10 !

quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle r? you must show all work and calculations to receive credit.

Step-by-step explanation:

Quadrilateral OPQR is inscribed inside a circle as shown in the given diagram. It is a shape bounded by four different sides and four different angles.

In a quadrilateral, the sum of all the angles is equal yo 360 degrees.

This means that

angle O + angle P + angle Q + angle R = 360 degrees.

Also, the opposite angles of the quadrilateral are supplementary. This means that the sum of the opposite angles is 180 degrees. Therefore,

Angle O + angle Q = 180

3y + 8 + y = 180

4y = 180-8 = 172 - - - - - - - -1

Angle R + angle P = 180

2x + 2x + 4 = 180

4x + 4 = 180- - - - - - - -2

From equation 1

y = 172/4 = 43

angle R = 3y + 8

= 3×43 +8 =137 degrees

i have no clue at all sorry

step-by-step explanation:

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.