This function f(x) has a domain of x = {-a, -b, a, b}.
in order, the x values are -a, -b, b, a.
in order, the f(x) values are 3c + 1, 2d - 5, 4d + 3, 6 - 2c.
which values of c and d make this an even function?
a. c = -7 and d = 1/3
b. c = 5 and d = 1/3
c. c = -5 and d = -4
d. c = 1 and d = -4
e. c = -7 and d = -4

d. c = 1 and d = -4

Step-by-step explanation:

If a function is even, then f(-x) = f(x).  Graphically, this means it's symmetrical about the y-axis.

f(-a) = f(a)

3c + 1 = 6 − 2c

5c = 5

c = 1

f(-b) = f(b)

2d − 5 = 4d + 3

-2d = 8

d = -4

Therefore, c = 1 and d = -4.

geometry: triangles

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answers archive

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+

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