Which is another way to check the sum of 52 + 23 + 10 + 78? a. 78 + 10 + 23 + 52 b. 78 – 52 – 10 – 23 c. 163 – 52 + 23 + 10 + 78 d. 78 – 52 + 10 + 23

A. 78 + 10 + 23 + 52

Step-by-step explanation:

We can solve the problem by using the commutative property: "in an addition, changing the order of the operands does not change the result.

The original addition is 52 + 23 + 10 + 78. We see that option A is exactly the same addition, only the order of the numbers has been changed:

78 + 10 + 23 + 52

Therefore, the two additions are equivalent.

good for u

step-by-step explanation:

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