<img src="https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B12a%5E%7B5%7D%20%7D%7B49a%7D%20%7D" id="TexFormula1" title="\sqrt{\frac{12

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2 years ago

14

a^{5} }{49a} }" alt="\sqrt{\frac{12a^{5} }{49a} }" align="absmiddle" class="latex-formula">

1 answer:

Inga [223]2 years ago

8 0

Answer:

18a

Step-by-step explanation:

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Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, whe

musickatia [10]

Rationalizing the denominator involves exploiting the well-known difference of squares formula,

$a^2-b^2=(a-b)(a+b)$

We have

$(\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14$

so that

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}$

Rewrite 16 and 32 as powers of 2, then simplify:

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7$

So we have <em>A</em> = 8, <em>B</em> = 2, <em>C</em> = 4, and <em>D</em> = 7, and thus <em>A</em> + <em>B</em> + <em>C</em> + <em>D</em> = 21.

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3 years ago

How many real solutions does this system of equations have? x2+y2=363x−y+1=0 A. 0 B. 3 C. 2 D. 1

Rus_ich [418]

Answer:

Correct option: C -> 2

Step-by-step explanation:

The first equation is:

$x^2+y^2=363$

And the second equation is:

$x-y+1=0$

From the second equation, we have:

$y = x + 1$

Using this value of y in the first equation, we have:

$x^2 + (x+1)^2 = 363$

$x^2 + x^2 + 2x + 1 = 363$

$2x^2 + 2x= 362$

$x^2 + x - 181 = 0$

Calculating the discriminant Delta, we have:

$\Delta = b^2 - 4ac = 1 + 4*181 = 725$

We have $\Delta > 0$ , so we have two real values for x, therefore we have two solutions for this system.

Correct option: C.

(If the system of equation is actually:

$x^2+y^2=36$

$3x-y+1=0$

We would have:

$y = 3x + 1$

$x^2+(3x+1)^2=36$

$x^2+9x^2+6x+1=36$

$10x^2+6x-35=0$

$\Delta = 36 + 1400 = 1436$

We also have $\Delta > 0$ , so we have two solutions for this system.

Correct option: C.)

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3 years ago

How do properties of integer exponents help you write equivalent expression?

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The properties of integer exponents can be used to write equivalent expressions by combining numeric or algebraic expressions that have a common base, distributing exponents to products and quotients, and simplifying powers of powers.

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4 years ago

A quiz consists of 20 multiple-choice questions find mean and standard deviation

worty [1.4K]

Since the problem is quite vague because the number of choice per question is not written here. I’ll just put for 4 choices and 5 choices each.

To compute for the 5 choices each:

Mean = np = 20 (1/5) = 4

Standard deviation = sqrt(npq) = sqrt (4*(4/5) = 1.79

To compute for the 4 choices each:

Mean = np = 20 (1/4) = 5

Standard deviation = sqrt(npq) = sqrt (5*(4/5) = 2

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3 years ago

What operation comes first?

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