Answer:
![x=5\ and\ y=-8](https://tex.z-dn.net/?f=x%3D5%5C%20and%5C%20y%3D-8)
The solution of the system can be given as (5,-8).
Step-by-step explanation:
Given system of equations:
![y=-x-3](https://tex.z-dn.net/?f=y%3D-x-3)
![5x+2y=9](https://tex.z-dn.net/?f=5x%2B2y%3D9)
To solve the given system of equations:
Solution:
We will use substitution to solve the given system.
We will substitute the
values in terms of
from the equation
into the other equation to solve for ![x](https://tex.z-dn.net/?f=x)
Substituting
into
.
We have:
![5x+2(-x-3)=9](https://tex.z-dn.net/?f=5x%2B2%28-x-3%29%3D9)
<em>Using distribution.</em>
![5x-2x-6=9](https://tex.z-dn.net/?f=5x-2x-6%3D9)
<em>Combining like terms.</em>
![3x-6=9](https://tex.z-dn.net/?f=3x-6%3D9)
Adding 6 both sides.
![3x-6+6=9+6](https://tex.z-dn.net/?f=3x-6%2B6%3D9%2B6)
![3x=15](https://tex.z-dn.net/?f=3x%3D15)
Dividing both sides by 3.
![\frac{3x}{3}=\frac{15}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B15%7D%7B3%7D)
∴ ![x=5](https://tex.z-dn.net/?f=x%3D5)
<em>Plugging in
into
.</em>
We have,
![y=-5-3](https://tex.z-dn.net/?f=y%3D-5-3)
∴ ![y=-8](https://tex.z-dn.net/?f=y%3D-8)
The solution of the system can be given as (5,-8).
Answer:
average atomic mass = 207.2172085 amu
Explanation:
To get the average atomic mass of an element using the abundance of its isotopes, all you have to do is multiply each isotope by its percentage of abundance and then sum up all the products.
For the question, we have:
203.97304 amu has an abundance of <span>1.390% (0.0139)
</span>205.97447 amu has an abundance of 24.11% (0.2411)
206.97590 amu has an abundance of 22.09% (0.2209)
207.97665 amu has an abundance of 52.41 % (0.5241)
The average atomic mass can be calculated as follows:
average atomic mass = 203.97304(0.0139) + 205.97447(0.2411)
+ 206.97590(0.2209) + 207.97665(0.5241)
average atomic mass = 207.2172085 amu
Hope this helps :)
Smallest 1/4 5/12 1/2 2/3 3/4 biggest
Answer:
Option A:
is the correct answer.
Step-by-step explanation:
The point-slope form of an equation of a line is given by:
![y-y_1 = m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%20%3D%20m%28x-x_1%29)
Here:
m is the slope of the line
are the coordinates of the point from which the line passes.
Now looking at the given question:
![m = 25\\(x_1,y_1) = (-4,-7)](https://tex.z-dn.net/?f=m%20%3D%2025%5C%5C%28x_1%2Cy_1%29%20%3D%20%28-4%2C-7%29)
Putting the values in the general form of point-slope form of equation of line
![y-(-7) = 25\{x-(-4)\}\\y+7 = 25(x+4)](https://tex.z-dn.net/?f=y-%28-7%29%20%3D%2025%5C%7Bx-%28-4%29%5C%7D%5C%5Cy%2B7%20%3D%2025%28x%2B4%29)
Hence, the point-slope form of given line is:
![y+7 = 25(x+4)](https://tex.z-dn.net/?f=y%2B7%20%3D%2025%28x%2B4%29)
Observing the option given, it can be concluded that Option A:
is the correct answer.