Is RS perpendicular to DF? Select Yes or No for each statement. R (6, −2), S (−1, 8), D (−1, 11), and F (11 ,4) R (1, 3), S (4,7), D (3, 9), and F (15, 0) R (−5, −5), S (0, 2), D (8, 3), and F (1, 8)

I'll do the first one to get you started.  

Find the slope of the line between R (6,-2) and S (-1,8) to get

m = (y2-y1)/(x2-x1)

m = (8-(-2))/(-1-6)

m = (8+2)/(-1-6)

m = 10/(-7)

m = -10/7

The slope of line RS is -10/7

Next, we find the slope of line DF

m = (y2 - y1)/(x2 - x1)

m = (4-11)/(11-(-1))

m = (4-11)/(11+1)

m = -7/12

From here, we multiply the two slope values

(slope of RS)*(slope of DF) = (-10/7)*(-7/12)

(slope of RS)*(slope of DF) = (-10*(-7))/(7*12)

(slope of RS)*(slope of DF) = 10/12

(slope of RS)*(slope of DF) = 5/6

Because the result is not -1, this means we do not have perpendicular lines here. Any pair of perpendicular lines always has their slopes multiply to -1. This is assuming neither line is vertical.

I'll let you do the two other ones. Let me know what you get so I can check your work.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

6mm^3 or .6cm^3

      216

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  36     6

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6     6   6

factor trees are nice.