Ill mark u brainliest if u answer pls answer fast& its worth 49 points:

What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 ?

Natali5045456 [20]

Answer:

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

$6x+y=-5$

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -2 , 7)

To Find:

Equation of Line that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?

Solution:

$x-6y=42$ ..................Given

which can be written as

$y=mx+c$

Where m is the slope of the line

∴ $y=\dfrac{x}{6}-7$

On Comparing we get

$Slope = m = \dfrac{1}{6}$

The Required line is Perpendicular to the above line.

So,

Product of slopes = - 1

$m\times m_{1}=-1\\Substituting\ m\\ \dfrac{1}{6} m_{1}=-1\\\\m_{1}=-6$

Slope of the required line is -6

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,

i.e equation in point - slope form

$(y-y_{1})=m(x-x_{1})$

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get

$(y-7)=-6(x--2)=-6(x+2)=-6x-12\\\\\therefore 6x+y=-5.......is\ the required\ equation\ of\ the\ line$

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

$6x+y=-5$

3 0

3 years ago

In experiments where participants were allowed to sleep for an unlimited amount of time, participants tended to sleep 12 or more

Butoxors [25]

Answer:

Sleep debt

Step-by-step explanation:

Also called sleep deficit, sleep debt can be likened to a deficit in the bank such as a loan that must be repaid. The deficit accumulates and will have to balanced or there would be mental or psychological effect on the affected person. Research by The national sleep foundation requires Americans to sleep at least 7.1 hours per day.

There two types of sleep deprivation or sleep deficit: partial sleep deprivation and total sleep deprivation. In Partial sleep deprivation, the person may not get enough sleep per day example not up to 7.1 hours per day. Total sleep deprivation means that the affected person does not sleep for up 24 hours ie a full day.

7 0

2 years ago

Please use the graphing method to solve the following system of the linear equation:

Vlad1618 [11]

Answer: I think c but im not too sure

Step-by-step explanation;

6 0

3 years ago

Read 2 more answers

The sea ice area around the North Pole fluctuates between about 6 million square kilometers in September to 14 million square ki

Aleksandr [31]

Answer:

there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Step-by-step explanation:

Given the data in the question;

Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,

t is the number of months since January.

Now, we use a cosine curve to model this scenario

Vertical shift will be;

D = ( 6 + 14 ) / 2 = 20 / 2

D = 10

Next is the Amplitude;

|A| = ( 6 - 14 ) / 2

|A| = 4

Now, the horizontal stretch factor will be;

B = 2π / 12

B = π/6

Hence;

S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1

Now we find when there will be less than 9 million square meters of sea ice;

S(t) = 9

so we have

9 = 4cos( π/6 × (t-2) ) + 10

9 - 10 = 4cos( π/6 × (t-2) )

-1 = 4cos( π/6 × (t-2) )

-1/4 = cos( π/6 × (t-2) )

so we have;

cos⁻¹( -1/4 ) = π/6 × (t₁-2) -------- let this be equation 2

2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2) -------- let this be equation 3

so we solve equation 2 and 3

we have'

t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )

t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )

t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )

t₁ - t₂ = 6/π × ( π - 104.4775 )

t₁ - t₂ = 5.035

therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

6 0

3 years ago

A ball is dropped out a wimdow that is 36 feet high. how long does it take for the ball to hit the ground

Readme [11.4K]

36 feet to metres = 10.97
first find the final velocity
vf^2 = vi^2 + 2ad
vf^2 = 0 + 2(9.81)(10.97)
vf^2 = 215.2314
vf = 14.6708

vf = vi + at
at = vf - vi
t = (vf - vi)/a
t = (14.6708)/9.81
t = 1.4955seconds

4 0

3 years ago