<span>one way to solve this kind of problems is by doing a little bit of reversal
75 % * X = 54
75/100 * X = 54
(we move 75/100 to the right, since it's a fraction the top and bottom number will be reversed)
X = 54 * 100/75
X = 5400 / 75
X = 72 Hope I helped! :) Cheers!</span>
Answer :
a. p²+q²=r²
According to the Pythagorean theorem :
p²+q²=r² ,because this is a right triangle and r is the length of the hypotenuse.
Answer:
3.5 pounds for 14 people
Step-by-step explanation:
Given
1 pound = 4 people
Required
Determine the pounds for 14 people
Represent this with x; so, we have:
![1\ pound = 4\ people](https://tex.z-dn.net/?f=1%5C%20pound%20%3D%204%5C%20people)
![x = 14\ people](https://tex.z-dn.net/?f=x%20%3D%2014%5C%20people)
Cross Multiply
![x * 4 = 1 * 14](https://tex.z-dn.net/?f=x%20%2A%204%20%3D%201%20%2A%2014)
![4x = 14](https://tex.z-dn.net/?f=4x%20%3D%2014)
Solve for x
![x = 14/4](https://tex.z-dn.net/?f=x%20%3D%2014%2F4)
![x = 3.5](https://tex.z-dn.net/?f=x%20%3D%203.5)
<em>Hence, 3.5 pounds for 14 people</em>
Answer:
![A(x) = 24x - 2x^3](https://tex.z-dn.net/?f=A%28x%29%20%3D%2024x%20-%202x%5E3)
Step-by-step explanation:
first we need to visualize what the question is trying to represent
- A rectangle with one of its sides on the x-axis
- The corners of the opposite two sides of the rectangle intersect with a parabola
- the equation of the parabola is
![y = 12 - x^2](https://tex.z-dn.net/?f=y%20%3D%2012%20-%20x%5E2)
the equation of the parabola can also be written as
this shows that the parabola has a
shape and the turning point (peak) lies at the y-axis at y = 12. The parabola is symmetric along the y-axis!
- right corner of the lower side of the rectangle has the coordinates (x,0)
we can also say that the coordinates of the lower left side are (-x,0). This is because the parabola is symmetric along the y-axis.
Solution:
We have enough information to express the sides lengths of the rectangle:
1) Lower side, (L)
We'll name the lower side 'L' and since this is a rectangle, this side length is the same as the upper side.
The lower side coordinates are (-x,0) and (x,0). Hence the side length is the difference of the two coordinates.
![L = x-(-x)](https://tex.z-dn.net/?f=L%20%3D%20x-%28-x%29%20)
![L = 2x](https://tex.z-dn.net/?f=L%20%3D%202x%20)
2) The Left and Right side have the same height (H)
since the the lower side is on the x-axis (y=0), the only side moving is the upper one, i.e the coordinates of the upper corners are (0,y) where
. The side length of either the left or right sides is
![H = y](https://tex.z-dn.net/?f=H%20%3D%20y)
![H = 12 - x^2](https://tex.z-dn.net/?f=H%20%3D%2012%20-%20x%5E2)
The Area of the rectangle is:
![Area\,\,= L \times H](https://tex.z-dn.net/?f=Area%5C%2C%5C%2C%3D%20L%20%5Ctimes%20H%20)
![Area\,\,= 2x(12 - x^2)](https://tex.z-dn.net/?f=Area%5C%2C%5C%2C%3D%202x%2812%20-%20x%5E2%29%20)
![Area\,\,= 24x-2x^3](https://tex.z-dn.net/?f=Area%5C%2C%5C%2C%3D%2024x-2x%5E3%20)
Answer:
-50
Explanation:
At sea level would be 0 so anything above would be a positive number and anything below a negative number.