Find the values for k so that the intersection of x=2k and 3x+2y=12 lies in the first quadrant.

Values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.

Step-by-step explanation:

Given two lines:

and

To find:

Values of 'k' such that the intersection of given two lines lie in the first quadrant.

Solution:

In 1st quadrant, the values of and both are positive.

So, let us find out intersection of the two lines.

Intersection of the two lines can be found by solving the two equations for the values of and .

Given that to be in the first quadrant, the value of k must be positive.

Let us put in the equation to find the intersection point.

For y to be positive:

So, values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.

a 270° rotation about point p says on e d g e n u it y (had to space it out because it says it's a misspelling so i couldn't submit it

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.