<span>Average mass of a kernel of popcorn = 0.125 g
</span><span>1 pound = 16 ounces, and 1 ounce = 28.3 g
</span><span>how many kernels of popcorn are there in 0.500 pounds of popcorn = ?
0.500 pound = 16 x 0.500 ounces = 8 ounces
8 ounces = 8 x 28.3g = 226.4 g
Now divide this quantity by average mass;
226.4 / 0.125
= 811.2 kernels of popcorn</span>
Answer:
![y = \frac{1}{2}x - 4](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%204)
Step-by-step explanation:
Given
![y = \frac{1}{2}x](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx)
Required
Shift
down and
right
![y = \frac{1}{2}x](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx)
<u>Shift 3 units down</u>
The rule is: (x,y)=> (x,y-a)
Where a is the number of units shifted down
In this case: ![a = 3](https://tex.z-dn.net/?f=a%20%3D%203)
So, we have:
== > ![y = \frac{1}{2}x - 3](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%203)
<u>Shift 2 units right</u>
The rule is: (x,y)=>(x-b,y)
Where b is the number of units shifted right
In this case: ![b = 2](https://tex.z-dn.net/?f=b%20%3D%202)
So, we have:
==> ![y = \frac{1}{2}(x - 2) - 3](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x%20-%202%29%20-%203)
Open bracket:
![y = \frac{1}{2}x - 1 - 3](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%201%20-%203)
![y = \frac{1}{2}x - 4](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%204)
Hence, the new equation after the transformation is:
![y = \frac{1}{2}x - 4](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%204)
If Manuel's final answer does not total to 60, he must have done an error.
Prime factorization of 60;
60=6*10
--------------------------
6=2*3
10=2*5