Given: Segment AC is perpendicular to segment BD Prove: ΔACB ~ ΔECD Reflect ΔECD over segment AC. This establishes that ∠ACB ≅ ∠E'C'D'. Then, . This establishes that . Therefore, ΔACB ~ ΔECD by the AA similarity postulate. translate point E' to point A; ∠E'D'C' ≅ ∠ABC
translate point D' to point A; ∠E'D'C' ≅ ∠BAC
translate point D' to point A; ∠D'E'C' ≅ ∠BAC
translate point E' to point A; ∠D'E'C' ≅ ∠BAC

the image of (6, 9) under a dilation is (4, 6). the scale factor is

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

step-by-step explanation:

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950