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
Factor x2+3x-18.
(x-3)(x+6)
\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 (3,-5) in slope-intercept form
y=-7/2x+11/2
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
Factor 10x2-19x-15
(5x+3)(2x-5)
-(-x-(1-x)^{x-(x-1)})-1
0
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
I set my watch to the correct time at noon, but when it is exactly 1:00pm, my watch reads 12:57:36. Assuming my watch keeps slowing at the same rate, what time will it actually be when my watch says 10:00pm?
10:25pm
Write a quadratic equation with integer coefficients whose roots are -1/2 and 5/6.
12x2-4x-5 (or any constant multiple of this)
\frac{\frac{4x}{3}-\frac{2x}{5}}{\frac{7}{3}-\frac{7y}{3}}
\frac{2x}{5(1-y)}
Eric strolls along the xy-plane in a straight line. At time t, he is standing on the point (2t+1, -t-3). What is the equation of the line he is walking along?
y=x/2+5/2
Last night for dessert, each member of my 5-person family drank 8 ounces of chai latte containing some tea and some milk (but different people drink different tea/milk ratios). The amount of milk in my latte was 1/4 of the total amount of milk my family drank, and the amount of tea was 1/6 the total amount of tea my family drank. How many ounces of milk did I drink?
4 ounces
All proofniks were given a two-question survey asking whether they preferred pie or cake and whether they preferred \pi or e. The results showed that 4/5 of proofniks preferred e to \pi and 3/4 of proofniks preferred cake to pie. If 65% of the school prefers both cake and e, what percent of the school likes both kinds of pi?
10
One of the roots of 4x2+bx-24 is 4. What is b?
-10
\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 a, b, and c:
a^2+ab+ac=2a
2^{x+1}\cdot a-3\cdot 2^x\cdot b+2^{x+2}\cdot c=5\cdot 2^x
b^2-c^2=7b+7c
a = 19
b = -5
c = -12
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
The sum of the squares of the roots of x2+bx-12 is 40. Find all possible values for b.
4 and -4