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:
Here is the full proof:
AC bisects ∠BCD Given
∠CAB ≅ ∠CAD Definition of angle bisector
DC ⊥ AD Given
∠ADC = 90° Definition of perpendicular lines
BC ⊥ AB Given
∠ABC = 90° Definition of perpendicular lines
∠ADC ≅ ∠ABC Right angles are congruent
AC = AC Reflexive property
ΔCAB ≅ ΔCAD SAA
BC = DC CPCTC
Since both equations equal Y, set them equal to each other and solve.
3x -1 = -2x +9
Add 2x to each side:
5x - 1 = 9
Add 1 to each side:
5x = 10
Divide both sides by 5:
x = 10/5
x = 2
Now replace x with 2 and solve for y:
y = 3(2) -1 = 6-1 = 5
x = 2, y = 5 (2,5)