Madison drew angle def in her triangle, angle d is represented as x degrees. the measure of angle e is half the measure of angle d. the measure of angle f is 2 degrees less than twice angle d. what is angle f?

The measure of angle ∠F is 102°.

Step-by-step explanation:

Given : Triangle DEF.

To find ∠F =?

Solution:

∠D = x

∠E = ∠D = 0.5x

∠F = 2∠D -2 = 2x-2°

Applying angle sum property of the triangle:

∠D + ∠E + ∠F = 180°

x = 52

∠F = 2x-2° = 2 × 52° - 2° = 102°

The measure of angle ∠F is 102°.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.