Hurry hurry! amber is solving the inequality |x - 6| -12< 13 by graphing. which equations should amber graph?

y1 = Ix+6I, y2 = 25

Answer with explanation:

The given inequality which is a combination of Modulus, variable x and integers, is

→ |x-6|-12 < 13

|x|=x,if x≥0

   and , -x if x<0.

|x-6|=x-6,when x-6≥0→x≥6

and, -(x-6),when x-6<0→x<6

→|x-6|-12<13

when , x≥6,the above inequality becomes

→x-6-12<13

→x-18<13

→x<18+13

→x<31

OR

when ,x<6,the inequality transforms to

→-(x-6)-12<13

→-x+6-12<13

→ -x-6<13

→ -x<13+6

→ -x<19

→ x>-19

The equations that Amber should graph

1. X < 31

2. x > -19

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.