For which values of a the system has at least one solution: 1.x≤7 ,x≥a

Given:

The system of inequalities

To find:

The values of a for which the system has at least one solution.

Solution:

We have,

    ...(i)

It means all real values of x which are less than or equal to 0.

      ...(ii)

It means all real values of x which are greater than or equal to a.

Using (i) and (ii), we get

The value of x is lies in the interval [a,7].

It means, if the value of a is less than or equal to 7, then system has at least one solution.

But if a is more than 7, then the system of inequalities have to solution.

Therefore, the value of a must be less than or equal to 7.

answer: h

step-by-step explanation:

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.