Pablo wishes to grow his baseball card collection to at least 3000 cards. he currently has 1200 and his favorite type of cards have 15 cards per package which inequality and solution represent the number of packages of cards that pablo wishes to buy , select all that apply

x ≥ 120

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

    15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

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

a triangular prism is a 3 dimensional shape composed of triangles and rectangles. it is made from two triangular bases and three rectangular sides.