Plz answer correctly..choose all that correctly describe the rotation that will carry the figure onto itself key: the pentagon is rotation of 72 degrees the decagon is rotation of 36 degrees the triangle has a rotation of 180 degrees the octagon has rotation of 32 degrees the nonagon has rotation of 40 degrees

These could all use the qualifier "regular."

the pentagon is rotation of 72 degrees

Yes, odd phrasing but the regular five sided shape has rotational symmetry when rotated by 360/5=72 degrees. CORRECT

the decagon is rotation of 36 degrees

360/10 = 36.  I'd say the regular decagon has 36 degree rotational symmetry. CORRECT

the triangle has a rotation of 180 degrees 

An arbitrary triangle may not have any symmetry at all beyond the identity.  An equilateral triangle has rotational symmetry by 360/3  = 120 degrees and its multiples; 180 isn't among them; NOT CORRECT.

the octagon has rotation of 32 degrees

The regular octagon (stop sign) has 360/8=45 degree rotational symmetry.  NOT CORRECT

the nonagon has rotation of 40 degrees

The regular octagon has 360/9=40 degree rotational symmetry.  CORRECT

I’m a smart person so that’s why i think it was 6

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.