Twice one number added to another
number is 18. If the second number is equal
to 12 less than 4 times the first number, find
the two numbers.
First complete the equations below, where x stands for
the first number and y stands for the second number.
2x + y = 18; y = [?]x-[]

The Answer is: The first number is 5 and the second one is 8.

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Step-by-step explanation:

Let f = first number and s = second number

Twice the first number added to the second number is 18:

2f + s = 18

The second number is equal to 4 times the first number minus 12:

s = 4f - 12

Substitute:

2f + (4f - 12) = 18

6f - 12 = 18

6f = 18 + 12

6f = 30

f = 5, is the first number.

Solve for the 2nd number:

s = 4(5) - 12 = 20 - 12 = 8, is the second number.

Proof:

2f + s = 18

2(5) + 8 = 18

18 = 18

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step-by-step explanation:

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