Simplification
27^{1/3}\cdot 5^{-1}\cdot 10/2\cdot37^0
3
Write an equation for a line going through the point (1,2) with a slope of -1 in slope-intercept form
y=-x+3
Solve for y:
2x-y=y+5
4y-3(x-1)=-1
y=7/2
Noah puts on a hat for every three silly math mistakes he makes, and he makes a silly math mistake for each 2 cups of coffee he drinks. If Noah drinks 48 cups of coffee, how many hats will he have to put on?
8
\frac{x/y +1/x}{1/y}
\frac{x^2+y}{x} or x+y/x
Write an equation for the line that goes through the points (1,2) and (1,0)
x=1
I left the window to the Pigeonhole room open, and a bunch of pigeons got inside. There are two types of pigeons currently needing to be removed: fancy pigeons, which weigh 9ozs/pigeon, and medieval pigeons, which weigh 50ozs/pigeon (because they're wearing suits of armor). There are twice as many fancy pigeons as medieval pigeons, and the total pigeonweight is 340ozs. How many more fancy pigeons are there than medieval pigeons?
5
Graham's secret laboratory is 60 miles away from Proof School. If Graham unicycles to school, it takes him 2 hours. If Graham takes a private plane to school, it takes him 8 minutes. If he unicycles to school and then takes a private plane back, what is his average speed in miles per minute?
15/16 miles per minute
\frac{\frac{4x}{3}-\frac{2x}{5}}{\frac{7}{3}-\frac{7y}{3}}
\frac{2x}{5(1-y)}
For what value of c is the graph of 3y-cx+8=0 parallel to the graph of 2y+4x-7=0?
-6
Solve the following for x and y:
{9x}/{2y}=12
3x-4y=1
x=2/3
y=1/4
Shelly, Ilyse, and Mr. Gregg are representing Proof School in a relay race. Shelly runs at 8 mph, Ilyse runs at 6mph, and Mr Gregg runs at 7 mph. The runner who goes second in the race has to go twice the distance as the runner who goes first, and the runner that goes last has to go twice the distance of the runner that goes second. The three runners together must go a combined distance of 21 miles. What is the fastest time that Team SIG can run the race?
20/7 hours
\frac{\frac{64^{(1/4)}}{3}-2^{(-1/2)}}{\sqrt{2}-(\frac{2^{(1/2)}}{2}-\frac{\sqrt{8}}{6})}
1/5
If L is the line that goes through the points (0,1) and (-3,5), and (2,y) is a point on the line perpendicular to L that goes through the origin, what is y?
-3/2
Solve the following for x, y, and z:
x-y=1
y-z=2
z+x=3
x=3, y=2, z=0
Noah's latte has a milk to coffee ratio of 3 to 7. Shelly's latte has a milk to coffee ratio of 7 to 1 (Shelly is not a huge fan of coffee). If Noah has 5 cups of his latte drink, how many cups of Shelly's latte does he need to add to get a drink which is exactly 75% milk?
18