What is the minimum number of degrees that an equilateral triangle can be rotated before it carries onto itself?

Minimum umber of degrees that an equilateral triangle can be rotated before it carries onto itself = 120°

Step-by-step explanation:

Refer the figure given below.

We need to find angle ADC to get the same equilateral triangle after rotation.

∠ADC = 180 - ( ∠DAC + ∠DCA) = 180 - ∠DAC - ∠DCA

∠DAC = ∠DCA = 0.5 x 60 = 30°

Substituting

 ∠ADC = 180 - 30- 30 = 180 - 60 = 120°

Minimum umber of degrees that an equilateral triangle can be rotated before it carries onto itself = 120°

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

hope this !

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