What is the value of x? identify the missing justifications. mpqr= x+11, msqr=x+7, and mpqs=100 mpqr+sqr=mpqs a. x + 11 + x + 7 = 100 b. substitution property 2x + 18 = 100 c. simplify 2x = 82 d. x = 41 e. division property of equality a. angle addition postulate; subtraction property of equality b. protractor postulate; addition property of equality c. angle addition postulate; addition property of equality d. protractor postulate; subtraction property of equality

The correct answer is:

A.Angle Addition Postulate; Subtraction Property of Equality

Explanation:

The angle addition postulate states that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two original angle measures.  This gives us m∠PQR+m∠SQR = m∠PQS.

The next missing justification is for the step that takes 2x+18=100 to 2x=82.  In order to get here, we subtract 18 from each side; the property that allows this is the subtraction property of equality.

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

equal to

step-by-step explanation: