Answer:
(x, y) = (2, 1)
Step-by-step explanation:
The x-coefficients are opposites of each other, so the x variable will be eliminated if the two equations are added.
(x +3y) +(-x -y) = (5) +(-3)
2y = 2
y = 1
Substituting into the first equation gives ...
x +3(1) = 5
x = 2 . . . . . . . subtract 3
The solution is (x, y) = (2, 1).
Answer:
5 hours
Step-by-step explanation:
35/5=7
7x5= 35
7 times 5 is 35 so if he was going 7 miles per hour it would take him 5 hours to travel 35 miles.
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
and ![a^{-1}=\dfrac{1}{a};\ a^{-n}=\dfrac{1}{a^3}](https://tex.z-dn.net/?f=a%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7Ba%7D%3B%5C%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5E3%7D)
![3^{-1}\cdot(4\cdot6)\cdot2^{-3}=\dfrac{1}{3}\cdot24\cdot\dfrac{1}{2^3}=\dfrac{24}{3}\cdot\dfrac{1}{8}=\not8^1\cdot\dfrac{1}{\not8_1}=1](https://tex.z-dn.net/?f=3%5E%7B-1%7D%5Ccdot%284%5Ccdot6%29%5Ccdot2%5E%7B-3%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Ccdot24%5Ccdot%5Cdfrac%7B1%7D%7B2%5E3%7D%3D%5Cdfrac%7B24%7D%7B3%7D%5Ccdot%5Cdfrac%7B1%7D%7B8%7D%3D%5Cnot8%5E1%5Ccdot%5Cdfrac%7B1%7D%7B%5Cnot8_1%7D%3D1)
Assume that each of the 6 numbers has an equal probability of showing up for each die.
The probability of obtaining a six from the red die is 1/6, or
P(6 from the red die) = 1/6.
Similarly,
P(6 from the green die) = 1/6.
The tossing of the red die, followed by the tossing of the green die are independent events. Therefore
P(6 from the red die AND 6 from the green die) = (1/6)*(1/6) = 1/36.
Answer: 1/36
<h2>
Hello!</h2>
The answer is:
d) ![\frac{(x-1)(11x+1)}{(x-1)(x+2)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-1%29%2811x%2B1%29%7D%7B%28x-1%29%28x%2B2%29%7D)
<h2>Why?</h2>
A hole is a point where rational functions lose its continuity, meaning that in that point, there is a discontinuity condition.
We can find the hole of a rational function if there are similar terms on the numerator and the denominator by finding:
First (x-component): The values of x that makes the function equal to 0 in both numerator and denominator.
Second (y-component): Re-evaluating the same term in the other factors of the function to know the y-component.
Finding the x component we have:
![f(1)=\frac{(1-1)(11*1+1)}{(1-1)(1+2)}=\frac{(0)(12)}{(0)(3)}=\frac{0}{0}](https://tex.z-dn.net/?f=f%281%29%3D%5Cfrac%7B%281-1%29%2811%2A1%2B1%29%7D%7B%281-1%29%281%2B2%29%7D%3D%5Cfrac%7B%280%29%2812%29%7D%7B%280%29%283%29%7D%3D%5Cfrac%7B0%7D%7B0%7D)
So, the x-component is 1,
Then, re-evaluating the function:
![f(1)=\frac{(x-1)(11*1+1)}{(x-1)(1+2)}=\frac{(12)}{(3)}=\frac{12}{3}=4](https://tex.z-dn.net/?f=f%281%29%3D%5Cfrac%7B%28x-1%29%2811%2A1%2B1%29%7D%7B%28x-1%29%281%2B2%29%7D%3D%5Cfrac%7B%2812%29%7D%7B%283%29%7D%3D%5Cfrac%7B12%7D%7B3%7D%3D4)
Therefore, the y-component is 4,
Hence,
The function has a hole at (1,4)
Have a nice day!