This question has two answers and i do not know how to solve this kind of question.

Let's look at what we know.

We know she traveled 24 miles in all (12 running 12 biking), and we also know she spent 2.25 hours to finish the race. And we also know she rides 8 mph than she runs.

x= biking y=riding

x+y=2.25

12/x - 12/y = 8

Solve top equation for y and plug in

y=2.25-x

12/x - 12/(2.25-x) = 8

Get common denominators.

[12(2.25 - x)]/[x(2.25-x)] - [12(x)]/[x(2.25-x)]= [8(x)(2.25-x)]/[x(2.25-x)]

Let's simplify and only work with the top part.

27-24x=18-8x^2

Let's get everything to one side.

8x^2 -24x +9

x equals -x plus or minus the square root b squared minus 4 a c all over 2 a

24 plus or minus \sqrt{288} divided by 16

if you subtract you get a negative number so add 24 to the \sqrt{288} to get roughly 40. Then divide by 16 to get 2.56 mi/hr for running. Add 8 to get mph for biking.

Source of information: Michael J. from www.wyzant.com

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:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be