Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) - 11?

the graph of y = f(x) will shift up 11 units.

the graph of y = f(x) will shift right 11 units.

the graph of y = f(x) will shift left 11 units.

the graph of y = f(x) will shift down 11 units.

The graph of y = f(x) will shift down 11 units.

Step-by-step explanation:

The parent function is y = f(x)

The transformation rule is:

Here the equation of the translated function is y = f(x) - 11. It means that

a = 11

And from the above rule, the function f(x) is translated 11 units down.

Last option is correct.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11