1. Solve 2x + b = c for x.
2x + b - b= c - b subtract b from both sides
2x = c - b combine like terms/simplify
2x - 2= c - b - 2 subtract 2 from both sides to get x isolated
x = c - b - 2 simplify/final answer
The above process has an error. What is the mistake?
What is the correct final answer?
2. Given the function:
y = 3x2 − 10
What can replace y?
What is the range if the domain value is 3?
3.Given f(x) = −2x2 + 5, evaluate f(4)
4.Which of the following can be used to find the slope between two points?
What is the slope of the line that connects the points (3, 2) and (6, 10)?
5.The table below shows the number of jumping jacks completed after a given period of time in minutes.
Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200
Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
What is the slope of the line that connects the 3rd and 4th point?
What is the slope of the line that connects the 1st and the 4th point?
Is the common difference (aka slope aka rate of change) constant?
Why is it or is it not constant?
1. The mistake in the process used to solve 2x + b = c for x is that when subtracting b from both sides, the terms should cancel out. So the correct step would be:
2x + b - b = c - b
2x = c - b
The correct final answer is x = (c - b) / 2.
2. In the given function y = 3x^2 - 10, any value can replace y because y represents the output or dependent variable of the function.
To find the range when the domain value is 3, we substitute x = 3 into the function and calculate the corresponding y value:
y = 3(3^2) - 10
y = 3(9) - 10
y = 27 - 10
y = 17
Therefore, when the domain value is 3, the range value is 17.
3. To evaluate f(4) in the function f(x) = -2x^2 + 5, we substitute x = 4 into the function:
f(4) = -2(4^2) + 5
f(4) = -2(16) + 5
f(4) = -32 + 5
f(4) = -27
Therefore, f(4) = -27.
4. The slope between two points can be found using the formula:
slope = (change in y) / (change in x)
Given the points (3, 2) and (6, 10), we can calculate the slope:
slope = (10 - 2) / (6 - 3)
slope = 8 / 3
Therefore, the slope of the line that connects the points (3, 2) and (6, 10) is 8/3.
5. The common difference in the jumping jacks sequence is the difference between consecutive terms. In this case, the sequence increases by 50 each time, so the common difference is 50.
Considering the table as a set of ordered pairs, the first two points are (1, 50) and (2, 100). To find the slope between these points, we can use the slope formula:
slope = (change in y) / (change in x)
slope = (100 - 50) / (2 - 1)
slope = 50 / 1
slope = 50
Therefore, the slope of the line that connects the first two points is 50.
The slope between the third and fourth point can be calculated as:
slope = (200 - 150) / (4 - 3)
slope = 50 / 1
slope = 50
So, the slope of the line that connects the third and fourth point is also 50.
The slope between the first and fourth point can be calculated as:
slope = (200 - 50) / (4 - 1)
slope = 150 / 3
slope = 50
Therefore, the slope of the line that connects the first and fourth point is again 50.
Yes, the common difference (slope) is constant. In this case, the common difference (50) represents the rate of change, and since it remains the same throughout, the rate of change is constant.
The common difference is constant because each jump in the sequence increases by the same amount (50) for every increase in time (minutes). This indicates a consistent rate of change, resulting in a constant common difference (slope).