Basic Algebra
-2x+2=-3
x=?
5/2
What is the solution of the following equation?
(2-x)2=0
x=2
What is the mean of the following dataset?
3, -2, 5, -6, 2, 7, -8
Mean = 1/7
Find the volume of the following cylinder:
Base diameter: 3, Height: 8
Use 3 for the value of pi.
54 cubic unit
The ideal gas Law PV = nRT. Robert Boyle found PV = a constant. That is, the product of the pressure of a gas times the volume of a gas is a constant for a given sample of gas. What is the expression of R in terms of the other variables?
R = PV/nT
x+2y=2
y-x=3
Find x and y.
x=-4/3, y=5/3
What is the solution to the following equation?
2x=8
x=3
The original dataset is: 3, -2, 5, -6, 2, 7, -8.
If we add another number to make the new mean 1, what number should we add?
7
What is the product of the slopes of two perpendicular lines?
-1
What is the x-intercepts of the following equation?
y=2x2-3x-2
(2,0) and (-1/2 ,0)
What is the intersection between:
2x-3y=1 and 4-2y=3x?
(14/13, 5/13)
What is the solution to the following equation?
3x2-8x-3=0
x=-1/3 or x=3
The original dataset is 4, -1, 0, 5, -6, 2, -3, 7, 6, 2.
If the median is removed, what is the new mean?
14/9
A equilateral triangle has a side length 2. What is its area?
What is the radius of the following circle?
x2-6x+y2+8y=-12
Sqrt (13)
In what case, k(2x-4)=3x-4 does not have a solution?
k=3/2
What is the ratio of the sum to the product of the solutions to the following equation?
4x2-5x-6=0
5:6
How would you determine which histogram/dot plot has a larger/smaller standard deviation?
Narrower + taller = smaller SD
Simply the following complex fraction into the form of a+bi:
(2-i)/(2i-1)
-4/5 - 3i/5
How many times does the following polynomial touch but NOT cross the x-axis?
f(x)=(2x-3)(x2-4x+3)(x2-6x+9)(x-1)2
2
In what case does the following system of equations have infinitely many solutions?
ax+2y=b
3x+by=2
a=3, b=2
What is the value of x?
(21/x) (1/4)-x (8)-x/3 (-2)2x = 16
x=1
The mean of the following two datasets are equal. Find the value of x.
Dataset A: 5, 3x, 2x2, -8x, 3x2
Dataset B: -2x2, x2+3x, x-3x2, 8
x=(1+sqrt(3))/2 or (1-sqrt(3))/2
Find the value of a:
(a+4i)/(i-1)=2-2i
a=0
A 20% nickel alloy is made by combining 6 grams of an x% nickel and 2 grams of 35% nickel alloy. What is the value of x?
15