What is the expression
1 answer:
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Answer:
1) Function h
interval [3, 5]
rate of change 6
2) Function f
interval [3, 6]
rate of change 8.33
3) Function g
interval [2, 3]
rate of change 9.6
Step-by-step explanation:
we know that
To find the average rate of change, we divide the change in the output value by the change in the input value
the average rate of change is equal to
step 1
Find the average rate of change of function h(x) over interval [3,5]
Looking at the third picture (table)
Substitute
step 2
Find the average rate of change of function f(x) over interval [3,6]
Looking at the graph
Substitute
step 3
Find the average rate of change of function g(x) over interval [2,3]
we have
Substitute
therefore
In order from least to greatest according to their average rates of change over those intervals
1) Function h
interval [3, 5]
rate of change 6
2) Function f
interval [3, 6]
rate of change 8.33
3) Function g
interval [2, 3]
rate of change 9.6
Answer:
Please check the explanation.
Step-by-step explanation:
- Two lines are parallel if their slopes are equal.
- Two lines are perpendicular if the product of their slope is -1
We also know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept
Given the lines
1)
- y = 6х - 3
Comparing with y=mx+b, the slope of y = 6х - 3:
m₁=6
- y = - 1/6x + 7
Comparing with y=mx+b, the slope of y = - 1/6x + 7:
m₂=-1/6
As
m₁ × m₂ = -1
6 × - 1/6 = -1
-1 = -1
Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.
2)
- y = 3x + 2
Comparing with y=mx+b, the slope of y = 3x + 2:
m₁=3
- 2y = 6x - 6
simplifying to write in slope-intercept form
y=3x-3
Comparing with y=mx+b, the slope of y=3x-3:
m₂=3
As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.
i.e. m₁ = m₂ → 3 = 3
Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.
3)
- 8x - 2y = 3
simplifying to write in slope-intercept form
y = 4x - 3/2
Comparing with y=mx+b, the slope of y = 4x - 3/2:
m₁=4
- x + 4y = - 1
simplifying to write in slope-intercept form
y=-1/4x-1/4
Comparing with y=mx+b, the slope of y=-1/4x-1/4:
m₂=-1/4
As
m₁ × m₂ = -1
4 × - 1/4 = -1
-1 = -1
Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.
4)
- 3x+2y = 5
simplifying to write in slope-intercept form
y = -3/2x + 5/2
Comparing with y=mx+b, the slope of y = -3/2x + 5/2:
m₁=-3/2
- 3y + 2x = - 3
simplifying to write in slope-intercept form
y = -2/3x - 1
Comparing with y=mx+b, the slope of y = -2/3x - 1:
m₂=-2/3
As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.
5)
- y - 5 = 6x
simplifying to write in slope-intercept form
y=6x+5
Comparing with y=mx+b, the slope of y=6x+5:
m₁=6
- y - 6x = - 1
simplifying to write in slope-intercept form
y=6x-1
Comparing with y=mx+b, the slope of y=6x-1:
m₂=6
As the slopes of y - 5 = 6x and y - 6x = -1 are equal.
i.e. m₁ = m₂ → 6 = 6
Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.
6)
- y = 3х + 9
Comparing with y=mx+b, the slope of y = 3х + 9:
m₁=3
- y = -1/3x - 4
Comparing with y=mx+b, the slope of y = 1/3x - 4:
m₂=1/3
As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.