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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Graphing and Functions | 25% | - Function notation and evaluation - Linear functions and their graphs - Coordinate plane and plotting points - Slope and equations of lines |
| Topic 2: Exponents, Radicals, and Quadratic Relationships | 15% | - Simplifying radical expressions - Solving quadratic equations - Properties of exponents - Basic quadratic graphs |
| Topic 3: Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Graphical solutions - Applications of systems |
| Topic 4: Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Operations with polynomials - Order of operations - Variables, constants, and coefficients |
| Topic 5: Linear Equations and Inequalities | 25% | - Real-world applications - Solving single-variable equations - Solving and graphing inequalities |
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NEW QUESTION # 59
The population of fish in a lake is changing according to the function
P(t)=24t+185
where tis the number of months since the beginning of the year and P(t)is the fish population at time t.
Which interpretation of the rate of change is correct?
Answer: D
Explanation:
The function is:
P(t)=24t+185
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In the function:
P(t)=24t+185
the coefficient of tis:
24
So the rate of change is:
24 " fish per month "
Because 24is positive, the fish population is increasing.
The number 185is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=24(0)+185=185
Therefore, the correct interpretation is:
" The number of fish in the lake is increasing at a constant rate of 24 fish per month. " So the correct answer is:
# ( " B " )
NEW QUESTION # 60
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: D
Explanation:
The graph compares the populations of two towns over time.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Population in thousands "
The graph shows:
Town A as the solid blue line.
Town B as the dashed blue line.
To determine which town's population is growing faster, we compare the slopes of the two lines.
In Applied Algebra, the slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
" Town A grows at about " 0.9 " thousand people per year "
" Town B grows at about " 1.6 " thousand people per year "
Now compare the growth rates:
1.6 > 0.9
So Town B's population is growing at a faster rate.
The values 8.0and 6.5describe starting populations, not growth rates. Since the question asks about growing at a faster rate, we must compare the slopes.
NEW QUESTION # 61
The graph shows the total cost of a lumber delivery based on the number of identical boards ordered.
What is the cost of each additional board?
Answer: A
Explanation:
The graph shows a linear relationship between:
" Number of boards "
and
" Total cost "
The cost of each additional board is the rate of change, or slope, of the line.
From the graph, two labeled points are:
(0#27)
and
(10#177)
This means:
When 0 boards are ordered, the total cost is $27.
When 10 boards are ordered, the total cost is $177.
Now calculate the slope:
m=(177-27)/(10-0)
m=150/10
m=15
So each additional board costs:
$15
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 62
A set of data was gathered and used to create a model for the number of subscribers to a blog. The function model is f(x)=190× # 0.99 #
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