Provide an appropriate response.Do all systems of linear inequalities have solutions? Why or why not?
What will be an ideal response?
No, all systems of linear inequalities do not have solutions. For example, consider the following system of linear inequalities:
x + y > 5,
x + y < 3
Since it is not possible for the sum of x and y to be both greater than 5 and less than 3, the system has no solution. Graphically, this would mean that the shaded area representing the first inequality would not overlap with the shaded area representing the second inequality.
You might also like to view...
Use the formula f'(x) = 
to find the derivative of the function.g(x) = 3x + 
A. 3 + 
B. 3 - 
C. 
D. 3 + 
Solve the problem.Suppose that 
= 1. Find 
and 
.
A. 3; 1 B. 1; -1 C. 0; -1 D. 0; 1
Solve the problem.A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 7 days if it starts out at 16 grams?
A. 8 g
B. 4 g
C. 
g
D. 
g
Solve the problem.If an object is thrown straight upward from the ground with an initial speed of 112 feet per second, then its height, h, in feet after t seconds is given by the equation h(t) = -16t2 + 112t. Find the instantaneous speed of the object at t = 6.
A. 112 ft/sec B. 16 ft/sec C. -80 ft/sec D. -464 ft/sec