Patterns
Find the next three terms in the pattern: 8, 15.5, 23, 30.5, ___, ___, ___ Describe the pattern.
38, 45.5, 53; First difference: +7.5
How do you solve fraction bars in Order of Operations?
Solve the numerator and denominator separately. Then divide at the end and simplify.
To rent a car, it costs a user fee of $40 and then $0.20 per mile. Write an equation to represent how much it costs to rent a car.
C = 0.2m + 40
Simplify by combining like terms: (4y - 5) + (-3y +2)
y - 3
In a negative correlation, as x _____, y_____.
As x increases, y decreases. OR As x decreases, y increases.
The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant +4, what are the first five terms of the sequence? ___, ___, 26, 40, ___
10, 16, 26, 40, 58; First difference: +6, +10, +14, +18; Second difference: +4
Evaluate: 4[(3 + 2 * 3) - 5] + 7
23
The local ice skating rink costs $5 to rent skates and $3 per hour. Jean has $45. How many full hours can she skate? Write an equation to represent the situation and answer the question.
45 = 3h + 5; h = 13.33333; Jean can skate for 13 hours and she will have $1 left.
Solve the equation: 4n + 1 = 12 + 5n
n = -11
What is the difference between an expression and an equation?
Equation has an = sign. Usually you have to solve an equation and simplify an expression.
Find the equation for the pattern (x,y). (0,45), (1,43), (2,41), (3,39); y = ___x + ___
y = -2x + 45; Note: Pattern is -2
Insert inclusion symbols to make the equation true. 108 - 17 * 2 + 3 = 23
108 - 17 * (2 + 3) = 23
The Goldstein family lives in a farmhouse that has a 1000-gallon water tank. The family uses 80 gallons of wtaer per day. Write an equation to represent how many days the family will have enough water. g = number of gallons d = number of days
g = 1000 - 80d
Solve the equation: 3(2r - 1) + 5 = 5(r + 1) what dose r equal
r = 3
Give an example of 3 situations representing a positive correlation, a negative correlation, and no correlation. Draw a simple graph for each.
Answers will vary.
Find the equation for the pattern. Use the equation to find the 10th term in the pattern. x=1, 2, 3, 4,...10; y=25, 29, 33, 37,...?
y = 4x + 21; 10th term (or when x = 10): y = 61
Evaluate if a = 6 and b = -3: 3b^2 + (2a)^2 - |ab|
153
A rectangular rug has a length of 3x and a width of 5x+2. Write two expressions to represent the perimeter and area of the rug. Simplify both expressions.
Perimeter = 16x + 4; Area = 15x^2 + 6x
Solve the equation: 2(8y - 7) = 2(3 + 8y) dose this equation have a solution
No solution
Make a table of values for the expression 3x - 2 (for x=1, 2, 3, 4, and 5). Then, draw a graph of the expression by plotting those values.
3x-2 = 1, 4, 7, 10, 13
Long Reach High School's soccer team is purchasing shirts that cost $21 each.They also have to pay a $10 shipping fee. Make a table to represent how much it costs for 1 shirt, 2 shirts, and 3 shirts. Use the table to find a pattern and write an equation to represent the situation.How many shirts can they get if they have raised $325?
Equation: C = 21s + 10; They can buy 15 shirts.
Evaluate the expression if a = -3, b = 5, and c = -4: [3a^3 + (b-c)] / |ab|
6
Fitness experts say that while working out, the optimal heart rate is between 65% and 85% of your maximum heart rate in beats per minute (bpm). You can estimate your maximum heart rate by subtracting your age, in years, from 220. Write an expression to represent the UPPER limit of the optimal training zone for a person of age "a".
0.85 (220 - a)
Solve the equation: (Answer in simplest form) 6 - (t/4) = 8 + (t/2)
what equals to t
t = -8/3
Create a word problem to represent this expression: 4(5x + 3)
Answers will vary.