Algebra & Modeling 1
You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per mile. Let m represent the number of miles ridden. Write an inequality to determine how many miles you can ride for $20.
What is: 5 + 2.50
The perimeter of a rectangle is given by the equation:
What is P - 2W / 2
Consider the relation below:
(4, 5) (-2, 3) (0, -2) (1, 2) (-6, 1) ( 2, 2) (7, 8) (-3, 6) (-4, 6) (9,-2)
Is the relation a function? Explain your reasoning.
What is yes: The relation is a function because every x or input maps to exactly one y or output.
Solve y2 − 3y = 28
What is x = -4 and x = 7; are zeros of the function
Rewrite the expression
What is x = 1?
A plot of land for sale has a width of
What is:
Love the inequality:
−4
What is x > -3?
Josie decided to save her birthday money and her weekly allowance to buy an iPad. Her weekly totals were $45, $57, $69, $81, $93, . . . Which type of function is represented by this sequence?
A. Absolute value function B. Exponential function C. Linear function. D. Quadratic function
What is C, a linear function
The mouse population is 25,000 and is decreasing in size at a rate of 20% per year. Would this situation be modeled by a linear or exponential function and why?
A) Linear; 20% decrease at a constant rate
B) Linear; 0.2 decrease at a constant rate
C) Exponential; 0.20 rate of decay
D) Exponential; 0.20 rate of growth
What is C: Exponential; 0.20 rate of decay?
In Lewis Carroll’s Through the Looking Glass, Tweedledum says, “The sum of your weight and twice mine is 361 pounds.” Tweedledee replies, “The sum of your weight and twice mine is 362 pounds.” Let x = the number of pounds Tweedledee weighs, and let y = the number of pounds Tweedledum weighs. Write a systems of equations that represents this situation.
What is: x + 2y = 361 and y + 2x = 362
Solve the following equation for x
What is
In a basketball tournament 64 teams compete in Round 1. Half of those teams proceed to Round 2. The number of teams at the beginning of each round can be represented by the sequence 64, 32, 16, 8, . . . Which type of function is represented by this sequence?
A. Absolute value function B. Exponential function C. Linear function D. Quadratic function
What is an Exponential function?
The cost of a taxi ride includes a $3 fee plus $2 for each mile traveled. So, a 1-mile ride costs $5 and a 2-mile ride costs $7. Is the rate of change constant for the problem? What is the rate of change?
What is Yes; $2?
You are purchasing jeans and T-shirts. Jeans cost $35 and T-shirts $15. You plan on spending $115 dollars and purchasing a total of 5 items.
Write a system of equations that could be used to solve the problem.
What is: 35x + 15y = $115 and x + y = 5
Solve this system of equations using elimination.
- 3x - 14y = - 95
- 18x - 42y = - 24
What is ( -3, 1)
Melina receives a chain e-mail that she forwards to 7 of her friends. Each of her friends forwards it to 7 of their friends. The process continues.
What is the domain of the function in relation to the context of the problem? Explain your answer.
What is {1, 2, 3, 4 . . .} or the set of natural numbers. The domain is limited to the natural numbers because you cannot have part of a friend.
A car is traveling down a long, steep hill. The elevation, E, above sea level (in feet) of the car when it is d miles from the top of the hill is given by E = 7500 – 250d.
What is the y-intercept and what does it mean in the context of this problem?
What is y-intercept: (0, 7500). Car starts out at 7500 feet in elevation?
The length of a rectangular garden is 4 meters more than 3 times its width. The perimeter of the garden is 48 meters.
The length and width of the garden is...
What is: 5 meters by 19 meters.
Factor the binomial x4 - y4 completely
What is (x2 + y2) (x + y) (x - y)
Ms. Harris has a taco stand. She has found that her daily costs are approximated by the following function: C(x) = x2 – 40x + 610.
Complete the square to find the vertex of C(x).
What are (x - 20)2 + 210 or (20 , 210)
Suppose a male and a female of a certain species of animal were taken to a deserted island. The population is modeled by f(n) = 2(4)n.
What does the 2 represent in the model in terms of the context of the problem?
What does the 4 represent in the model in term of the context of the problem?
What is the initial value and what is the rate of growth?