Nick has a square sheet of paper 15 centimeters on a side. he folds the paper along the diagonal and makes a 45degree- 45 degree - 90degree triangle. find the length of the hypotenuse of this triangle

15√2

Step-by-step explanation:

They tell us the triangle was made from a 15cm sided square sheet. These sides will be our A and B in the pythagorean theorem:

C² = A² + B², C is the hypotenuse. Solving:

C² = 15cm² + 15cm² = √(15cm)²+(15cm)²

C = 15√2

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

for future students the answer is b

hope i

-lavira: )