A ribbon with straight edges has an area of 24 square inches . Its width is x and its length is 2x+13. What is the width of the ribbon in inches. (Solve by completing the square)

Width is 1.5

Step-by-step explanation:

width:  x

length:  2x + 13

Area = Length * Width

24 = (2x + 13)x

24 = 2x² + 13x

2x² + 13x - 24 = 0

(x + 8)(2x - 3) = 0

x + 8 = 0

x = -8         width cannot be negative so discard this value  

2x - 3 = 0

2x = 3

x = 1.5

width:  x = 1.5

length:  2x + 13 = 2(1.5) + 13 = 16

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

you would have to sell 24 bracelets.

step-by-step explanation:

84/3.5 = 24