Algebraic Reasoning
5x+15=0
What is -3?
I am a rational number, whole number and integer but not a Natural Number.
What is 0?
How many triangles can fit in a circle?
What is infinite?
Probability that compares total trials vs Successful trials
What is experimental probability?
In a small company of 10 employees, everyone earns $50,000$ a year. If the CEO gives themselves a raise to $1,000,000$ a year, which measure of central tendency—the Mean or the Median—will change the most, and why?
The Mean will increase because it is more easily influenced by outliers while the median remains 50,000.
Find the solution to the system of linear equations.
4x+2y=10
2x-5y=12
What is 2?
i^47
What is
-i
If every Square is a Rhombus, is every rhombus a square? Explain.
A rhombus only needs 4 congruent sides while a square needs 4 congruent sides and 90 degree angles.
In a 1v1 game of Black Jack vs the Dealer, the dealer has K-K and cannot hit anymore. You have K-7. What are the chances of you losing on your next hit?
What is 66.67%?
On Earth, the acceleration due to gravity is approximately 9.8m/s^2. On the Moon, gravity is much weaker, at 1.6m/s^2. If an astronaut on the Moon drops a hammer from a height of 20 meters, how many seconds will it take to hit the surface?
d=1/2at^2
What is 5 seconds?
Find the zeros of the given Polynomial
f(x)=x^2+4x-21
What is -7 and 3?
Take the number 8, multiply it by 5, divide it by 9, square it, find the cube root, minus 1 and square it again. Now find 0 divided by that solution.
What is no solution?
In a proof, if you start with the statement
angle1 cong angle 2
what conclusion allows you to say the lines are parallel?
What is converse of AIA?
Two die are rolled simultaneously, what are the odds that the sum of those die are exactly 10?
What is 8.3%?
A scientist has a mysterious metal cube with a mass of 160 grams. Each side of the cube measures 2 cm. What is the density of the metal?
What is 20 g/cm^3?
x^2+35=10
What is
5i and -5i
4+4
What is 8?
A square has an area of
50m^2
Find the length of its diagonal
What is
sqrt2 * sqrt50
White Pine's Boys Basketball Team went 4/27 from the 3pt line yesterday(True story btw). What is the probability that they miss their first 5 threes next game?
What is 44.9%?
A specific type of bacteria doubles its population every 20 minutes. If you start a petri dish with a single bacterium at 12:00 PM, how many bacteria will be in the dish at 4:00 PM?
What is 4096?
Find the zeros of the given polynomials
f(x)=x^2-6x+25
What is
3+4i and 3-4i
2i(4+3i)(6-5i)
What is
4 + 78i
Given: Quadrilateral ABCD is a parallelogram.
Prove:
triangleABDcongtriangleCDB
AB||CD & BC||AD Def of Parallelogram
[ a ] [ b ]
BD congDB Ref Prop
triangleABDcongtriangleCDB
[c]
What is
angleABDcongangleCDB
b) Alternate Interior Angle Theorem
c) ASA or SAS
In a 1v1 game of Black Jack vs the Dealer, the dealer has K-K and cannot hit anymore. You have K-7. What are the chances of you winning or the game ending in a tie.
What is 19.4%?
The European Space Agency (ESA) is headquartered in Paris, France. However, they do not launch their rockets from France. Instead, they ship them to French Guiana in South America, which is located almost exactly on the Equator. Using the math of Earth's rotation, explain the mathematical and physical advantage of launching from the Equator versus launching from Europe.
At the Equator, the Earth is spinning at approximately 1,000 mph. In Europe, it is spinning at only about 700 mph. By launching from the Equator, the rocket starts with an extra 300 mph of "free" velocity. This allows the rocket to carry less fuel and more "payload" (satellites or equipment), making the mission significantly cheaper and more efficient.