9. Evaluate the ceiling function for the given value. A. f(x) = ⌈x⌉; x = −7.4

B. g(x) = ceiling (x, 0.50);
x = 21.27

Given:

A. f(x) = ⌈x⌉; x = −7.4

B. g(x) = ceiling (x, 0.50);  x = 21.27

To find:

The values of ceiling function for the given value.

Solution:

A.

We have,

f(x) = ⌈x⌉; x = −7.4

Here, f(x) is a ceiling function, so we need to find the nearest next integer value because if m < x ≤ n, then ⌈x⌉ = n, where m and n are integers.

Now,

f(-7.4) = ⌈-7.4⌉

f(-7.4) = -7

Therefore, the value of f(x) is -7 at x=-7.4.

B.

g(x) = ceiling (x, 0.50);  x = 21.27

Here, g(x) is a ceiling function with 0.50, so we need to find the nearest next multiple of 0.50 because if m < x ≤ n, then ⌈x⌉ = n, where, m and n are multiples of 0.50.

Now,

g(21.27) = ceiling (21.27, 0.50)

g(21.27) = 21.50

Therefore, the value of g(x) is 21.50 at x=21.27.

3; 9 is 8 to -4

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is