On a coordinate plane, 3 triangles are shown. Triangle D E F has points (5, negative 2), (1, negative 2), (1, negative 4). Triangle D prime E prime F prime has points (2, 5), (2, 1), (4, 1). Triangle D double-prime E double-prime F double-prime has points (negative 3, 5), (negative 3, 1), (negative 1, 1). Which rule describes the composition of transformations that maps ΔDEF to ΔD''E''F''?

R0,90° ∘ T5,0(x, y)
T–5,0 ∘ R0,90°(x, y)
T5,0 ∘ R0,90°(x, y)
R0,90°(x, y) ∘ T–5,0

geometry: triangles

solvers

lessons

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer: do we write it

step-by-step explanation:

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)