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| Section | Weight | Objectives |
|---|---|---|
| Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Applications of systems - Graphical solutions |
| Linear Equations and Inequalities | 25% | - Solving single-variable equations - Real-world applications - Solving and graphing inequalities |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Properties of exponents - Basic quadratic graphs - Solving quadratic equations - Simplifying radical expressions |
| Graphing and Functions | 25% | - Function notation and evaluation - Coordinate plane and plotting points - Slope and equations of lines - Linear functions and their graphs |
| Algebraic Expressions and Operations | 20% | - Variables, constants, and coefficients - Simplifying and evaluating expressions - Operations with polynomials - Order of operations |
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NEW QUESTION # 44
The graph shows the progress of a manufacturing team, modeling the number of widgets the team is able to produce each day since the team was formed.
How should the average rate of change from day 16 to day 18 be interpreted?
Answer: A
Explanation:
The graph models the number of widgets the manufacturing team can produce each day.
The horizontal axis represents:
" Days "
The vertical axis represents:
" Widgets produced each day "
The two labeled points are:
(16#9.1)
and
(18#12.4)
This means:
On day 16, the team could produce about 9.1widgets per day.
On day 18, the team could produce about 12.4widgets per day.
The average rate of change is:
(12.4-9.1)/(18-16)
=3.3/2
=1.65
Rounded to the nearest tenth:
1.7
So from day 16 to day 18, the team's production increased by an average of about:
1.7 " widgets each day "
NEW QUESTION # 45
A contractor charges a flat rate plus a fixed rate per hour to come and make repairs. For a job that takes 3 hours, the contractor charges $220. For a job that takes 5 hours, the contractor charges $340.
Which function correctly represents the total charge Cfor a job that takes thours?
Answer: A
Explanation:
The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:
C(t)=mt+b
where:
m= " hourly rate "
and
b= " flat rate "
We are given two points:
(3#220)
and
(5#340)
These mean:
A 3-hour job costs $220.
A 5-hour job costs $340.
First, find the hourly rate using slope:
m=(340-220)/(5-3)
m=120/2
m=60
So the contractor charges:
$60 " per hour "
Now the function has the form:
C(t)=60t+b
Use the point (3#220)to find the flat rate:
220=60(3)+b
220=180+b
b=40
So the function is:
C(t)=60t+40
Check with t=5:
C(5)=60(5)+40
C(5)=300+40
C(5)=340
This matches the given information.
NEW QUESTION # 46
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: C
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 # 47
The graphed function n(t)represents the number of animals, n, at a feeding station thours after 5:00 a.m. The plotted points Aand Bhave coordinates (1#10.6)and (8#6.59).
Which statement gives the correct interpretation of the average rate of change of the number of animals over the interval from point Ato point B?
Answer: B
Explanation:
The average rate of change tells how much the output changes per one unit of input.
Here:
t= " hours after 5:00 a.m. "
and
n(t)= " number of animals "
The two given points are:
A=(1,10.6)
and
B=(8,6.59)
Use the average rate of change formula:
(y_2-y_1)/(x_2-x_1 )
Substitute the coordinates:
(6.59-10.6)/(8-1)
=(-4.01)/7
#-0.573
The negative sign means the number of animals is decreasing.
So the correct interpretation is:
" The number of animals at the station decreases at an average rate of " 0.573 " animals per hour. " Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 48
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.
What does the horizontal asymptote mean?
Answer: B
Explanation:
The graph shows a decreasing exponential model.
The vertical axis represents:
" Licensed sellers "
The horizontal axis represents:
" Time in years "
The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:
y=100
That horizontal line is the horizontal asymptote.
A horizontal asymptote represents the long-term value the function approaches as time continues.
So the correct interpretation is:
" In the long run, the number of licensed sellers nears 100. "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 49
......
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