Algebra I
3x-5=10
What is x?
x=5
A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter?
34 cm
Solve for x: x^2-5x-14=0
x=7, x=-2
If f(x)=3x^2-5x+2, find (-2).
24
What is 67+67 equal to?
134
4(x-2)x-2=3(x+1)-11
Solve for x.
x=-2
Two angles of a triangle measure 45° and 60°. What is the measure of the third angle?
75°
log_3(2x-1)=3
x=14
Solve for x: log_2(x)+log_2(x-2)=3.
x=4
What do all the angles of a triangle add up to?
180 degrees
Tickets to a school play costs $5 for adults and $3 for students. If 120 total tickets were sold for $480, how many student tickets were sold?
60 student tickets
A right-angled triangle has a base leg of 6 cm and a hypotenuse (the longest side) of 10 cm. What is the length of the missing vertical leg?
8 cm
Solve for x: sqrt(2x+7)-x=2
x=1
Simplify the expression (sinx/1+cosx)+(1+cosx/sinx) into a single simple term.
(2/sinx) or (2cscx)
What is the derivative of the function: f(x)=3x+5?
3
Find all intersection points (x,y) of the line y=7-2x and the quadratic equation 2x+y=x^2-4x-1.
(4,-1) and (-2,11)
A square has a side length of 14 cm. A circle is perfectly inscribed inside this square so that it touches all four sides. What is the area of the circle?
49pi cm^2
Find all real solutions (x, y) for the system: y=x^2-4x+3 and y=2x-2.
(5,8) and (1,0)
Find the coordinates of any holes and the equations of any vertical and horizontal asymptotes for the function f(x)=(x^2-x-6)/(x^2-4).
Hole: x=2
VA: x=-2
HA: y=1
What is the derivative of 5^x?
ln(5)*5^x
If the positive square root of an unknown number x lies strictly between 3 and 11, and the x also satisfies the absolute value equation |x-50|=y, find all possible integer values of y where x is a whole number.
(23≤x≤41)
Two cubes, Cube A and Cube B, are geometrically similar. The surface area of Cube A is 24 cm² and the surface area of Cube B is 216 cm². If the volume of Cube A is 8 cm³, what is the volume of Cube B?
216 cm³
Solve for x: |3x-4|=11
x=-7/3, x=5
Let f(x)=sqrt(9-x^2) and g(x)=1/(sqrt(x-1)). Find the domain of the composite function (g(f(x))).
Domain: x-2 sqrt(2) < x < 2sqrt(2)
What is the shape created by the function: x^2+y^2+z^2=1?
Sphere or Ellipsoid