Write an equation of the line that passeg through (8, 1) and is perpendicular to the line 2y + 4x = 12

y=1/2x-3

Step-by-step explanation:

First, let's put the line into slope intercept form

2y+4x=12

subtract 4x from both sides

2y=-4x+12

divide by 2

y=-2x+6

the slopes of perpendicular lines are negative and reciprocal. If you multiply the slopes of the lines together, the result is -1. Therefore, to find the slope of the perpendicular line, use this formula:

-2m=-1

divide by -2

m=1/2

so the slope of the perpendicular line is 1/2

here is the new line so far:

y=1/2x+b (b is a place holder)

now, since the line passes through the point (8,1), it means that (8,1) is a solution of the line. So we can substitute it into the equation

1=1/2(8)+b

1=4+b

subtract 4 from both sides

-3=b

so the line is y=1/2x-3

Hope this helps!

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.