Find the x-intercepts of the parabola with
vertex (6,-5) and y-intercept (0,175).
write your answer in this form: (x1,,42).
if necessary, round to the nearest hundredth.
enter the correct answer.

The x-intercepts are (5,0) and (7,0)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(6,-5)

substitute

Find the coefficient a

with the y-intercept (0,175) substitute the value of x and the value of y in the equation

For x=0, y=175

substitute

Find the x-intercepts

Remember that the x-intercepts are the values of x when the value of y is equal to zero

For y=0

simplify

square root both sides

therefore

The x-intercepts are (5,0) and (7,0)

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