A) 1
b) 5
c) -1/2
d) sqrt. 3

not multiple choice, those are all the problems i need answered

a) x² − √3 x + ½

b) 5x² − 5√3 x + ⁵/₂

c) -½ x² + ½√3 x − ¼

d) √3 x² − 3 x + ½√3

Step-by-step explanation:

Write the factored form of the quadratic:

(x − (√3 + 1)/2) (x − (√3 − 1)/2)

Distribute using FOIL (first, outer, inner, last):

x² − (√3 − 1)/2 x − (√3 + 1)/2 x + (√3 + 1)/2 (√3 − 1)/2

Combine like terms:

x² − ((√3 − 1)/2 + (√3 + 1)/2) x + (√3 + 1)(√3 − 1)/4

Simplify:

x² − ((√3 − 1 + √3 + 1)/2) x + (√3 + 1)(√3 − 1)/4

x² − √3 x + (√3 + 1)(√3 − 1)/4

x² − √3 x + (3 − √3 + √3 − 1)/4

x² − √3 x + ½

Now multiply by each new coefficient.

b) 5x² − 5√3 x + ⁵/₂

c) -½ x² + ½√3 x − ¼

d) √3 x² − 3 x + ½√3

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

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!