Factoring
Factor: 9x² – 49
(3x – 7)(3x + 7)
Write log₄(x³ · y⁶) in expanded form.
3 log₄x + 6 log₄y
In a right triangle, the hypotenuse is 15 and one angle is 35°. Find the side opposite 35°.
x = 15 · sin(35°) ≈ 8.60
Convert 240° to exact radian measure in terms of π.
(4π)/3
Write a quadratic in standard form with complex roots x = 3 + 4i and x = 3 – 4i.
Y = x² – 6x + 25
Simplify: (x² – x – 6)/(x – 3)
x + 2
Factor: 3x² + x – 10
(3x – 5)(x + 2)
Write log₅(x² / y³) in expanded form.
2 log₅x – 3 log₅y
In a right triangle, the adjacent leg is 10 and the angle is 42°. Find the hypotenuse.
hyp = 10 / cos(42°) ≈ 13.46
Convert
(5pi)/4
radians to degrees.
225°
Write a quadratic in standard form with roots x = ⅔ and x = –4.
Y = 3x² + 10x – 8
Simplify the complex fraction: (2/x + 3/y) ÷ (1/y)
(2/x + 3/y) ÷ (1/y)
(2y + 3x)/x
Factor completely: 4x³ – 20x² + 24x
4x(x – 2)(x – 3)
Solve
Log(5x) =2
x = 20
A triangle has sides 5, 12, and 13. Is it a right triangle? Explain.
Yes — 5² + 12² = 25 + 144 = 169
Find the reference angle for 7π/12.
(5pi)/12
What is the remainder?
(3x⁴ + 2x³ – 5x + 4)/(x+2)
46
Simplify: (x² + x – 12)/(x² – 4x + 3) × (x² – 2x + 1)/(x² + 4x)
(x – 1)/x
Factor completely: 5x³ – 40
5(x – 2)(x² + 2x + 4)
Log(5x) + Log(x) = Log 25
sqrt5
In a LAW of SINES triangle the side opposite angle A is 30 cm.
Angle B is 70 degrees and b = 40. Find angle A
angleA = 44.81
Find the exact value of
cos((5π)/3).
.
1/2
Given the points on the polynomial curve (1,5) and the equation below, find the value of stretch factor a.
P(x) = a(x-2)(x+3)(x-6)^2
a = 1/20
(3(x – 1))/(x + 3)
(3(x – 1))/(x + 3)
Factor completely: 27x³ + 64
(3x + 4)(9x² – 12x + 16)
Find the inverse of
g(x) = 2^(x + 3)
.
g⁻¹(x) = log₂(x) – 3
In a 45-45-90 triangle, one leg is 6√2. Find the hypotenuse.
Hypotenuse = 12
State the amplitude and period of y = 5 cos4(x).
Amplitude = 5; Period = π/2
Find the roots of the equation
x(x-4)(x+5) = 0
The roots are 0, 4, and -5.
Solve for x: 4/(x + 1) + 2/(x – 3)
(6x+14)/((x+1)(x+3))