Answer:
9
Step-by-step explanation:
Equation
Sum = s = 180*(n - 2)
Solution
1260 = 180*(n - 2) Divide by 180
1260 / 180 = 180 * (n -2 ) / 180
7 = n - 2 Add 2 to both sides
9 = n
Answer
The polygon has 9 sides.
Because completementary angles add up to 180 degrees (angle 3 and angle 4)
and interior angles of a triangle will also add up to 180 degrees
if you compare these two facts, then angle 4 equals the 2 non adjacent interior angles
I believe it is DC
180 degrees is about halfway, so DC definitely captures that.
Answer:
g(x) = (x-3)³ is the transformed function.
Step-by-step explanation:
Horizontal shift:
If f(x) is the parent function.
Then horizontal shift can be expressed as:
, will shift left units.
, will shift 
right c units.
Given the parent function
f(x) = x³
From the graph, it is clear that the transformed function is indicating that the parent function has been horizontally shifted right 3 units.
Therefore, according to the rule, :
g(x) = (x-3)³ is the transformed function.
From the graph,
- The Red graph indicates the parent function i.e. f(x) = x³
- The Blue graph indicates the transformed function i.e. g(x) = (x-3)³
It is clear that the blue graph is obtained when the parent function has been horizontally shifted right 3 units.
Therefore, g(x) = (x-3)³ is the transformed function.
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29
We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)
We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify
The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
