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2 years ago

What is the distance from the origin to the point P(3,2)

Mathematics

2 answers:

qaws [65]2 years ago

8 0

Distance = sqaure_root(3^2 + 2^2)
= square_root(13)
= 3.61

Alenkasestr [34]2 years ago

3 0

Uhmmmm not sure hope you get help tho

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How do you simplify <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%20%2B%5Csqrt%7B6%7D%20%7D%7B%5Csqrt%7B8%7D%20%2B%

blondinia [14]

The trick is to exploit the difference of squares formula,

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

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

$(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2$

Whatever you do to the denominator, you have to do to the numerator too. So

$\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2$

Expand the numerator:

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)$

$(\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}$

So we have

$\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2$

But √12 = √(3•4) = 2√3, so

$\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}$

7 0

2 years ago

Estimate the product of 67 an 73 round each number to the neares tenes

vampirchik [111]

Answer:

4900

Step-by-step explanation:

73*67

70*70

7*7(10^2)

49(100)

4900

6 0

2 years ago

Read 2 more answers

Write in slope-intercept form the equation of the line passing through the given point and perpendicular to the given line.

Ksivusya [100]

Answer:

y = x + 1

Step-by-step explanation:

First you find the slope of the first line using the rise over run method. Here you can see that the line goes up 1 and to the right one in order to reach the next point making the slope 1x or just x. Then you need to make it so that the line intercepts the point by changing the y intercept to 1 making the equation y = x + 1.

I hope this helped!!

4 0

2 years ago

Please help me with number 9

Mrrafil [7]

The answer is 8 pints

8 0

2 years ago

A man goes into business for himself selling dog houses. The materials for the dog houses cost him $45 per house. He sells them

Aleks [24]

Answer:

$600

Step-by-step explanation:

subtract 45 from 75, you get 30. multiply 30 by 20, and there is your answer.

7 0

2 years ago