If the perimeter is fixed and you want to use it to enclose the greatest
possible area, then you form the perimeter that you have into a circle.
If it must be a rectangle, then the greatest possible area you can enclose
with the perimeter that you have is to form it into a square.
Since the perimeter that you have is 18 inches, form it into a square
with sides that are 4.5 inches long.
The area of the square is (4.5)² = 20.25 square inches.
There is no such thing as the 'least possible' area of the rectangle.
The longer and skinnier you make it, the less area it will have, even
if you keep the same perimeter. No matter how small you make the
area, it can always be made even smaller, by making the rectangle
even longer and skinnier. You can make the area as small as you
want it. You just can't make it zero.
Example:
Width = 0.0001 inch
Length = 8.9999 inches
Perimeter = 18 inches
Area = 0.00089999 square inch.
So, the difference between the greatest and least possible area
of the rectangle with the perimeter of 18 inches is
<em> (20.25) - (the smallest positive number you can think of)</em> square inches.
For a triangle, there is a proven inequality<span> that states that</span><span>, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side
21 + 37 >= 15
58 >= 15
21 + 15 >= 37
36 >= 37
37 + 15 >= 21
52 >= 21
We can see that the second inequality doesn't comply, thus there is not such triangle.</span>
Start by adding up the total sales in 2011 and 2012. You can make approximate estimates for the bars that are between lines. Since everything is in millions, you can ignore the 6 zeros behind every number to speed up your calculation:
1) In 2011, Asia sold 250, America sold 325, Europe sold ~210, Africa sold 150. The total in 2011 was 250+325+210+150 = 935.
2) In 2012, Asia sold ~130, America sold ~280, Europe sold ~230, and Africa sold ~140. The total in 2012 was 130+280+230+140=780.
Now find the percent decrease. Percentage decrease is basically what percent of your original number was subtracted from that original number to get the new number.
Percent decrease is calculated by (1) calculating the decrease from original number-new number, then (2) dividing that decrease by the original number, and then (3) multiplying your quotient by 100% to get a percentage:
1) Your original number is 935, from 2011, because that's the year you started out with. Your final number is 780, from 2012. The decrease is: 935-780 = 155.
2) Divide 155 by your original number. 155/935 ≈ 0.17
3) Finally multiply your quotient from step 2 by 100% to get your percent decrease: 0.17*100% = 17%.
The answer is A) 17.
H(x) = 4x² - 8x - 60
0 = 4x² - 8x - 60
0 = 4(x²) - 4(2x) - 4(15)
0 = 4(x² - 2x - 15)
4 4
0 = x² - 2x - 15
0 = x² - 5x + 3x - 15
0 = x(x) - x(5) + 3(x) - 3(5)
0 = x(x - 5) + 3(x - 5)
0 = (x + 3)(x - 5)
0 = x + 3 or 0 = x - 5
- 3 - 3 + 5 + 5
3 = x or 5 = x
