Jim and Dwight went to the paint store together. Jim bought 6 cans of paint and 1 paintbrush for $67. Dwight bought 4 cans of the same paint and 3 of the same type of paintbrushes. Dwight's total cost was $54. a. Write a linear equation to represent Jim's purchase and another to represent Dwight's purchase. Let x represent the cost of a can of paint and y represent the cost of a paint brush.

b. Solve the system of equations using substitution.

c. What was the cost for a can of paint? The cost of a paintbrush?

A can of paint cost $10.50 and a paintbrush costs $4

Step-by-step explanation:

Using x as the cost of a can of paint and y as the cost of a paint brush, we can write the following system of equations:

6x+y=67

4x+3y=54

We can isolate y in the first equation which gives us:

y=-6x+67

Then we can solve using substitution (substitute -6x+67 for y):

4x+3(-6x+67)=54

4x-18x+201=54

Combine like terms

-14x+201=54

Subtract 201 from both sides

-14x=-147

Divide both sides by -14

x=10.5

Then plug 10.5 back in for x:

y=-6(10.5)+67

y=-63+67

y=4

A can of paint cost $10.50 and a paintbrush costs $4

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