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3 years ago

Factor the equation 45x - 81

Mathematics

1 answer:

alex41 [277]3 years ago

5 0

Answer:

Step-by-step explanation:

45x = 9*5*x

81 = 9*9

GCF = 9

Take 9 out using distributive property { a*b - c*b = b*(a-b)}

45x - 81 = 9*5x - 9*9

= 9*(5x - 9)

=9(5x-9)

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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

What is the height of an equilateral triangle with side lengths of 14?

olganol [36]

If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.
If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.

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3 years ago

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You and your family are planning a vacation of a lifetime around the world that will cost $25,000. You borrowed this amount from

labwork [276]

Answer:

$13,125

Step-by-step explanation:

8 0

2 years ago

A plane travels 600 miles in 3 hours. at this rate how far could the jet fly in 10 hours? math

IgorLugansk [536]

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3 years ago

Your job pays $8 an hour. Write a variable expression for your pay in dollars for working h hours.

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