The equation of the line that passes through (3, −2) and is perpendicular to y = (3/4)x + 6 will be y = -(4/3)x + 2. Then the correct option is B.

<h3>What is the equation of a perpendicular line?</h3>

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. Or if the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

y = (3/4)x + 1/3

The slope of the line is 3/4. Then the slope of the perpendicular line will be

Slope = - 1 / (3/4)

Slope = - 4 / 3

Then the equation of the line will be

y = -(4/3)x + D

The line is passing through (3, -2), then the value of D will be

-2 = (-4/3) × 3 + D

-2 = - 4 + D

D = 2

The equation of the line that passes through (3, −2) and is perpendicular to y = (3/4)x + 6 will be y = -(4/3)x + 2. Then the correct option is B.

More about the equation of a perpendicular line link is given below.

brainly.com/question/14200719

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7 0

1 year ago

Read 2 more answers

Please help with number 7

DedPeter [7]

Answer:

Step-by-step explanation:

cos 2α=1-2 sin² α

$sin \alpha =\sqrt{\frac{1-cos2\alpha }{2} } \\put~ \alpha =\frac{\pi }{8} \\2\alpha =\frac{\pi }{4} \\cos 2\alpha =cos \frac{\pi }{4}=\frac{1}{\sqrt{2} } \\\\sin(\pi/8)=\sqrt{\frac{1-\frac{1}{\sqrt{2} } }{2}} =\sqrt{\frac{\sqrt{2}-1 }{2\sqrt{2} }$

6 sin 3 \theta+6 sin \theta

$6 sin 3 \alpha +6 sin\alpha =6(sin 3\alpha +sin \alpha )\\=6 *2sin \frac{3\alpha+\alpha }{2} cos \frac{3\alpha-\alpha }{2} \\=12 sin 2\alpha cos \alpha$

please change α to \theta

5 0

3 years ago