Answer:
Since there are 4 green bars for every 3 red bars and we are trying to find the number of red bars if there are 200 green bars, we can create the ratio:
4
x
:
3
y
Where x is equal to the number of green bars and y
is the number of red bars.
We know the number of green bars is equal to 200, so we can divide it by 4, giving us:
200
/4=50
Then we can solve for y
, the number of red bars.
// Multiple y by 50
3
⋅
50
=
150
So for every 4 green bars, there are 3 red bars.
For every 200 green bars, there are 150 red bars
Step-by-step explanation:
5). Radius = 6 km. Circumference = 12π km. Area = 36π km²
6). Diameter = 8 mm. Circumference = 8π mm. Area = 16π mm²
Answer: -8
Step-by-step explanation:
<span>Length = 1200, width = 600
First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as:
W = (2400 - L)/2
And area is:
A = LW
Substitute the equation for width, giving:
A = LW
A = L(2400 - L)/2
And expand:
A = (2400L - L^2)/2
A = 1200L - (1/2)L^2
Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
A = 1200L - (1/2)L^2
A = 1200(1200+e) - (1/2)(1200+e)^2
A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
A = 720000 - (1/2)e^2
And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.</span>
Answer:
(x, y) --> (x + 4, y - 3)
Step-by-step explanation:
The x value concerns left and right, while the y value concerns up and down. Adding to x makes it move right, and adding to y makes it move up.
