The total cost of a jacket and a pair of pants was $66.12. If the price of the jacket was $3.26 less than the pair of pants, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.

The price of the jacket was $31.43

Step-by-step explanation:

Let the cost of a jacket = x

Let the cost of a pair of pants = y

Such that,

x + y = $66.12Equation 1.

From the conditional statement,

x = y - $3.26Equation 2.

Solve both equations simultaneously, using the substitution method

From Equation 2;

x = y - 3.26

Substitute y - 3.26 for x in Equation 1.

x + y = 66.12, now becomes,

y - 3.26 + y = 66.12

collect like terms

y + y = 66.12 + 3.26

2y = 69.36

y= 69.36/2 = $34.69.

Put y = $34.69 in Equation 2. to obtain x

x = 34.69 - 3.26

x = $31.43

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

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