Maria is ordering trophies for school. Company Christopher charges $3.50 for each trophy and a one-time engraving fee of $25. Company Asya charges $7.50 for each trophy and a one-time engraving fee of $17 Develop an equation where the two companies would be the same.

An equation where the two companies would be the same is given as:

25 + 3.50x = 17 + 7.50x

Step-by-step explanation:

Let the number of trophies ordered be represented by x

Maria is ordering trophies for school. Company Christopher charges $3.50 for each trophy and a one-time engraving fee of $25.

$25 + $3.50 × x

25 + 3.50x

Company Asya charges $7.50 for each trophy and a one-time engraving fee of $17

$17 + $7.50× x

17 + 7.50x

An equation where the two companies would be the same is given as:

Company Christopher = Company Asya

25 + 3.50x = 17 + 7.50x

Simplifying further:

Collect like terms

25 - 17 = 7.50x - 3.50x

8 = 4.00x

x = 8/4

x = 4

Hence, the two companies would be the same after 4 trophies.

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