What are the first four terms of the sequence represented by the expression n(n – 2) – 3?
To find the first four terms of the sequence represented by the expression n(n – 2) – 3, we need to substitute the first four positive integers (1, 2, 3, and 4) for n and evaluate the expression.
For n = 1:
n(n – 2) – 3 = 1(1 – 2) – 3 = -2
For n = 2:
n(n – 2) – 3 = 2(2 – 2) – 3 = -3
For n = 3:
n(n – 2) – 3 = 3(3 – 2) – 3 = 0
For n = 4:
n(n – 2) – 3 = 4(4 – 2) – 3 = 5
Therefore, the first four terms of the sequence are -2, -3, 0, and 5.
A car traveling at 46 mi/h slows to a speed of 23 mi/h in 5 seconds. It maintains that speed for 5 seconds and then slows to a stop after 5 more seconds. Which graph shows the car’s speed over time?
We can break down the car's motion into three parts:
1. The car slows down from 46 mi/h to 23 mi/h in 5 seconds.
2. The car maintains a constant speed of 23 mi/h for 5 seconds.
3. The car slows down from 23 mi/h to a stop in 5 seconds.
To create a graph of this motion, we can plot the car's speed (in mi/h) on the y-axis and time (in seconds) on the x-axis.
For the first part of the motion, the car's speed is decreasing, so the graph will have a negative slope. It starts at 46 mi/h and ends at 23 mi/h after 5 seconds.
For the second part of the motion, the car's speed is constant, so the graph will be a horizontal line at y = 23.
For the third part of the motion, the car's speed is decreasing again, so the graph will have a negative slope. It starts at 23 mi/h and ends at 0 mi/h after 5 seconds.
Using this information, we can eliminate options A and C right away, since they do not show a constant speed in the second part of the motion.
Option B shows a steep line at the beginning, indicating a rapid decrease in speed, which is accurate for the first part of the motion. It then shows a horizontal line for the constant speed, which is correct. Finally, it shows a less steep line towards the end, indicating a slower decrease in speed, which is also accurate for the third part of the motion. Therefore, Option B is the correct graph for the car's speed over time.
Option D is a bit tricky, as it shows the correct slopes for the first and third parts of the motion. However, it shows a non-zero speed during the second part of the motion, which is incorrect. Therefore, Option D is not the correct graph.
Therefore, the correct graph is Option B.
Which statement describes the speed of the remote-control car over time?
A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
B. The speed of the car increases from 4 mi/h to 2 mi/h in the first 3 seconds, decreases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
C. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 6 mi/h in the next second, and then remains at 6 mi/h for the last 6 seconds.
D. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 5 seconds, and then remains at 5 mi/h for the last 10 seconds.
The correct statement that describes the speed of the remote-control car over time is:
A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
This matches the information given in the graph, where the car initially slows down, then speeds up, and then maintains a constant speed for the last part of the motion.
Given the function rule f(x) = x² – 5x + 1, what is the output of f(–3)?
A. 7
B. –5
C. 25
D. 5
Given the function rule f(x) = x² – 5x + 1, we need to find the output of f(-3), which means we need to substitute -3 for x in the expression for f(x) and evaluate.
f(-3) = (-3)² - 5(-3) + 1
= 9 + 15 + 1
= 25
Therefore, the output of f(-3) is 25.
Hence, the option is (C).
Suppose you earn $15 for each car you wash. Which function describes the relationship between your total earnings E and the number of cars you wash, c?
A. E(c) = c + 15
B. E(c) = 15c
C. c = 15E
D. E(c) = c – 15
Since you earn $15 for each car you wash, your total earnings E will be equal to 15 times the number of cars you wash, c.
Therefore, the function that describes the relationship between your total earnings E and the number of cars you wash, c, is:
B. E(c) = 15c
Option B states that E(c) (total earnings) is equal to 15c (15 times the number of cars you wash). This is the correct relationship between E and c, so option B is the correct answer.
Hence, the answer is (B).
The data in the table illustrate a linear function.
x –3 0 3 6
y –6 –2 2 6
What is the slope of the linear function? Which graph represents the data?