Caroline is planting flowers in her garden. she plants her first 7 flowers in 4 minutes. after 12 minutes, she has planted 21 different flowers. if caroline keeps planting flowers at this rate, how long will it take her to plant all 70 flowers that she has?

a.
28 minutes
b.
40 minutes
c.
56 minutes
d.
70 minutes

i say 40 minutes

Step-by-step explanation: in  the first 4 minutes she planted 7 flowers, in the next 8 minutes she planted 21 flower. so what i did was divide 70 by 7... since the amount of flowers is going up by 7's. so 70 divided by 7 is 10... now every 4 minutes  you plant flowers so 10 by 4= 40 minutes

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

x=30

step-by-step explanation: