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3 years ago

HELPP ILL GIVE MAD POINTS!! Which series has a sum of 5?

Mathematics

2 answers:

jeka943 years ago

8 0

Its the first choice

s344n2d4d5 [400]3 years ago

5 0

Answer:

Step-by-step explanation:

The formula is S=a1/1-r

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Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, $A +B+C+D = 5+6-10+2 = \bold3$

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Which of these points is on circle with a center at (0, 0) that includes the point (-1, -3)?

Tatiana [17]

Answer:(0,10)

Step-by-step explanation:

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The exponent form of 3 under root 7

viva [34]

Answer: 3 $\sqrt{x} 7$

Step-by-step explanation:

3 under root 7

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In Navada, sales tax are 6.18%. what is the tax on items that total $111.39 before tax?

Harrizon [31]

The answer would be $104.5

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3 years ago

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How many digits in hex do you need to represent integers up to 1, 000?

shepuryov [24]

You can convert 1000 to hex and see how many digits that requires:

$1000_{10}=(3\cdot16^2+14\cdot16+8)_{10}=3\mathrm e8_{16}$

So every integer below 1000 needs up to 3 digits.

Alternatively, we know that $16^2=256$ , and that $16^n$ requires $n+1$ digits in its hex representation (e.g. $16_{10}=10_{16}$ ). Taking the logarithm, we get $\log_{16}16^2=2$ , and adding 1 gives the number of digits needed to represent $16^2$ . Similarly,

$\lfloor\log_{16}1000\rfloor+1=3$

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3 years ago