Graph the equation below by plotting the y-intercept and a second point on the line. Y=3/2x-5
2 answers:
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The only interval with a negative rate of change is the last one:
[1, 2.5]
<h3>When the rate of change is negative?</h3>
For an interval (a, b) and a function f(x), the rate of change is defined as:
So the rate of change is only negative when the function evaluated on the first value of the interval is larger than the function evaluated in the second one.
For example, on the interval [1, 2.5} we can see that:
f(1) = 3
f(2.5) = -1
Then on this interval, the rate of change will be negative, meaning that this is the correct option.
If you want to learn more about rates of change, you can read:
Answer:
The coordinates of the vertices of the reflected figure are :
R' is (-3 , -7), S' is (5 , -3), T' is (6 , 5) ⇒the right answer is figure (a)
Step-by-step explanation:
* Lets study the matrices of the reflection
- The matrix of the reflection across the x-axis is
- Because when we reflect any point across the x-axis we
change the sign of the y-coordinate
- The matrix of the reflection across the y-axis is
- Because when we reflect any point across the y-axis we
change the sign of the x-coordinate
* Now lets solve the problem
- We will multiply the matrix of the reflection across the x-axis
by each point to find the image of each point
- The dimension of the matrix of the reflection across the x-axis
is 2×2 and the dimension of the matrix of each point is 2×1,
then the dimension of the matrix of each image is 2×1
∵ Point R is (-3 , 7)
∴
∴ R' is (-3 , -7)
∵ Point S is (5 , 3)
∴
∴ S' is (5 , -3)
∵ Point T is (6 , -5)
∴
∴ T' is (6 , 5)
* Look to the answer and find the correct figure
- In figure (d) R' is (-3 , -7), S' is (5 , -3), T' is (6 , 5)
∴ The right answer is figure (a)