If δopq is dilated from point q by a scale factor of 3, which of the following equations is true about segment r prime s prime?

segment r prime s prime = segment rs
segment r prime s prime = two segment rs
segment r prime s prime = segment rs
segment r prime s prime = three segment rs

look at image plzz. brainliest for first answer

translation: the image segment r's' is three times longer than the original pre-image segment rs

let's consider an example where r = (1,2) and s = (5,2). if you graphed these two points, you would find that rs is 4 units long. simply count the spaces between the two points. this works because both points have the same y cordinate. if they didnt, then you would have to use the distance formula.

now multiply each coordinate of points r and s by the value 3

r = (1,2) turns into r' = (3,6)

s = (5,2) turns into s' = (15, 6)

next, plot the points r' = (3,6) and s' = (15,6). you should find the distance from r' to s' is exactly 12 units. note how 12 is the result of tripling the length of rs (which was 4). this example support that r's' = 3*rs

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

a king of hearts and a 2 of spades