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| Section | Weight | Objectives |
|---|---|---|
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Simplifying radical expressions - Properties of exponents - Solving quadratic equations |
| Systems of Equations and Inequalities | 15% | - Applications of systems - Graphical solutions - Solving by substitution and elimination |
| Graphing and Functions | 25% | - Coordinate plane and plotting points - Slope and equations of lines - Linear functions and their graphs - Function notation and evaluation |
| Algebraic Expressions and Operations | 20% | - Operations with polynomials - Order of operations - Simplifying and evaluating expressions - Variables, constants, and coefficients |
| Linear Equations and Inequalities | 25% | - Real-world applications - Solving and graphing inequalities - Solving single-variable equations |
>> Positive Applied-Algebra Feedback <<
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NEW QUESTION # 52
The graph shows the number of people watching a live video. The number of minutes since the video began is on the horizontal axis, and the number of viewers is on the vertical axis. When were there 432 viewers?
Exhibit:
Answer: D
Explanation:
This problem requires reading a value from a graph. The horizontal axis gives time in minutes, and the vertical axis gives the number of viewers. To solve it, find 432 on the vertical axis, locate where the graph reaches that value, and then move down to the horizontal axis. From the exhibit, the graph reaches 432 viewers at minute 1. That means the ordered pair is approximately (1, 432), so the input is 1 minute and the output is 432 viewers. The other listed minutes correspond to different viewer counts on the graph. In graphical depictions, matching the correct input-output pair is the key step. Therefore, the correct answer is B.
NEW QUESTION # 53
The function d(x)=14+65xrepresents the distance, in meters, from a tower to an object at time x, in seconds.
What is the value of d(1.5)?
Answer: A
Explanation:
We are given the function:
d(x)=14+65x
This is a linear function because it has the form:
d(x)=mx+b
where 65is the rate of change and 14is the starting value.
We need to find:
d(1.5)
That means substitute x=1.5into the function:
d(1.5)=14+65(1.5)
Now multiply:
65(1.5)=97.5
Then add:
d(1.5)=14+97.5
d(1.5)=111.5
So the distance from the tower to the object at 1.5seconds is:
111.5 " meters "
NEW QUESTION # 54
As a drone travels away from an operator, the function G(x)=24+47x models the distance, in yards, between the drone and the operator at x minutes. What is the value of G(1.9)?
Answer: C
Explanation:
This is a linear function evaluation problem. The function G(x)=24+47x gives the drone's distance from the operator after x minutes. The constant 24 is the starting distance, and 47 is the rate of change in yards per minute. To evaluate G(1.9), substitute 1.9 for x. Then compute G(1.9)=24+47(1.9). Multiplying first gives
47×1.9=89.3. Adding 24 gives 113.3. Because the function measures distance in yards, the result means the drone is 113.3 yards from the operator after 1.9 minutes. The other options do not result from correctly substituting 1.9 into the function. Therefore, the correct answer is D.
NEW QUESTION # 55
The function P(t)represents the daily profit, in hundreds of dollars, for a hardware store since opening. The graph of P(t)is shown.
How should the maximum value be interpreted?
Answer: C
Explanation:
The graph shows P(t), where:
t= " years since opening "
and
P(t)= " daily profit in hundreds of dollars "
The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.
From the graph, the highest point occurs at approximately:
t=9
So the maximum daily profit happened approximately:
9 " years after opening "
The vertical value at this maximum point is approximately:
P(t)=29
But the graph measures profit in hundreds of dollars, so:
29×100=2900
Therefore, the maximum daily profit was approximately:
$2,900
So the correct interpretation is:
" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "
NEW QUESTION # 56
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 # 57
......
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