A) A ratio system
B) The 4 lb peanuts and the 1 lb mixture because the 4lb added to the 1lb of mixture give the correct percentages.
Answer:
80 ft
Step-by-step explanation:
<em>hey there,</em>
<em />
< We know that the rope is 3 pieces long. To make this into an equation, let's just write x + y + z = 150.
Assuming "y" is our second piece, we can tell y = 2x, because it is two times the size of the first piece, which is "x". We also know "z" (our third piece): z = 30.
We can try inputting all the things we know now. x + (2x) + 30 = 150. From here, we can find that x = 40. Since y is our second piece, y = 2x, so 2 x (40) = 80. The second piece would be 80 feet long. >
<u>Hope this helped! Feel free to ask anything else.</u>
Let
be the dimensions of the rectangle. We know the equations for both area and perimeter:
![A=xy=36](https://tex.z-dn.net/?f=A%3Dxy%3D36)
![P=2(x+y)=36 \iff x+y=18](https://tex.z-dn.net/?f=P%3D2%28x%2By%29%3D36%20%5Ciff%20x%2By%3D18)
So, we have the following system:
![\begin{cases}xy=36\\x+y=18\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dxy%3D36%5C%5Cx%2By%3D18%5Cend%7Bcases%7D)
From the second equation, we can deduce
![y=18-x](https://tex.z-dn.net/?f=y%3D18-x)
Plug this in the first equation to get
![xy=x(18-x)=-x^2+18=36](https://tex.z-dn.net/?f=xy%3Dx%2818-x%29%3D-x%5E2%2B18%3D36)
Refactor as
![x^2-18x+36=0](https://tex.z-dn.net/?f=x%5E2-18x%2B36%3D0)
And solve with the usual quadratic formula to get
![x=9\pm3\sqrt{5}](https://tex.z-dn.net/?f=x%3D9%5Cpm3%5Csqrt%7B5%7D)
Both solutions are feasible, because they're both positive.
If we chose the positive solution, we have
![x=9+3\sqrt{5} \implies y=18-x=18-9-3\sqrt{5}=9-3\sqrt{5}](https://tex.z-dn.net/?f=x%3D9%2B3%5Csqrt%7B5%7D%20%5Cimplies%20y%3D18-x%3D18-9-3%5Csqrt%7B5%7D%3D9-3%5Csqrt%7B5%7D)
If we choose the negative solution, we have
![x=9-3\sqrt{5} \implies y=18-x=18-9+3\sqrt{5}=9+3\sqrt{5}](https://tex.z-dn.net/?f=x%3D9-3%5Csqrt%7B5%7D%20%5Cimplies%20y%3D18-x%3D18-9%2B3%5Csqrt%7B5%7D%3D9%2B3%5Csqrt%7B5%7D)
So, we're just swapping the role of
and
. The two dimensions of the rectangle are
and ![9-3\sqrt{5}](https://tex.z-dn.net/?f=9-3%5Csqrt%7B5%7D)
Answer:
A) 2/15
Step-by-step explanation:
So just divide it normally, do keep change flip
2/3*1/5
2/3 keep
divison change
Denomeinator, flip it, 5 to 1/5
now multiply
2/15
Answer:
Step-by-step explanation:
When one variable depends on another variable according to a rule it is known as function:
For example if you want an output of 2 and the input value is 4. Then you will subtract 4 from x
We have to find x f(x).
x f(x) =?
f(x) = x-4
Now input value is: x= 3
x f(x)
3 (x-4)
3 (3-4)
3 -1
Now x= 4
x f(x)
4 (x-4)
4 (4-4)
4 0
Now x=5
x f(x)
5 (x-4)
5 (5-4)
5 1
Now x=6
x f(x)
6 (x-4)
6 (6-4)
6 2 ....