Simplify:
5m²n³ +9mn
(8mn - 4m²n³ ÷ 4)​

mn(5mn² + 9) ;

2mn(1 - 1/2mn²)

Step-by-step explanation:

Given:

5m²n³ +9mn

(8mn - 4m²n³ ÷ 4)​

5m²n³ + 9mn

mn(5mn² + 9)

(8mn - 4m²n³ ÷ 4)​

8mn/ 4 - 4m²n³ / 4

2mn - m²n³

2mn(1 - 1/2mn²)

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.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204