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3 years ago

Which of these numbers is a prime number 1,11,21,51

Mathematics

2 answers:

Alinara [238K]3 years ago

5 0

11 because it cannot be divided by any whole number besides 1.

julia-pushkina [17]3 years ago

5 0

11 is a prime number because it cannot be divided by any number equally.

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

5 0

3 years ago

(1,3)(0,2)(-4,0) are they collinear

mariarad [96]

Answer: No, they are not collinear.

6 0

3 years ago

Evaluate -16 - 9x<br> When x= 3

vfiekz [6]

Answer:

-43

Step-by-step explanation:

first we need to do 9x witch would be 9x3 so 9x3 is 27 now its down to -16 - 27 and that is -43

8 0

3 years ago

You may remember that the perimeter of a rectangle is P=2(W+L) where W is the width and L is the length. Suppose that the perime

Anna71 [15]

Answer:

5 feet

Step-by-step explanation:

P = 2(w + l)

P = 34

l = w + 7

34 = 2 (w + w + 7)

34 = 2w + 2w + 14

34 - 14 = 4w

20 = 4w

w = 5 feet

Since l = w + 7

l = 5 + 7

l = 12 feet

5 0

3 years ago

Select all the situations that can be represented by the tape diagram. 99 W W W W W 4 Clare buys 4 bouquets, each with the same

enot [183]

Answer:

Third one 33333333333333333

5 0

3 years ago

Read 2 more answers