What do probability and odds tell you about life's risks?

what is an equation of the line that passes through the point (-1,4) and is perpendicular to the line x-6y=12

Alecsey [184]

Answer:

6x + y = 3

Step-by-step explanation:

The product of two lines that are perpendicular to each other is -1

If line A has a slope of m1

and line B has a slope of m2 and they are perpendicular to each other,

then the product of the two lines is

m1 X m2 = -1

We are given two lines that are perpendicular to each other in the question.

The first line has the equation

x - 6y =12

We can write the slope form of the equation y = mx + c

m = slope

x - 6y = 12

Make y subject of formula

6y = x - 12

y = x/6 - 12/6

y = x/6 - 2

y =(1/6)x - 2

Comparing y=mx+c and y=(1/6)x-2,

m corresponds to 1/6

Therefore, we can say that the slope, m of the line x-6y=12

is 1/6

Recall, for two lines that are perpendicular to each other,

m1 X m2 = -1

m1 = 1/6

1/6 X m2 = -1

m2/6 = -1

Cross multiply

m2 = 6 X -1

m2 = -6

Step 3

To find the equation of the second line with slope, m2 = -6 and that passes through the point (-1,4)

Points are represented by coordinates (x, y)

the slope of a line is given by

m = (y - y1)/(x-x1)

Given in the question, the point (-1,4) corresponds to (x1, y1).

As calculated earlier, the slope of the second line is -6

-6 = (y - 4)/[x - (-1)]

-6 = (y - 4)/(x + 1)

Cross multiply

y - 4 = -6(x + 1)

y - 4 = -6x - 1

y = -6x - 1 + 4

y = -6x + 3

this equation is the slope form equation of the line

6x + y = 3 is the general form of the equation

4 0

4 years ago

What is the length of an arc cut off by an angle of 1.5 radians on a circle of radius 8 inches?

Natali [406]

To solve this problem, we should first recall that the circumference is the measure of the total arc enclosing the circle. The formula for circumference is:

Circumference = 2 π r

where r is the radius of the circle

Now since we are only looking for a fraction of the arc, not the total arc, therefore this simply means we are finding for a portion of the circumference. Now we use the formula:

Arc length = (θ / 360) * 2 π r

Where θ/360 represents how much of the fraction is the arc

Convert angle to degrees: θ = 1.5 rad (180° / π rad) = (270/π)°

Therefore the arc length is:

Arc length = (270/π / 360) * 2 π (8 inches)

Arc length = 12 inches

5 0

3 years ago

Six times the lesser of the two consecutive even integers is 4 times the greater even integer. What are the integers?

Paladinen [302]

Answer:

Integers are 4 and 6