Consider the system of inequalities
1. Plot all lines that are determined by equalities (see attached diagram)
2. Determine which bounded part of the plane you should select:
- means that you should take points with y-coordinates greater than or equal to 2 (top part of the coordinate plane that was formed by the red line);
- means that you should take points with x-coordinates less than or equal to 6 (left part of the coordinate plane that was formed by the blue line);
- for you can check where the origin is placed. Since , the origin belongs to the needed part and you have to take the right part of the coordinate plane that was formed by green line.
- for you can check where the origin is placed. Since , the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.
3. According to the previous explanations, the shaded region is as in A diagram.
Answer: correct choice is A.
3, 6, 12
I guessed and checked. So if 3 is the smallest number, I would, multiply it by 3, which is 9. 9 is 3 less than the largest number which would be 12. 12 + 3 is 15. To find the third number, subtract 21 and 15 which is 6
500 = 10x + 2 * 15 * 5 + 15x
500 = 25x + 150
500 - 150 = 25x
350 = 25x
x = 14
Triangular ends: 14 * 10 = 140
Base rectangle: 14 * 15 = 210
side rectangles: 5 * 15 * 2 = 150
140 + 210 + 150 =
To write this equation in simplest form, we simply need to combine all like terms. The like terms in this particular expression are the terms with an n-variable and the terms with no variable. So we can combine them to simplify our expression.
5n - 6 + n - 1
First step, we can reorder our terms so that like terms are near each other
5n + n - 6 - 1
Now we can combine easily
(5n + n) - (6 - 1)
6n - 5
And that is your simplified expression.
5n - 6 + n - 1 in simplest form is 6n - 5.
Hope that helped! =)