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2 years ago

Solve the equation for y. 4x - 5y = 9

Mathematics

1 answer:

babymother [125]2 years ago

3 0

Answer:

y = (4x - 9) / 5 or y = 4/5x - 9/5

Step-by-step explanation:

Solving for y

4x - 5y = 9

-5y = -4x + 9

5y = 4x - 9

y = (4x - 9) / 5 or y = 4/5x - 9/5

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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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The diameter of the average cell in the human body is 1 x 10-5 meters. The diameter of a grain of sand is about 2 x 10-4 meters.

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The area of a square quilt is 289 square inches. There is a smaller square patch on the quilt with an area of 121 square inches.

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Perimeter of big square = 17 inches * 4 = 68 inches
perimeter of small square = 11 inches * 4 = 44 inches

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