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3 years ago

Write the equation of a line perpendicular to 3x + 4y = 9 that passes through (8, - 4)

1 answer:

5 0

keeping in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of 3x + 4y = 9, by simply putting it in slope-intercept form.

$\bf 3x+4y=9\implies 4y=-3x+9\implies y=-\cfrac{3x+9}{4}\implies y=\stackrel{slope}{-\cfrac{3}{4}}x+\cfrac{9}{4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{4}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{4}{3}}\implies \cfrac{4}{3}}$

so we're really looking for the equation of a line whose slope is 4/3 and runs through 8, -4.

$\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{4}{3} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{4}{3}(x-8) \implies y+4=\cfrac{4}{3}x-\cfrac{32}{3} \\\\\\ y=\cfrac{4}{3}x-\cfrac{32}{3}-4\implies y=\cfrac{4}{3}x-\cfrac{44}{3}$

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SCORPION-xisa [38]

Answer:

A. y - 7 < 2 x - 6

Step-by-step explanation:

When you put the given values into the inequalities, you get ...

A: -7 < -6 . . . . true

B: -6 < -7 . . . . false

C: 7 < -6 . . . . .false

D: 7 < 6 . . . . . false

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3 years ago

5 0 = - in = in quadrant II Given cos = Find sin 3

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Answer:

sinΘ = $\frac{2}{3}$

Step-by-step explanation:

using the identity

sin²x + cos²x = 1 ( subtract cos²x from both sides )

sin²x = 1 - cos²x ( take square root of both sides )

sinx = ± $\sqrt{1-cos^2x}$

given

cosΘ = - $\frac{\sqrt{5} }{3}$ , then

sinΘ = ± $\sqrt{1-(-\frac{\sqrt{5} }{3})^2 }$

= ± $\sqrt{1-\frac{5}{9} }$

= ± $\sqrt{\frac{4}{9} }$

= ± $\frac{2}{3}$

since Θ is in quadrant II where sinΘ > 0 , then

sinΘ = $\frac{2}{3}$

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2 years ago

Quadrilateral ABCD is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation

Vlad [161]

Try this suggested option (all the details are in the attachment), the correct orientation is marked with red and green colours.

P.S. The point C has coordinates: (3;1). If to traslate it 6 units right and 5 units down, then (3+6;1-5) ⇒ (9;-4). The same principle is for the others points A, B and D. Note, after translation point A is point E, B⇒F, C⇒G and D⇒H.

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Answer:

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3 years ago

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g100num [7]

No such thing as cot (61,4). I think you meant to say cot (61.4°). See the difference?

So, cot (61.4°) is approximately -0.139844.

Rounded to 3 decimal places we get -0.140.

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3 years ago