Below are two different functions, f(x) and g(x). what can be determined about their slopes? f(x) = 2x + 3 the function g(x) going through 0, −2 and 1, 3

we are given two functions  f(x) and g(x)

now, we can find slopes

slope of f(x):

we are given

now, we can compare it with

where m is slope

b is y-intercept

we can compare

and we get

so, slope is 2

slope of g(x):

we are given two points as

(0,-2) and (1,3)

x1=0 , y1=-2 , x2=1 , y2=3

now, we can use slope formula

now, we can plug values

so, we get

so, slope is 5..........Answer

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