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3 years ago

Which is the equation of a line that is perpendicular to 8x + 6y = –5?

Mathematics

1 answer:

IrinaVladis [17]3 years ago

4 0

The perpendicular line will have an equation of y=3/4x-3/4

To find this, we first have to solve our equation for slope intercept form.

8x + 6y = -5 ----> subtract 8x

6y = -8x + -5 ----> divide by 6

y = -4/3x - 5/6.

So we know the slope of this equation to be -4/3. Since perpendicular lines have opposite and reciprocal slopes, we know we can simply flip the fraction and make it a negative to get the new slope of 3/4. Since B is the only option with that slope, we know it to be the correct answer.

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A members only speaker series allows people to join for $17 and then pay $1 for every event attended. What is the maximum number

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Step-by-step explanation:

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2 years ago

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3 years ago

Read 2 more answers

The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr

san4es73 [151]

First get the tangent vectors by differentiating r1 and r2
$r_1 '(t) = (4,2t,3t^2) \\ \\ r_2'(t) = (cos (t), 5 cos(5t), 2)$
Evaluate at t=0
$r_1' = (4,0,0) \\ \\ r_2' = (1,5,2)$

Use identity for angle between 2 vectors:
$u*v = |u| |v| cos \theta$

Evaluate dot product and unit vectors:
$u*v = (4,0,0)*(1,5,2) = 4 \\ \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\ \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}$

Sub into identity and solve for theta:
$4 = 4 \sqrt{30} cos \theta \\ \\ cos\theta = \frac{1}{\sqrt{30}} \\ \\ \theta = 79.48$

Answer:
Angle of intersection is about 79 degrees.

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3 years ago

Beth runs a catering business and needs 64 pints of water every day. She gets water in 2-gallon jugs. So, she gets jugs of water

luda_lava [24]

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3 years ago

Solve the equation and show each step:<br> 25 - 4x = 15 - 3x + 10 - X

dimulka [17.4K]

Answer:

All real numbers.

Step-by-step explanation:

25-4x=15-3x+10-x

25-4x-(-3x)-(-x)=15+10

25-4x+3x+x=25

25-x+x=25

25=25

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3 years ago