∠lmn and ∠nmo are a linear pair of angles. if ∠lmn = 4x + 3 and ∠nmo = 10x – 5, then find the value of x. (1 point) x = 10 x = 12 x = 14 x = 13

The value of x is 13

The sum of linear pair sums up to 180 degrees. This shows that:

Given the following parameters:

Taking the sum and equating to 180 degrees

4x + 3 + 10x - 5  = 180

14x - 2 = 180

14x = 180 + 2

14x = 182

x = 182/14

x = 13

Hence the value of x is 13

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x = 13

Step-by-step explanation:

Given: ∠LMN and ∠NMO are a linear pair of angles.

We know that linear pair of angles are supplementary.

Then ∠LMN + ∠NMO=180°

If ∠LMN = and ∠NMO = ,

Hence, the value of x=13 .

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