Suppose you had d dollars in your bank account. you spent $21 but have at least $53 left. how much money did you have initially? write and solve an inequality that represents this situation.

a. d + 21 ≥ 53; d ≥ 95

b. d – 21 ≥ 53; d ≥ 74

c. d + 21 ≤ 53; d ≤ 95

d. d – 21 > 53; d > 74

D. d – 21 > 53; d > 74

Step-by-step explanation:

x−21≥53

x−21+21≥53+21

x≥74

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

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step-by-step explanation: