Nicole has x dimes and y nickels. She has at least 15 coins worth a maximum of $1 combined. Solve this system of inequalities graphically and determine one possible
solution.

The solution of the inequalities is required.

One of the solutions is

Number of dimes is

Number of nickels is

Minimum number of coins is 15.

So,

Maximum total value of the coins is $1

So,

The equations are

Points of the first equation

and

Graph the points and draw a line through them.

Points of the second equation

and

Graph the points and draw a line through them.

The shaded regions can be determined by substituting the point in the equations.

One of the solutions is

This means there are 5 dimes and 10 nickels.

Hence, one of the solutions is .

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Step-by-step explanation:

we want to put it into terms of Y

the graph is in the attached image. Any point in the shaded overlap region where x is greater than or equal to 0 (assuming you cannot have negative coins) works, e.g. (2, 14)

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

answer: -1

step-by-step explanation: