Marissa bought x shirts that cost $19.99 each and y pairs of shorts that cost $14.99 each. The next day she went back to the store and bought 3 more shirts that cost $19.99 each and 4 more pairs of shorts that cost $14.99 each. Which expression represents the total amount Marissa spent? StartFraction x + 3 over 19.99 EndFraction + StartFraction y + 4 over 14.99 EndFraction
StartFraction 3 x over 19.99 EndFraction + StartFraction 4 y over 14.99 EndFraction
19.99 (x + 3) + 14.99 (y + 4)
(3 x) 19.99 + (4 y) 14.99

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

51-50

step-by-step explanation:

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh

what is the rest of the question? ?