Algebra
5x−12=3x+8 solve for x
x=10
A 3D pyramid has a 10-sided polygon (a decagon) as its flat base. How many total edges does this entire pyramid have?
20 edges
There are 3 red flags, 4 blue flags, and 2 white flags. They are arranged in a single row to create a signal. How many different signals can be made?
1260
Compute real and imaginary part of z=(i-4)/(2i-3).
Re (z) = 14/13
Im (z) = 5/13
x2+9=0 solve for x
x=3i or x=-3i
The sum of the interior angles of a regular polygon is 1080°. How many sides does this polygon have?
8 sides
A box contains 100 apples, 100 bananas, 100 oranges, and 100 pears. If one piece of fruit is taken out of the box each minute, what is the minimum number of minutes needed to guarantee that at least 12 pieces of the same type of fruit have been drawn?
45
Write in the “algebraic” form (a + ib) the following complex number
z =i5+ i + 1
1+2i
Solve the system: 3x + 2y = 16 and 2x - y = 3
x = 22/7, y = 23/7
The angle formed by the radius of a circle and a tangent to that circle has a measure of:
90 degrees
If a, b, c, d ∈ {1,2,3}, how many ordered quadruples (a, b, c, d) are there such that a+b+c+d is even?
41
Find the value of x and the value of y in the following equation.
(x+iy)(2+i)=3-i
x=1
y=-1
x4-13x2+36=0 solve for x
x=-3, -2, 2, 3
Slide for 400 points
1)
Eleven soccer players, numbered 1 through 11, are standing in a line. If no player with a number greater than 6 can stand in front of Player 6, in how many different ways can the 11 players be arranged?
(You can write your answer in the factorial form)
11!/6
The cubic equation 2z3-z2+4z+p=0 is satisfied by z = 1+2i. Find the other two roots of the equation.
1-2i, -3/2
2x+1+2x=96 solve for x
x=5
Slide for 500 points
14
An ant crawls along the edges of a cube with side length 1. It starts at one vertex and takes exactly 1 minute to move to an adjacent vertex. After crawling for 7 minutes, the distance between the ant’s current vertex and its starting vertex is √3. How many possible paths could the ant have taken?
546
For two complex numbers, z and w,
z+2i=w-iz
2z+i=1-iw
Find the product, zw, of these two complex numbers. Write your answers in Cartesian form, a+bi
5-5i