Mckenzie and Cara both tried to find the missing side of the right triangle. A right triangle is shown. One leg is labeled 5 and the other is labeled 13. A right angles is labeled in between the legs.

Mckenzie's Work Cara's Work

a2 + b2 = c2 a2 + b2 = c2

52 + 132 = c2 52 + b2 = 132

25 + 169 = c2 25 + b2 = 169

194 = c2 b2 = 144

Square root 194 equals square root c squared. Square root b
squared equals
square root 144.

13.93 ≈ c b ≈ 12

Is either of them correct? Explain your reasoning.

Step-by-step explanation:

Makenzie is correct,  13.93 ≈c

the sides with determined lengths (see image) are A (13) and B (5). C however is not determined.

the correct equation would be to solve for c.

13² + 5² = c²

c ≈ 13.93

Clara solved for b and not c, which is incorrect.

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

step-by-step explanation: