If pr = 4x – 2 and rs = 3x – 5, which expression represents ps?
x – 7
x – 3
7x – 7
7x + 3

PS = 7x-7

Step-by-step explanation:

Given the two expression

PR = 4x – 2 and RS = 3x – 5,

Adding the two vectors PR+RS = PS

PS = (4x-2)+(3x-5)

Expanding the bracket will give;

PS = 4x-2+3x-5

Collecting the like terms

PS = 4x+3x-2-5

PS =7x-7

The expression that represent PS is 7x-7

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

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.