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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Systems of Equations and Inequalities | 15% | - Applications of systems - Graphical solutions - Solving by substitution and elimination |
| Topic 2: Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Simplifying radical expressions - Properties of exponents - Basic quadratic graphs |
| Topic 3: Linear Equations and Inequalities | 25% | - Solving and graphing inequalities - Solving single-variable equations - Real-world applications |
| Topic 4: Graphing and Functions | 25% | - Coordinate plane and plotting points - Function notation and evaluation - Slope and equations of lines - Linear functions and their graphs |
| Topic 5: Algebraic Expressions and Operations | 20% | - Operations with polynomials - Variables, constants, and coefficients - Simplifying and evaluating expressions - Order of operations |
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NEW QUESTION # 65
The function f(z) represents the relationship between the number of units in two inventories, where z is the number of units in inventory A and f(z) is the number of units in inventory B. The number of units in inventory B is 2 more than the number of units in inventory A. Which function represents this situation?
Answer: D
Explanation:
This problem translates a verbal statement into function notation. The variable z represents the number of units in inventory A, and f(z) represents the number of units in inventory B. The phrase "2 more than" tells us to add 2 to the number of units in inventory A. That gives the rule f(z)=z+2. For example, if inventory A has
10 units, then inventory B has f(10)=12 units. Option A subtracts 2, option C multiplies by 2, and option D divides by 2, so those do not match the stated relationship. Because inventory B is always exactly 2 more than inventory A, the correct function is f(z)=z+2. Therefore, the answer is B.
NEW QUESTION # 66
The number of property sales in a region this year is expected to be 9 more than the number of property sales in the region last year. The function H(x) represents the number of property sales this year, where x represents 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 140?
Answer: A
Explanation:
This question asks for correct function notation. The input x represents the number of properties sold last year, and the output H(x) represents the expected number of property sales this year. Since this year's number is expected to be 9 more than last year's number, the function rule is H(x)=x+9. The problem states that 140 properties were sold last year, so the correct input is x=140. Substituting gives H(140)=140+9=149. This means that when last year's sales were 140, this year's expected sales are 149. The input must be inside the parentheses, and the output must follow the equals sign. Therefore, the correct answer is B.
NEW QUESTION # 67
The graphed function n(t)represents the number of people, n, at a park thours after 8:00 a.m. The plotted points Aand Bhave coordinates (2#110)and (6#182).
Which statement gives the correct interpretation of the average rate of change of the number of people over the interval from point Ato point B?
Answer: B
Explanation:
The average rate of change measures how much the output changes per one unit of input.
Here:
t= " hours after 8:00 a.m. "
and
n(t)= " number of people at the park "
The two given points are:
A=(2,110)
and
B=(6,182)
This means:
At t=2hours after 8:00 a.m., there were 110people at the park.
At t=6hours after 8:00 a.m., there were 182people at the park.
Now calculate the average rate of change:
" Average rate of change " =(182-110)/(6-2)
=72/4
=18
Because the value is positive, the number of people is increasing.
So the correct interpretation is:
" The number of people at the park increases at an average rate of 18 people per hour. "
NEW QUESTION # 68
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: B
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 # 69
The number of people auditioning for a game show is expected to be 4 times the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 330 people auditioned last year?
Answer: B
Explanation:
We are told that the number of people expected to audition this year is 4 times the number of people who auditioned last year.
Let:
t=number of people who auditioned last year
and
A(t)=number of people expected to audition this year
Since this year's number is 4 times last year's number, the function is:
A(t)=4t
The question says that 330 people auditioned last year, so:
t=330
Now substitute 330 into the function:
A(330)=4(330)
A(330)=1320
So, the correct function notation is:
A(330)=1,320
This means: when 330 people auditioned last year, 1,320 people are expected to audition this year.
Therefore, the correct answer is:
B
NEW QUESTION # 70
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