Emily is solving the equation 2(x+9)=4(x+7)+2

x=-6

Step-by-step explanation:

2(x+9)=4(x+7)+2

Distribute

2x+18 = 4x+28+2

Combine like terms

2x+18 = 4x+30

Subtract 2x from each side

2x-2x+18 = 4x-2x+30

18 = 2x+30

Subtract 30 from each side

18-30 =2x+30-30

-12 = 2x

Divide each side by 2

-12/2 =2x/2

-6 =x

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a