Arectangle is 5 times as long as it is wide. the perimeter is 70 cm. find the dimensions of the rectangle. round to the nearest tenth if necessary. a. 14 cm by 70 cm c. 11.7 cm by 29.2 cm b. 5.8 cm by 64.2 cm d. 5.8 cm by 29.2 cm

Let the width = X, then the length would be 5x ( 5 times as long as the width).

The perimeter is adding the 4 sides.

x + x + 5x + 5x = 70

Combine the like terms:

12x = 70

Divide both sides by 12:

x = 70/12

x = 5.83

The width = 5.83 cm.

The length = 5 x 5.83 = 29.15

Now round each length to the nearest tenth:

5.8 and 29.2 cm.

The answer is d.

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

after simplifying it i got: -36.25 as my answer. hope that !