A department store sold 51 51 shirts one day. All short-sleeved shirts cost $14.00 $ 14.00 each and all long-sleeved shirts cost $23.00 $ 23.00 each. Total receipts for the day were $921.00 $ 921.00 . How many of each kind of shirt were sold?

28 short-sleeved shirts were sold and 23 long-sleeved shirts were sold.

Step-by-step explanation:

We can solve this question by a system of equations.

I am going to say that:

x is the number of short-sleeved shirts sold.

y is the number of long-sleeved shirts sold.

A department store sold 51 shirts one day.

This means that

All short-sleeved shirts cost $14.00 each and all long-sleeved shirts cost $23.00 each. Total receipts for the day were $921.00.

This means that

How many of each kind of shirt were sold?

We have to solve the system of equations.

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28 short-sleeved shirts were sold and 23 long-sleeved shirts were sold.

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

y-3=-3/2(x+4)

ur very much welcome