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| Section | Weight | Objectives |
|---|---|---|
| Systems of Equations and Inequalities | 15% | - Graphical solutions - Solving by substitution and elimination - Applications of systems |
| Graphing and Functions | 25% | - Linear functions and their graphs - Coordinate plane and plotting points - Slope and equations of lines - Function notation and evaluation |
| Algebraic Expressions and Operations | 20% | - Operations with polynomials - Simplifying and evaluating expressions - Order of operations - Variables, constants, and coefficients |
| Linear Equations and Inequalities | 25% | - Real-world applications - Solving single-variable equations - Solving and graphing inequalities |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Simplifying radical expressions - Solving quadratic equations - Properties of exponents |
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NEW QUESTION # 132
Consider the graph of h(t) shown. The function represents the height, h, in feet, of a ball t seconds after being launched.
What is the point, if any, at which the concavity changes from concave down to concave up?
Answer: A
Explanation:
The graph represents the height of a launched ball over time. Such height functions are typically quadratic because gravity causes the ball to rise, slow down, reach a maximum height, and then fall. The graph shown is a downward-opening parabola. A downward-opening parabola is concave down for its entire domain.
Concavity changes only if the curve switches from bending downward to bending upward, or from bending upward to bending downward. Since this graph bends downward the entire time, there is no point where the concavity changes from concave down to concave up. The vertex is a maximum point, but it is not a change in concavity. Therefore, the correct statement is that the graph is always concave down.
NEW QUESTION # 133
The number of property sales in a region this year is expected to be 8 times 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 360?
Answer: B
Explanation:
We are told that the number of property sales this year is expected to be 8 times the number of property sales last year.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 8 times last year's sales, the function rule is:
H(x)=8x
The question says that last year's property sales were:
x=360
Substitute 360into the function:
H(360)=8(360)
H(360)=2,880
So the correct notation is:
H(360)=2,880
This means: if 360 properties were sold last year, then 2,880 property sales are expected this year.
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 134
A coach is placing an order for team shirts. The graph shows the total cost based on the number of shirts.
What is the cost of each additional shirt?
Answer: D
Explanation:
This question asks for the cost of each additional shirt, which means we need to find the rate of change of the linear function.
On a graph, the rate of change is the slope:
" slope " = " change in total cost " / " change in number of shirts "
From the graph, two labeled points are:
(0#33)
and
(10#173)
This means:
When 0shirts are ordered, the cost is $33.
When 10shirts are ordered, the cost is $173.
Now find the slope:
m=(173-33)/(10-0)
m=140/10
m=14
So the cost increases by:
$14
for each additional shirt.
The $33represents a fixed starting cost, not the cost per shirt.
NEW QUESTION # 135
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: C
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 # 136
A team was assembled at a manufacturing plant in order to boost productivity. The team was tasked with producing as many widgets each day as possible. The results are shown in the graph.
What is the correct interpretation of the average rate of change from day 6 to day 14?
Answer: A
Explanation:
The graph models the number of widgets the team can produce each day.
The horizontal axis represents:
" days "
The vertical axis represents:
" widgets "
The graph gives two labeled points:
(6#3.4)
and
(14#23)
The average rate of change is:
" change in widgets " / " change in days "
Substitute the values:
(23-3.4)/(14-6)
=19.6/8
=2.45
Rounded to the nearest tenth:
2.5
This means the team increased production by an average of approximately:
2.5 " widgets each day "
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 137
......
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