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| Section | Objectives |
|---|---|
| Topic 1: Linear Functions and Systems | - Linear Equations
|
| Topic 2: Functions and Graphs | - Function Concepts
|
| Topic 3: Foundations of Algebra | - Equations and Inequalities
|
| Topic 4: Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Topic 5: Polynomial and Rational Expressions | - Polynomials
|
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NEW QUESTION # 101
The function F(n) represents the relationship between the number of animals in two enclosures, where n is the number of animals in enclosure A and F is the number of animals in enclosure B. The number of animals in enclosure B is 20 more than the number of animals in enclosure A.
Which function represents this situation?
Answer: B
Explanation:
The function F(n) gives the number of animals in enclosure B.
The input n represents the number of animals in enclosure A.
The problem says enclosure B has 20 more animals than enclosure A. The phrase "20 more than" means we add 20:
F(n)=n+20
For example, if enclosure A had 30 animals, then enclosure B would have:
F(30)=30+20=50
So the function that represents the situation is:
F(n)=n+20
NEW QUESTION # 102
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 # 103
The graph shows the number of user accounts on a social media website over time.
When did the number of user accounts reach 4,500?
Answer: B
Explanation:
The graph represents the number of user accounts over time.
The horizontal axis represents:
" Time in months "
The vertical axis represents:
" Number of user accounts "
We need to find when the number of user accounts reached:
4,500
On the vertical axis, 4,500is halfway between:
3,000
and
6,000
So we look for the point where the blue curve reaches that height.
From the graph, the curve reaches approximately 4,500user accounts at:
x#2.0
That means the website had about 4,500user accounts after approximately:
2.0 " months "
NEW QUESTION # 104
The graph shows the value, O, in dollars, of an investment account over time.
What represents the value of the account after 8 years?
Answer: C
Explanation:
The graph shows the total value of an investment account as time increases.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Total value in dollars "
We need to find the value of the account after:
8 " years "
From the graph, when t=8, the curve is slightly above $2,200. The closest answer choice is:
$2,221.12
So the value of the account after 8 years is approximately:
$2,221.12
Therefore, the correct answer is:
# ( " D " )
NEW QUESTION # 105
A cart is being loaded with boxes, and each box has the same weight. After 4 boxes are loaded, the total weight of the boxes and cart is 116 pounds. After 9 boxes are loaded, the total weight is 161 pounds.
What is the weight of each box?
Answer: C
Explanation:
This situation can be modeled with a linear relationship because each box has the same weight.
We are given:
4 " boxes " #116 " pounds "
and
9 " boxes " #161 " pounds "
The weight increases because more boxes are added.
First, find the change in total weight:
161-116=45
Then find the change in the number of boxes:
9-4=5
Since 5 additional boxes increased the total weight by 45 pounds, the weight of each box is:
45/5=9
So each box weighs:
9 " pounds "
Check:
If each box weighs 9 pounds, then adding 5 more boxes adds:
5(9)=45
116+45=161
This matches the given information.
NEW QUESTION # 106
......
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