If B is the midpoint of AC, AB = 8x + 5, and BC = 5x2 - 16, then find x and AC

Step-by-step explanation:

AB = 8x + 5

BC = 5x² - 16

5x² -  16 = 8x + 5

5x² - 8x - 21 = 0

Quadratic formula

x = [8 ± √(8² – 4·5(-21))] / [2·5]

 = [8 ± √484] / 10

 = [8 ± 22] /10

 = -1.4, 3

-1.4 is an extraneous solution.

x = 3

AB = 8x+5 = 29

AC = 58

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:

6 cm

step-by-step explanation: