arithmetic sequences
What is the common difference in the arithmetic sequence: 5, 9, 13, 17, …?
The common difference is 4.
What is the slope of the line y = 4x – 2?
4
Solve: x – 4 < 10
x < 14
Write a system of linear inequalities that represents the shaded region below the line y = 3x + 2 (dashed) and above the line y = –x + 4 (solid).
y < 3x + 2 y
≥ –x + 4
A car travels 150 miles in 3 hours. What is its rate in miles per hour?
50
In an arithmetic sequence, the first term is 12 and the common difference is –3. What is the 4th term?
The 4th term is 3.
3x + 6 = 21
x = 5
Solve: 5x ≥ 20
x ≥ 4
Solve the system by graphing: y ≤ 2x + 1 y > –x + 4
The solution is the region below or on the line y = 2x + 1 and above the line y = –x + 4. The overlapping shaded area is the solution set.
A faucet fills 12 liters in 4 minutes. What is the rate in liters per minute?
3 L/min
The 10th term of an arithmetic sequence is 42, and the common difference is 5. What is the first term?
The first term is –3.
Write the equation of a line with slope 2 and y‑intercept –3
y = 2x – 3
Solve: –2x > 12
x < –6
What does the solution to a system of linear inequalities represent?
The solution is all points that satisfy every inequality at the same time, shown as the overlapping shaded region on the graph.
A runner completes 2.5 miles in 20 minutes. What is the rate in miles per hour?
7.5 mph
Write a formula for the nth term of the arithmetic sequence: 7, 2, –3, –8
an=7+(n−1)(−5)
A line passes through (1, 2) and (3, 10). What is the slope?
4
Write an inequality for: A number n is no more than 8
n ≤ 8
A system models a business situation: x = number of bracelets y = number of necklaces The inequalities are: x + y ≤ 40 y ≥ 2x
You can make no more than 40 total items, and you must make at least twice as many necklaces as bracelets.
What is 20% of 50?
10
An arithmetic sequence has a first term of 6. The sum of the first 20 terms is 1,060. What is the common difference?
The common difference is 5.5.
Write the equation of the line passing through (–2, 5) with slope –3
y = –3x – 1
Solve: 3 < 2x + 1 ≤ 11
1 < x ≤ 5
A school club is selling snacks. They must sell at least 50 items in total. They also must sell no more than twice as many chips as cookies
x + y ≥ 50 x ≤ 2y
A population increases from 800 to 1,000. What is the percent increase?
25%