Algebra 2
Factor.
(x2 - 16)
(x + 4)(x - 4)
In triangle ABC,
angle A = 50 degrees
angle B = 60 degrees
What is the measure of angle C?
angle C = 70 degrees
In a right triangle, angle theta = 30 degrees and the side adjacent to theta is 10 cm. Find the length of the hypotenuse.
11.5 cm
Evaluate
log3(81)
4
Take the Derivative
f(x) = 12x3 + 12x2 + 7x -6
f'(x) = 36x2 + 24x +7
Solve the system
2x + y = 7
x - y = 2
x = 3
y = 1
A right triangle has legs that measure 6 inches and 8 inches.
What is the length of the hypotenuse?
Hypotenuse = 10 units
A circle has a radius of 6 cm. Find the arc length intercepted by an angle of ((2pie)/3))
12.57
Complete the square
x2 + 6x + 5
(x + 3)2 - 4
Take the derivative.
f(x) = 6x(5x2 - 1)4
f'(x) = 24x(5x2 -1)3 * 10x
Solve:
x2 - 5x + 6 = 0
x = 2, x = 3
A circle with a radius of 5 units has a tangent line drawn from an external point P. If the distance from point P to the point of tangency is 12 units, what is the straight-line distance from P to the center of the circle?
13
Prove the identity
((1-sin2x)/(cosx)) = cos x
for all permissible values of x
Answer on the board)
Determine the horizontal asymptotes
h(x) = (4x3 - 5x)/(2x3 + 7)
y = 2
The intergral of 2xcos(x2)dx
sin(x2) + C
The Problem: Simplify
((x2 - 9)/(x2 + 5x + 6)) / ((x - 3)/(x + 2))
1; x cannot equal 3, -2, and -3
In triangle ABC
AB = AC
angle A = 20 degrees
A point D is on AC such that angle DBC = 60 degrees
Find the measure of angle BDC
angle BDC = 30 degrees
Find all solutions.
2cos2x + cosx - 1 = 0
where 0 degrees <_ x < 360 degrees
x = 60 degrees, x = 80 degrees, and x = 300 degrees
Find the slant asymptote
f(x) = (2x2 - 5x +7)/(x - 2)
(Long division)
y = 2x - 1
lim as x approaches 0 ((x - 9)1/2 - 3)/x
1/6
2x+4 = 42x-1
x = 2
In triangle ABC
angle B = 90 degrees
Two angle bisectors are drawn: line segment AQ, which bisects angle A (with Q on side BC), and line segment CP, which bisects angle C (with P on side AB)
If the lengths of these two bisectors are given as AQ = 9 and CP = 8*21/2
Find the exact length of the hypotenuse AC.
13.42
Prove that, sin(10 degrees)sin(30 degrees)sin(50 degrees)sin(70 degrees)= (1/6)
This will be on the board
Find the inverse of the function
f(x) = (2x + 1)/(x - 3)
f-1(x) = (3x + 1)/(x - 2)
A 13 foot ladder is leaning against a vertical wall. The bottom of the latter is pulled horizontally away from the wall at a constant rate of 2 ft/s.
How fast is the top of the ladder sliding down the wall at the exact instant when the bottom of the ladder is 5 feet away from the wall
5/6 ft/s