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2 years ago

Given the points (-4,8)and(6,-12)

Mathematics

1 answer:

MissTica2 years ago

3 0

Answer:

$midpoint = ( \frac{ - 4 + 6}{2} , \: \frac{ - 12 + 8}{2} ) \\ = (1, \: - 2)$

$distance = \sqrt{ {( - 4 - 6)}^{2} + {( - 12 - 8)}^{2} } \\ = \sqrt{500} \\ = 22.4 \: units$

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Convert from rectangular to polar coordinates: note: choose rr and θθ such that rr is nonnegative and 0≤θ<2π0≤θ<2π (a)(9,0

DochEvi [55]

Answer:

Step-by-step explanation:

Convert rectangle (x , y) to polar coordinates ( r , θ)

$x=r \cos \theta, y= r \sin \theta$

$r=\sqrt{x^2+y^2} , \theta =tan^-^1 (\frac{y}{x} )$

a) converts (9, 0) to polar coordinates ( r , θ)

$r=\sqrt{x^2+y^2} \\\\=\sqrt{9^2+0} \\\\=9$

$\theta= \tan^-^1 (\frac{0}{9} )\\\\=0$

b) Convert $(18,\frac{18}{\sqrt{3} } )$ to polar coordinates ( r, θ)

$r = \sqrt{18^2+(\frac{18}{\sqrt{3} })^2 } \\\\=\sqrt{324+108} \\\\=\sqrt{432}$

$\frac{x}{y} \theta = \tan^-^1(\frac{\frac{18}{\sqrt{3} } }{18} )\\\\= \tan ^-^1(\frac{1}{\sqrt{3} } )\\\\= \frac{\pi}{6}$

c) converts (-5, 5) to polar coordinates ( r , θ)

$r =\sqrt{(-5)^2+(5)^2} \\\\=\sqrt{50} \\\\=5\sqrt{2}$

$\theta=\tan^-^1(\frac{5}{-5} )\\\\= \tan^-^1(-1)\\\\=\frac{3\pi}{4}$

d) converts (-1, √3) to polar coordinates ( r , θ)

$r=\sqrt{(-1)^2+(\sqrt{3})^2 } \\\\= \sqrt{4} \\\\=2$

$\theta=\tan^-^1(\frac{\sqrt{3} }{-1} )\\\=\tan^-^1(-\sqrt{3} )\\\\=\frac{2\pi}{3}$

$= \frac{2\pi}{\sqrt{3} }$

6 0

3 years ago

kkurt [141]

Parallel lines have equal slopes.

-x + y = 5

y = x + 5

Slope = 1

y + 5 = 1(x - 2)

y + 5 = x - 2

y = x - 2 - 5

y = x - 7

Answer: Choice A

7 0

3 years ago

Select all that apply.

Mila [183]

First we need to have same units before comparing them. That is, either both of them are in cm or both of them are in mm. So if we need to convert 12.5 cm to mm, we know that 1 cm =10 mm. So we have to find out how many mm are in 12.5 cm. And let 12.5 cm =x mm. So to find the value of x , we set a proportion and solve for x. That is

$\frac{1cm}{10mm}=\frac{12.5cm}{x mm}$

The units cancel out and we do cross multiplication. That is

$1*x =12.5*10$

x=125

So 12.5 cm =125 mm. Therefore the correct proportion is C.

3 0

2 years ago

The boys wrestling team scored a total of 36 points. Pins are worth 6 points. Major

shtirl [24]

Answer:

6p + 4d = 36

Step-by-step explanation:

If p = number of pins and d = number of major decisions, then the equation is 6p + 4d = 36.

Hope this helps!

5 0

3 years ago

Irrational numbers are imaginary. true or false

Vedmedyk [2.9K]

Imaginary numbers are not rational which may lead you to believe that they must be irrational. Though logical, you would still be incorrect because “irrational” also applies only to real numbers.

Step-by-step explanation:

3 0

2 years ago

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