Answer:
asymptotes: x = 16 zeros: x = 0
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x -16 = 0 . . . . . true for x=16
__
The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4
asymptotes: x = 16 zeros: x = 0
learn more about asymptotes and zeros here:
brainly.com/question/16908830
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These are four questions and four answers:
Question 1. What is the petrochemical production in 2005?
Solution:
1) The table reports the the annual Petrochemical Production p (Billion metric tons) for 2005 - 2011.
2) The years are indicated as 0, 1, 2, 3, 4, 5, 6.
3) There is a contradiction in the stament because there is a note telling that t = 0 is year 2002, which meant that the years are from 2002 - 2008, contradicting that the years are 2005 - 2011.
4) If you take for good the note the t = 3 is year 2005 and the corresponding production is 12.0, which is the option A).
5) If you take for good the initial statement that the years are 2005 - 2011, then t = 0 is 2005 and the corresponding production is 10.8
So you have to clarify with your teacher which is the right statement.
Question 2. What are the units.
Solution:
The units are indicated in parenthesis after the label of the row.
The label of the row is Petrochemical production p and the units are Billion metric tons.
So, the answer is the option D) billion metric tons.
Question 3. Graph the function f(x) = log base 2 of x
Solution:
You might create a table with some four points or use the knowledge about logarithm function.
Thiis is the knowledge you need to answer the question:
1) logarithm is an increasing function: as x increase f(x) increase)
2) log base a of a = 1
3) limit of log base a of x when x approaches 0 is negative infinity.
With those three properties you know that the answer is the first figure with certainty.
Question 4. Graph the function f(x) = 2^x
Solution:
These properties will give you the answer:
1) 2^x is the inverse function of log base 2 of x (the function of the question 2)
2) 2^0 = 1
3) 2^x is a growing function (as x increases 2^x increases)
4) 2^x is always positive.
5) limit of 2^x when x approaches negative infinity is 0.
With that you are sure that the graph of 2^x is the second figure.
Given:
The given functions are:
To find:
The transformations performed of f(x) to create g(x).
Solution:
The translation is defined as
.... (i)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
Using these two function, we get
...(ii)
On comparing (i) and (ii), we get
It means the graph of f(x) is vertically stretched with a scale factor of 3, shifts 5 units left and 2 units down to get g(x).
Therefore, the correct options are A and C.
Answer:
448
Step-by-step explanation:
aₙ = a₁ + (n-1)d
a₈ = a₁ + (8-1)d = a₁ + 7d
a₁₂ = a₁ + 11d
a₈ + a₁₂ = 246 = 2a₁ + 18d a₁ + 9d = 123
a₁₀ + a₁₄ = a₁ + 9d + a₁ + 13d = 298 a₁ + 11d = 149
2d = 26
d = 13
a₁ = 6
a₃₅ = 6 + (35-1) x 13 = 448
You change a whole a number by simply make the denominator of that whole number 1.
For example, 6.
If you wanted to change 6 into a fraction, you just put 6/1.
Hope that helps!
