Answers:
- Domain is (-4, 3]
- Range is (-5, 5]
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Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that 
. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is 
. This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.
Let would be the annual interest rate such that,
I = P x r^t
For the 1st
160.67 = (2000) x r*8/12 ; r = 0.02277
The second case is just the same.
Log(2x*12)=3
10^3=2x*12
1000=24x
1000/24=x
x=41.667
Answer:
B
Step-by-step explanation:
hope this helps with the work
Answer:
x = 60
Step-by-step explanation:
Vertical opposite angles are formed when two straight lines intersect each other.
Given that AD and CD are two straight lines intersecting at O, the two vertical opposite formed are, ∠AOD and ∠COB. Therefore:
∠AOD = ∠COB (Vertical opposite angles are congruent)
∠AOE = 90° (right angle)
∠DOE = x
∠COF = 30°
∠BOF = 2x
m∠AOE + m∠DOE = m∠AOD (angle addition postulate)
90 + x = ∠AOD (Substitution)
m∠COF + m∠BOF = m∠COB (Angle addition postulate)
30 + 2x = ∠COB
m∠AOD = m∠COB (vertical opposite angles)
90 + x = 30 + 2x (Substitution)
Collect like terms
90 - 30 = 2x - x
60 = x
x = 60
