Combinatorial Enumeration. That whole class was a rollercoaster ride of mind-blowing generating functions to prove crazy things. The exam had ridiculous questions like 'count the number of cactus trees with n vertices such that etc etc etc' and you'd do three pages of terrible terrible sums and algebra. Then your final answer would be something beautiful like n/2 and you'd breath a sigh of relief and thank the math gods.
Step-by-step explanation:
equation.
2(m+10)=4(m−15)
(2)(m)+(2)(10)=(4)(m)+(4)(−15)(Distribute)
2m+20=4m+−60
2m+20=4m−60
Step 2: Subtract 4m from both sides.
2m+20−4m=4m−60−4m
−2m+20=−60
Step 3: Subtract 20 from both sides.
−2m+20−20=−60−20
−2m=−80
Step 4: Divide both sides by -2.
−2m−/2=−80/−2
m=40
Answer:
R is not collinear.
S is collinear.
Step-by-step explanation:
The equation of the graph is given by y =x +2 ........ (1).
Now, the points P and Q having coordinates (5,7) and (-1,1) respectively lie on the graph of the equation (1) because those points satisfy the equation.
Now, if we consider another point R having coordinates (1,-1), then it does not lie on the graph of equation (1) as it does not satisfy the equation.{If you put x=1, then y will be 3 but not -1}
Therefore, P, Q, R are not collinear. (Answer)
Again if we consider the point S(-3,-1), it satisfies equation (1).{If you put x=-3 in the equation (1), y will be -1}.
Therefore, P, Q, and S lie on the same straight line. and they are collinear. (Answer)
Answer: 
Step-by-step explanation:
From the origin we can see to get to the point plotted we have to go down 1 and right three giving us the slope 
These are in the form of y=mx+b
b is the y-intercept and m is the slope
since the y-intercept is 0 b is 0 and isn't need leaving us with y=mx
We can put our slope into the equation giving us the answer in C