answer to your question is r = 10

Step-by-step explanation:

Data

(x² + 10x ) + (y² - 8y ) = 59

Process

1.- Complete the perfect square trinomials

(x² + 10x + (5)²) + (y² - 8y + (4)²) = 59 + (5)² + (4)²

2.- Simplify

(x² + 10x + 25) + (y² - 8y + 16) = 59 + 25 + 16

3.- Factor

(x + 5)² + (y - 4)² = 100

or (x + 5)² + (y - 4)² = 10²

4.- Compare the result with the standard form

(x - h)² + (y - k)² = r²

then r² = 10²

and r = 10

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If x and y are integers greater than 1, is x a multiple of y ? (1) \small 3y^{2}+7y=x (2) \small x^{2}-x is a multiple of y. Sta

Nata [24]

Answer:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Step-by-step explanation:

A multiple of a number is obtained after multiplying the number by an integer.

Here,

x, y are any two integers greater than 1,

(1) We have,

$\small 3y^{2}+7y=x$

$\implies y(3y+7) = x$

∵ y is an integer ⇒ 3y + 7 is also an integer,

⇒ y × an integer = x

That is, when we multiply y by a number we obtain x,

∴ x is a multiple of y.

Thus, statement (1) ALONE is sufficient.

(2),

$\small x^{2}-x\text{ is a multiple of y}$

I.e.

$y\times a = x^2-x$ , where a is an integer,

$\implies y\times a = x(x-1)$

∵ x and x - 1 are disjoint numbers,

There are three possible cases,

Case 1 : x is multiple of y

Case 2 : (x-1) is a multiple of y,

Case 3 : neither x nor x - 1 are multiple of y but their product is multiple of y,

Thus, statement (2) is not sufficient.

8 0

3 years ago

Which expression is equivalent to

KonstantinChe [14]

Given the expression:

$\sqrt[4]{ \frac{24x^{6}y}{128x^{4}y^{5}}}$

Simplifying:

$\sqrt[4]{ \frac{3x^{2}}{16y^{4}}}$

Then the answer is:

$\frac{ \sqrt[4]{3x^{2}}}{2y}$

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3 years ago

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goblinko [34]

C is the correct answer. using the equation (y-y1)=m(x-x1)

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3 years ago

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Lady_Fox [76]

Simplifying 4y + -70 = 12y + 2

Add -12y to each side of the equation. -70 + 4y + -12y = 2 + 12y + -12y

Add 70 to each side of the equation. -70 + 70 + -8y = 2 + 70

Divide each side by -8.

So y = -9 is your answer.

Hope I Helped!!!

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Cerrena [4.2K]

Answer:

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Step-by-step explanation:

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