Mystery!
Simplify.
root 243
9sqrt3
Write an explicit formula given the recursive formula.
a_1 = -3, a_n = a_(n-1) -4
a_n = 1-4n
Susie begins fishing with 9 worms. She uses 3 worms every 2 hours. Write a linear function for f(x) where x is the number of worms used. After how many hours will all the worms be gone?
f(x) = -3/2 x + 9; 6 hours
Convert the equation from standard form to slope-intercept form.
6x - 2y = -20
y = 3x + 10
-x < -3
Is the circle open or shaded? Is the line of solutions pointing left or right?
Open; right
The x-values you choose for your ordered pairs are -2, -1, 0, 1, 2. Based on the function, what are the corresponding y-values?
f(x) = -3|x|
-6, -3, 0, -3, -6
Write an recursive formula given the explicit formula, and identify the first term.
a_n = 8 + 20n
a_1 = 28, a_n = a_(n-1) +20
Two points on a line are A(1, 2) and B(4, 1). Write a linear function for f(x) to represent this line. What is f(-9)?
f(x) = -1/3 x + 7/3; 16/3
Write an equation in standard form which passes through the points (4, 0) and (0, -2).
x - 2y = 4
Solve.
- 2x < 4 or 4x > 20
x > -2
The y-intercept is (0, -2). The slope is 3/4. The line is dashed. The shade is below the line. What is the inequality representing this situation?
y<3/4 x-2
Write an explicit formula given the arithmetic sequence.
a_n = a_(n-1) + 2.4; a_1 = -1
a_n = -3.4 + 2.4n
Bob is competing in a 10-mile race. He runs at a constant speed of 5 miles per hour. Write a linear function for f(x) where x represents the number of hours to determine how many miles Bob has left to run. How many hours will it take Bob to finish the race?
f(x) = -5x + 10; 2 hours
Name the coordinates of the point on each axis where the line crosses it.
-x + 4y = -20
(0, -5) and (20, 0)
Solve.
-3x > - 6 or 5x > -5
x < 2 or x > -1
Line m has a y-intercept of (0, 1) and slope of 1/2. Line n has a y-intercept of (0, 7) and a slope of -3/2. What is the solution?
(3, 2.5)
The cost to rent a bicycle is $26 for the first day, then $12 for each day thereafter. Write an explicit formula, then determine the cost to rent the bicycle for 10 days.
a_n = 14 + 12n; $134
A gym membership costs $12 per month, but charges a one-time enrollment fee of $120. Write a linear function f(m) where m represents the number of months to determine the total cost of your gym membership. How much will you spend on your gym membership after the first year? How much will you spend the second year?
f(m) = 12m + 120; $264; $144
A line passes through the points A(n, 4) and B(6, 8) and is perpendicular to y = 2x + 5. What is the value of n?
14
Solve.
-5 < -3x - 2 < 4
-2 < x < 1
A rectangle has a perimeter of 56 cm and an area of 115 cm^2. Its length is 3 more than four times its width. Find the length and width of the rectangle.
Length 23 cm, width 5 cm
An online store charges $5 to ship one box and $10 to ship two boxes. Write an explicit formula for an arithmetic sequence to represent the amount the online store charges to ship n boxes. Then determine how much the online store charges when shipping 11 boxes.
a_n = 5n; $55
A local restaurant offers you your first job. They start you at $14.70 per hour minimum wage since you have 0 years of experience. Every year thereafter, your wages will increase $0.55. Write a linear function f(x) where x is the number of years of experience to determine your wages. How much will your wages be after 3 years of experience?
f(x) = .55x + 14.70; $16.35
Find the equation of a line perpendicular to the given line passing through the point (-20, 4).
5x - 2y = 3
y = -2/5 x - 4
Solve.
9x - 1/7 x - 2 > 17/7
x > 1/2