The right choice is: A <em>whole</em> number constant could have been <em>subtracted</em> from the <em>exponential</em> expression.
Let be an <em>exponential</em> function of the form 
, where 
and 
are <em>real</em> numbers. A <em>horizontal</em> asymptote exists when 
, which occurs for 
.
For this function, the <em>horizontal</em> asymptote is represented by 
and to change the value of the asymptote we must add the <em>parent</em> function by another <em>real</em> number (
), that is to say:
(1)
In this case, we must use 
to obtain an horizontal asymptote of -3. Thus, the right choice is: A <em>whole</em> number constant could have been <em>subtracted</em> from the <em>exponential</em> expression.
To learn more on asymptotes, we kindly invite to check this verified question: brainly.com/question/8493280
<h3>Answers:</h3>
- Congruent by SSS
- Congruent by SAS
- Not congruent (or not enough info to know either way)
- Congruent by SAS
- Congruent by SSS
- Not congruent (or not enough info to know either way)
- Congruent by SAS
- Congruent by SAS
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Explanations:
- We have 3 pairs of congruent sides. The tickmarks tell us how the congruent sides pair up (eg: the double tickmarked sides are the same length). So that lets us use SSS. The shared overlapping side forms the third pair of congruent sides.
- We have two pairs of congruent sides (the tickmarked sides and the overlapping sides), and an angle between the sides mentioned. Therefore, we can use SAS to prove the triangles congruent.
- We don't have enough info here. So the triangles might be congruent, or they might not be. The convention is to go with "not congruent" until we have enough evidence to prove otherwise.
- We can use SAS like with problem 2. Vertical angles are always congruent.
- This is similar to problem 1, so we can use SSS here.
- There isn't enough info, so it's pretty much a repeat of problem 3
- Same idea as problem 4.
- Similar to problem 2. We have two pairs of congruent sides and an included angle between them allowing us to use SAS
The abbreviations used were:
- SSS = side side side
- SAS = side angle side
The order is important with SAS because the angle needs to be between the sides mentioned.
Answer:
Step-by-step explanation:
Number of hurricanes in year 2008 = 8
Number of hurricanes in year 2009 = 3
Decrease in number of hurricanes = 8 - 3 = 5
Percent of decrease in number of hurricanes = 
= 62.5%
Number of hurricanes in year 2010 = 12
Number of hurricanes in year 2011 = 7
Decrease in number of hurricanes = 12 - 7 = 5
Percentage decrease in number of hurricanes = 
= 41.7%
Decrease in numbers of hurricanes in year 2010 - 11 was same as in year 2010 - 11.
Percentage decrease in hurricanes were more in year 2008 - 09 than percentage decrease in year 2010 - 11.
Answer:
x=4
Step-by-step explanation:
Let one piece of the rope be x
Let the other piece of rope be x + 5
These two pieces put together will make 20 feet.
So we say:
x + (x +5) = 20
What is x? We expand the equation.
x + x + 5 = 20
x + x = 20 - 5
2x = 15
x = 7.5
The shorter piece is therefore 7.5 feet.
The longer piece is 7.5 + 5 = 12.5 feet.
