When miss. Johnson saw the sale she decided to get clothes for each child in her family. She bought each of her 6 children a pair of jeans and a T-shirt . She paid $14.35 in sales tax. How much was mrs. Johnson's total bill?

Mrs. Johnson's total bill was of $229.35.

Step-by-step explanation:

Assume that the cost of 1 pair of jeans is, $29.95 or 2 pairs of jeans is $55.00.

Also assume the cost of 1 T-short is, $9.95 or 3 T-shirts is $25.00.

As Mrs. Johnson bought the clothes after seeing the sale she bought the items at the sale amount.

That is, she bought 6 pair of jeans for,

And 6 shirts for,

The cost of items is,

Cost of Items = Price of Jeans + Price of T-shirts

        = 165.00 + 50.00

        = 215.00

The sales tax amount spent be Mrs. Johnson was $14.345.

The total bill paid by her is,

Total Cost = Cost of items + Sales Tax

Thus, Mrs. Johnson's total bill was of $229.35.

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

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.