Mai bought 3 pairs of socks and 2 pairs of shoes. A pair of shoes costs one dollar less than 5 times the price of a pair of socks. She spent $56.50. How much does a pair of socks cost and how much does a pair of shoes cost? (use one varible)

Cost of a pair of socks = x = $4.5

Cost of a pair of shoes = y = $21.5

Step-by-step explanation:

Let us represent

Cost of a pair of socks = x

Cost of a pair of shoes = y

Mai bought 3 pairs of socks and 2 pairs of shoes.

She spent $56.50.

Hence:

3x + 2y = 56.50

A pair of shoes costs one dollar less than 5 times the price of a pair of socks.

y = 5x - 1

Hence, we substitute 5x - 1 for y

3x + 2y = 56.50

3x + 2(5x - 1) = 56.5

3x + 10x - 2 = 56.5

13x - 2 = 56.5

13x = 56.5 + 2

13x = 58.5

x = 58.5/13

x = $4.50

Solving for y

y = 5x - 1

y = 5(4.5) - 1

y = 22.5 − 1

y = $ 21.5

Cost of a pair of socks = x = $4.5

Cost of a pair of shoes = y = $21.5

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

21

step-by-step explanation: