All categories

3 years ago

Determine if the given lines are parallel, perpendicular, or neither.

Mathematics

1 answer:

Leni [432]3 years ago

4 0

Answer:

The lines are parallel.

Step-by-step explanation:

Given the lines

$-2x-3y=9$

$4x+6y=24$

Writing the equations in the slope-intercept form

$y=mx+b$

where m is the slope and b is the y-intercept

$-2x-3y=9$

$y=-\frac{2}{3}x-3$

Thus, the slope = m₁ = -2/3

also

$4x+6y=24$

$y=-\frac{2}{3}x+4$

Thus, the slope = m₂ = -2/3

We know that parallel lines have equal slopes

m₁ = m₂

Thus, the lines are parallel.

You might be interested in

If sec theta = - √30 / 3, find cos theta.<br> if sin(-theta) = -0.97, find cos (π/2 - theta).

Cloud [144]

Step-by-step explanation:

$\cos \theta = \frac{1}{ \sec\theta } = - \frac{3}{ \sqrt{30} } = - \frac{3 \sqrt{30} }{30} = - \frac{ \sqrt{30} }{10}$

$\cos( \frac{\pi}{2} - \theta )= \cos \frac{\pi}{2} \cos \theta + \sin \frac{\pi}{2} \sin \theta$

Note that

$\sin( - \theta) = - \sin \theta$

$\cos \frac{\pi}{2} = 0 \: \: \: \: \: \sin \frac{\pi}{2} = 1$

Therefore,

$\cos( \frac{\pi}{2} - \theta ) = 0.97$

5 0

3 years ago

Please help me out with this

neonofarm [45]

Answer:

I believe the answer is 12.57

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The art teacher has 30 boxes of crayons with 16 cans in each box she gives the students 10 of the boxes to use explain how to fi

Mamont248 [21]

I'm going to assume you meant crayon instead of can:

First step is to find how many boxes she/he has left.

30 - 10 = 20

So the teacher has 20 boxes left;

Now, knowing that each box has 16 crayons, then we simply multiply the 20 by 16 to find the total number of crayons left over:

20 x 16 = 320

So the art teacher has 320 crayons left over.

Hope this helps!

3 0

3 years ago

PLEASE HELP WITH THIS ONE QUESTION

AveGali [126]

Answer:

step 1: move the -4 to the right: x^2 -2x = 4

step 2: add 1 to each side: x^2 -2x + 1 = 4 + 1

step 3: factor the left side and simplify the right side: (x-1)^2 = 5

step 4: take the square root of each side: x - 1 = sqr root of 5

step 5: move the 1 to the other side: $x=\sqrt{5} + 1$ and $x = \sqrt{5} -1$