By definition, the average rate of change is given by:
We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:
Evaluating for x = 3:
Then, the AVR is:
For f (x) = 3x - 8:
Evaluating for x =4:
Evaluating for x = 5:
Then, the AVR is:
For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:
Evaluating for x = 4:
Then, the AVR is:
For f (x) = x ^ 2 - 5:
Evaluating for x = -1:
Evaluating for x = 1:
Then, the AVR is:
Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]
A parallelogram.
All the angles in a parallelogram must add up to 360° as well as the exterior angles.
Hope that helps!
:D®
Let number of yellow marbles = x
Let number of red marbles = y
Let number of blue marbles = z
Given that Finley has 152 yellow, red, and blue marbles in a bag.
So we get equation:
x+y+z=152...(i)
"He has seven more red marbles than yellow marbles" means:
y=x+7...(ii)
"three times as many blue marbles as yellow marbles." means:
z=3x...(iii)
Now we just need to solve those equations to find the answer.
Plug (ii) and (iii) into (i)
x+(x+7)+(3x)=152
x+x+7+3x=152
Which looks similar to choice (B)
5x+7=152
5x=145
x=29
Hence final answer is choice B.
Required equation is
x+x+7+3x=152
Number of yellow marbles = 29
Use 7 scale point.
132/20 = 6.6
to its better to use more than 6.6 scale. to make it easier use 7, so to avoid decimals
<span>When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.</span>
