Answer:
$9$
Step-by-step explanation:
Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.
To find: number that Thea originally entered
Solution:
The final number is $243$.
As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,
the number before $243$ must be $324$.
As previously the number was squared, so the number before $324$ must be $18$.
As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,
the number before $18$ must be $81$
As previously the number was squared, so the number before $81$ must be $9$.
X = 2
18 / 3 = 2
2 * 6 = 6
6 + 6 + 6 = 18
Hope this helps.
First of all, let's consider the line, since it's simpler to graph: we draw the endpoints and connect them:
So, you just need to draw the points
As for the trigonometric function, we have to start from the parent function 
and derive the graph of its child function via transformations:
- When we multiply the whole function by 2, we stretch the graph vertically. So, the function has still period
, but now it ranges from -2 to 2 instead of from -1 to 1 (amplitude 2) - When we multiply the argument by 2, we compress the function horizontally. So, the new period becomes
, and the function makes two complete oscillations from 0 to
You can see the two functions in the image below. You can also see that the two graphs cross 4 times, meaning that the equation
has four solutions.
Solve equation [1] for the variable x [1] x=(3y+6)
Plug this in or variable x in equation [2]
[2] 2(-3y+6)-y= 10
[2] -7y=-2
// solve equation [2] for the variable y
[2] 7y= 2
[2] y=2/7
By now we know this much
X= -3y+6
Y=2/7
Use the y value to solve for x
X=-3(2/7)+6=36/7
(x,y)=(36,7), (2/7)
