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| Section | Weight | Objectives |
|---|---|---|
| Exponents, Radicals, and Quadratic Relationships | 15% | - Properties of exponents - Solving quadratic equations - Basic quadratic graphs - Simplifying radical expressions |
| Systems of Equations and Inequalities | 15% | - Applications of systems - Solving by substitution and elimination - Graphical solutions |
| Linear Equations and Inequalities | 25% | - Real-world applications - Solving and graphing inequalities - Solving single-variable equations |
| Graphing and Functions | 25% | - Coordinate plane and plotting points - Linear functions and their graphs - Slope and equations of lines - Function notation and evaluation |
| Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Order of operations - Operations with polynomials - Variables, constants, and coefficients |
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NEW QUESTION # 118
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 # 119
The number of registered voters in a district is modeled by a decreasing exponential function, where x represents the number of years since 2005 and f(x) represents the number of registered voters.
Which interval is associated with the slowest average decrease in the number of registered voters?
Answer: A
Explanation:
A decreasing exponential function falls quickly at first and then levels off over time. The "slowest average decrease" occurs where the graph is flattest, because the output changes by the smallest amount per year.
Earlier intervals, such as 2005 to 2008, occur when the graph is steepest, so those intervals have a faster average decrease. Later intervals occur after the exponential decay has slowed. From the graph, the interval from 2015 to 2025 is farthest to the right and has the least steep downward trend. Therefore, the number of registered voters decreases most slowly during that interval. This is why the correct answer is D.
NEW QUESTION # 120
The number of property sales in a region this year is expected to be 6 less than the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 330?
Answer: A
Explanation:
We are told that this year's number of property sales is 6 less than last year's number of property sales.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 6 less than last year's sales, the function rule is:
H(x)=x-6
The question says that the number of properties sold last year was:
x=330
Substitute 330into the function:
H(330)=330-6
H(330)=324
So the notation that correctly represents the number of property sales this year is:
H(330)=324
This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.
NEW QUESTION # 121
The values, in dollars, of two accounts over time are modeled by
A_1 (t)=6,500× # 1.05 #
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