Answer:
part A: 3yx
Part B: (x+y)+z
C: 3xy-6x
Step-by-step explanation:
Commutative property: change the orders in which numbers are multiplied
associative: when all the integers are in addition you can add parentheses wherever u like
distributive: multiply the number just outside the parentheses with the every numbers inside the parentheses
Hope this heps!
Answer:
Technically it is 5/12, but as a percentage it would be 41.6666%
The profit for 25 products sold and 150 products sold are 3159 and 19190.25 respectively.
<u><em>Explanation</em></u>
The profit of a company receives is given by the expression: ![0.15(855p - 315)](https://tex.z-dn.net/?f=0.15%28855p%20-%20315%29)
Simplifying this expression using distributive property, we will get .....
![0.15(855p - 315) \\ \\ = (0.15*855p)-(0.15*315)\\ \\ =128.25p-47.25](https://tex.z-dn.net/?f=0.15%28855p%20-%20315%29%20%5C%5C%20%5C%5C%20%3D%20%280.15%2A855p%29-%280.15%2A315%29%5C%5C%20%5C%5C%20%3D128.25p-47.25)
So, the simplified expression for profit will be: ![128.25p-47.25](https://tex.z-dn.net/?f=128.25p-47.25)
As
represents the number of products sold, so for finding the profit for 25 products sold and 150 products sold, <u>we need plug
and
separately into the above expression</u>.
For
, Profit ![=128.25(25)-47.25 = 3206.25-47.25= 3159](https://tex.z-dn.net/?f=%3D128.25%2825%29-47.25%20%3D%203206.25-47.25%3D%203159)
For
, Profit ![=128.25(150)-47.25 = 19237.50-47.25= 19190.25](https://tex.z-dn.net/?f=%3D128.25%28150%29-47.25%20%3D%2019237.50-47.25%3D%2019190.25)
Answer:
Step-by-step explanation:
A=2i+3j+4k
B=i-2j+3k
Sum of the vectors:
A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k
Direction of the sum of the vectors:
![\widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\](https://tex.z-dn.net/?f=%20%5Cwidehat%7BA%20%2B%20B%7D%20%3D%5Cfrac%7B%5Coverrightarrow%7BA%20%2B%20B%7D%7D%7BMagnitude%5C%3A%20of%20%5C%3A%5Coverrightarrow%7BA%20%2B%20B%7D%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Cwidehat%7BA%20%2B%20B%7D%20%3D%5Cfrac%7B3i%20%2B%20j%20%2B%207k%7D%7B%5Csqrt%20%7B59%7D%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Cwidehat%7BA%20%2B%20B%7D%20%3D%5Cfrac%7B3%7D%7B%5Csqrt%20%7B59%7D%7D%20i%20%2B%5Cfrac%7B1%7D%7B%5Csqrt%20%7B59%7D%7D%20j%2B%5Cfrac%7B7%7D%7B%5Csqrt%20%7B59%7D%7D%20k%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3EDirection%20%5C%3A%20of%20%5C%3A%20%5Coverrightarrow%7BA%20%2B%20B%7D%20%3D%20%5Cfrac%7B3%7D%7B%5Csqrt%20%7B59%7D%7D%20%2C%20%5C%3A%5Cfrac%7B1%7D%7B%5Csqrt%20%7B59%7D%7D%20%2C%20%5C%3A%5Cfrac%7B7%7D%7B%5Csqrt%20%7B59%7D%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E)