Is x^2 + 20x - 100 a perfect square trinomial? explain why or why not.

No.

This is almost a perfect square trinomial, but it is not.

We can verify this by looking at the first two terms.

With only x^2 + 20x, we could complete the square to make this a perfect square trinomial by performing the following steps:

Divide the middle term by 2.

20 / 2 = 10

Square the quotient.

10^2 = 100.

Add 100 to both sides.

x^2 + 20x + 100 = 100

As the provided trinomial is x^2 + 20x - 100, it is not a perfect square trinomial.

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