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Natasha_Volkova [10]

3 years ago

11

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. perpendicu

lar to 8y = x − 4 and passes through the point (−2, 1)

1 answer:

Tanya [424]3 years ago

3 0

Answer:

point-slope form;

(y - 1) = -8(x+2)

slope-intercept form;

y = -8x - 15

Step-by-step explanation:

The first step is to determine the slope of the given line;

8y = x − 4

y = 1/8(x) - 1/2..... After dividing both sides by 8

The slope of the line is thus 1/8, the coefficient of x when the equation is written in slope-intercept form.

The required line is perpendicular to this given line which implies that the product of the slopes will be equal to -1. Let the slope of the required line be m;

m * 1/8 = -1

m = -8

The slope of the required line is thus -8. Using the given point, (−2, 1), the equation of this line in point-slope form becomes;

(y - 1) = -8(x - -2)

(y - 1) = -8(x+2)

We make y the subject of the formula;

y = -8x - 16 + 1

y = -8x - 15

This is the slope-intercept form of the equation of the line.

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Put y + 3 = -3(x + 2) in slope-intercept form.

alexgriva [62]

Answer:

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3 years ago

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Find the angle between the given vectors. Round your answer, in degrees, to two decimal places. u=⟨2,−6⟩u=⟨2,−6⟩, v=⟨4,−7⟩

NISA [10]

Answer:

$\theta = 108.29$

Step-by-step explanation:

Given

$u =$

$v =$

Required:

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The angle $\theta$ is calculated as thus:

$cos\theta = \frac{u.v}{|u|.|v|}$

For a vector

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$A = a * b$

$cos\theta = \frac{u.v}{|u|.|v|}$ becomes

$cos\theta = \frac{.}{|u|.|v|}$

$cos\theta = \frac{2*6+4*-7}{|u|.|v|}$

$cos\theta = \frac{12-28}{|u|.|v|}$

$cos\theta = \frac{-16}{|u|.|v|}$

For a vector

$A =$

$|A| = \sqrt{a^2 + b^2}$

So;

$|u| = \sqrt{2^2 + 6^2}$

$|u| = \sqrt{4 + 36}$

$|u| = \sqrt{40}$

$|v| = \sqrt{4^2+(-7)^2}$

$|v| = \sqrt{16+49}$

$|v| = \sqrt{65}$

So:

$cos\theta = \frac{-16}{|u|.|v|}$

$cos\theta = \frac{-16}{\sqrt{40}*\sqrt{65}}$

$cos\theta = \frac{-16}{\sqrt{2600}}$

$cos\theta = \frac{-16}{\sqrt{100*26}}$

$cos\theta = \frac{-16}{10\sqrt{26}}$

$cos\theta = \frac{-8}{5\sqrt{26}}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{-8}{5\sqrt{26}})$

$\theta = cos^{-1}(\frac{-8}{5 * 5.0990})$

$\theta = cos^{-1}(\frac{-8}{25.495})$

$\theta = cos^{-1}(-0.31378701706)$

$\theta = 108.288386087$

<em></em> $\theta = 108.29$ <em> (approximated)</em>

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2 years ago

If the sum of twice a number and 3 is 15. what is the value of 8x?

Aloiza [94]

Answer:

48

Step-by-step explanation:

2x + 3 = 15

2x = 15-3

2x = 12

x = 12 ÷ 2

x = 6

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Answer:

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Hi! how do i do this?

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Answer:

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2 years ago