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| Section | Weight | Objectives |
|---|---|---|
| Linear Equations and Inequalities | 25% | - Real-world applications - Solving single-variable equations - Solving and graphing inequalities |
| Algebraic Expressions and Operations | 20% | - Order of operations - Operations with polynomials - Simplifying and evaluating expressions - Variables, constants, and coefficients |
| Graphing and Functions | 25% | - Slope and equations of lines - Linear functions and their graphs - Coordinate plane and plotting points - Function notation and evaluation |
| Systems of Equations and Inequalities | 15% | - Graphical solutions - Solving by substitution and elimination - Applications of systems |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Simplifying radical expressions - Properties of exponents - Solving quadratic equations |
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NEW QUESTION # 125
The graph shows the number of trees sold by a nursery, where the number of days since the beginning of the month is along the horizontal axis and the number of trees sold per day is along the vertical axis. The greatest number of trees are sold when the temperature is over 70°F.
When was the temperature likely over 70°F?
Answer: A
Explanation:
The problem states that the greatest number of trees are sold when the temperature is over 70°F. Therefore, we need to identify the days on the graph when tree sales are highest. The graph shows two major peaks in the number of trees sold per day. These peaks occur around day 2 and day 10. Since higher tree sales are linked to temperatures over 70°F, those two days are the most likely days when the temperature exceeded 70°F. Day 6 appears near a low point, so it is not likely associated with high temperature based on the given relationship.
Day 12 also does not match the main peaks. Therefore, the correct answer is C.
NEW QUESTION # 126
The population of fish in a lake is changing according to the function P(t)=31t+438, where t is 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: C
Explanation:
The function P(t)=31t+438 is linear and follows the form P(t)=mt+b. In this form, m is the rate of change and b is the initial value. Here, the coefficient of t is 31, so the fish population changes by 31 fish per month.
Because 31 is positive, the population is increasing rather than decreasing. The number 438 is the initial fish population at the start of the year, not the rate of change. Therefore, the correct interpretation is that the number of fish in the lake is increasing at a constant rate of 31 fish per month. That matches option A.
NEW QUESTION # 127
The graph shows the estimated wait time, in minutes, based on the number of hours after 7:00 a.m.
What is the average rate of change of the wait time from point Ato point B?
Answer: C
Explanation:
The average rate of change tells us how much the output changes, on average, for each 1-unit increase in the input.
Here:
x= " hours after 7:00 a.m. "
and
y= " estimated wait time in minutes "
From the graph, point Ais approximately:
A=(5,88.3)
and point Bis approximately:
B=(9,65)
Now use the average rate of change formula:
" Average rate of change " =(y_2-y_1)/(x_2-x_1 )
Substitute the values:
(65-88.3)/(9-5)
=(-23.3)/4
=-5.825
Rounded to two decimal places:
-5.83
The negative sign means the estimated wait time is decreasing from point Ato point B.
So the average rate of change is approximately:
-5.83 " minutes per hour "
NEW QUESTION # 128
The graph shows the number of books, N, checked out from a library each week. The number of weeks since the beginning of the year is on the horizontal axis, and the number of books checked out per week is on the vertical axis. Point A represents 165 books checked out in the first week, or N(0)=165. Which statement represents an accurate conclusion?
Exhibit:
Answer: A
Explanation:
This question asks for the correct interpretation of a labeled point on a graph. In function notation, N(x)=y means when the input is x weeks, the output is y books checked out. The exhibit shows several plotted points.
Point B is located at approximately x=2.8 and y=177, so Point B represents N(2.8)=177. To verify a graph statement, both the horizontal coordinate and vertical coordinate must match the actual point on the graph. If either coordinate is wrong, then the statement is not accurate. Since Point B matches the stated coordinates and output value, it is the valid conclusion. Therefore, the correct answer is A.
NEW QUESTION # 129
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 5 sacks are removed, the total weight of the wagon and remaining sacks is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. What is the weight of each sack?
Answer: D
Explanation:
This situation has a constant rate of change because each sack weighs the same amount. After 5 sacks are removed, the total weight is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. From 5 to
9 sacks removed is 4 more sacks. Over the same interval, the total weight decreases by 135#87=48 pounds.
Since 4 sacks account for a 48-pound decrease, each sack must weigh 48÷4=12 pounds. This uses the linear idea that equal changes in the input produce equal changes in the output. Therefore, the weight of each sack is
12 pounds, which is answer A.
NEW QUESTION # 130
......
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