Mystery!
Factor:
x2 - x - 6
(x - 3)(x - 2)
Write a recursive formula and the simplified explicit formula for the following sequence:
-7, -14, -28, -56,...
a_1 = -7
a_n = 2(a_(n-1))
a_n = -7(2)^(n-1)
Solve:
-27x + 12y = 21
7x - 12y = 39
(-3, -5)
What is the vertex?
f(t) = -2x^2 + 12x + 4
(3, 22)
Factor:
x2 - x - 6
(x - 3)(x - 2)
Write the product:
(5x^2 - 2)(4x^2 - 9x + 7)
20x^4 - 45x^3 + 27x^2 + 8x - 14
Write an recursive formula given the explicit formula, and identify the first term.
a_n = -2 + 12n
a_1 = 10, a_n = a_(n-1) +22
The formula
A = 6V^(2/3)
relates the surface area A of a cube to the volume V. What is the volume of a cube with surface area 384 in^2?
512 in3
Write an equation in standard form which passes through the points
(4, 0) and (0, -2).
x - 2y = 4
Simplify:
(625^4)^(1/8)
25
Simplify:
(-3x - 2) - (x^2 - 6x + 7)
-x^2 + 3x - 9
Write the simplified explicit formula given the recursive formula:
a_n = a_(n-1) - 4; a_1 = 3
a_n = 7 - 4n
Dawn is cleaning all the rooms in her house. There are 4 rooms left to clean, and she takes 6 hours to clean them. Write the equation in standard form of the line that represents the number of rooms Dawn has left to clean, y, after x hours.
2x + 3y = 12
Rewrite the following equation to solve for r:
V = (4pir^3)/3
r=root(3)((3V)/(4pi))
Evaluate with positive exponents:
27^(1/6)/27^(1/2)
1/3
What is the vertex of the function? Does the function open upward or downward?
f(x) = -1/4|x - 2|
(2, 0)
downward
Write an explicit formula for the sequence:
12, 4, 4/3, 4/9,...
a_n = 12(1/3)^(n-1)
Solve:
4x - 9y - 2 = 0
12x - 5y = -38
(-4, -2)
After 30 seconds a scuba diver is 60 feet below the surface. He continues downward for another 30 seconds and then turns back and returns to a depth of 60 feet below the surface after 90 seconds. What is the axis of symmetry?
Factor the perfect square trinomial:
9x2 - 24x + 16
(3x - 4)(3x - 4)
Simplify:
216^(1/3) + root(3)81
6 + 3root(3)3
The population of a city, P, in 2020 was 25,000. The population is decreasing by 3% annually. What is the exponential function to represent this situation if x represents the number of years after 2020?
P(x) = 25,000(.97)^x
Mr. Berry buys 4 pounds of cheese and 4 pounds of sausage for a total cost of $36. The cheese costs $4.00 less per pound than the sausage. What is the combined cost of 1 pound of cheese and 1 pound of sausage? How much would Mr. Berry pay for 7 pounds of cheese and 2 pounds of sausage?
1 pound of cheese and 1 pound of sausage costs $9.00. 7 pounds of cheese and 2 pounds of sausage costs $13.00
The function h(t) = −12t2 + 20t models the height, in feet, of a ball t seconds after it is thrown into the air. What is the maximum height the ball reaches after it is thrown?
25/3 ft
Factor:
-18y2 + 120y + 42
-3(y - 7)(6y + 2)