Using the concepts of asymptotes and inverse function, we have that:
a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.
b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]
c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.For this problem, the function is given by:
[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]
The zero of the denominator is:
6x + 4 = 0
6x = -4
x = -4/6 = -2/3.
Hence the vertical asymptote is x = -2/3.
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]
How to find the inverse function?To find the inverse function of a function y = f(x), we exchange x and y then isolate y.
Exchanging x and y, we have that:
[tex]x = \frac{y + 10}{6y + 4}[/tex]
Applying cross multiplication:
x(6y + 4) = y + 10
6xy - y = 10 - 4x
y - 6xy = 4x - 10
y(1 - 6x) = 4x - 10
[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]
Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.
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Two cyclists, 30 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as
the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr
The equation as r + 2 r = 30 miles / 2 hours and the speed of faster cyclist as 10 miles per hour.
We are given that:
The distance between the two cyclist = 30 miles.
Now let the speed of one cyclist be x miles / hour.
Speed of other cyclist = 2 x miles / hour.
Now, 2 hours later they meet.
Distance covered by 1st cyclist in 2 hours = 2 x
Distance covered by 2st cyclist in 2 hours = 4 x
Equation will be:
2 x + 4 x = 30 miles
6 x = 30 miles
x = 5 miles.
Equation for the cyclist in terms of r will be :
r + 2 r = 30 miles / 2 hours
Speed of faster cyclist = 10 miles per hour.
Therefore, we get the equation as r + 2 r = 30 miles / 2 hours and the speed of faster cyclist as 10 miles per hour.
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Find the population variance ad standard deviation
6,12,20,24,28
The population variance ad standard deviation are 64 and 8 respectively.
The variance for a population is calculated by the below steps :
1) First find the mean (the average).
2) Subtracting the mean from each number in the data set and then squaring the result. The results are squared to make the negatives value positive
3) Averaging the squared differences.
Here, the data set of population is given as :
population difference difference²
6 -12 144
12 -6 36
20 2 4
24 6 36
28 10 100
₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋
∑ 90 ∑ 320
Now, the average population will be :
∑ 90/5 = 18
Now finding the variance σ² using the formula :
σ² = ∑(x- x')²/N
σ² = 320/5
σ² = 64
Now, the standard deviation σ will be :
standard deviation = √σ²
standard deviation = √64
standard deviation = 8
Therefore, the population variance ad standard deviation are 64 and 8 respectively.
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What is: -6.7 x 3 + (-5.8)
Answer: -25.9 or -25 9/10
Step-by-step explanation:
Answer:
-25.9
Step-by-step explanation:
-6.7 × 3 gives you -20.1 adding on the 5.8 gives you 25.9
Can someone help me please?
Answer:
60 or 6x10^1 dogs in two days
Step-by-step explanation:
Saturday: 2x10^1 dogs
Sunday: 2(Saturday) = 2 (2x10^1)
-----------------------------------------------------
2x10 = 20
2(20) = 40
20 + 40 = 60
60 or 6x10^1 dogs in two days
Which of the following is equivalent to sum from n equals 1 to infinity of 12 times quantity negative five eighths end quantity to the power of n question mark
-60/13
60/13
−20
20
The sum to infinity of the sequence is 96/13
Sum to infinity of a geometric sequenceGiven the nth term of a geometric sequence expressed as:
Tn = Σ12(-5/8)^n
The sum to infinity of the sequence is expressed as;
S∞ = a/1-r
where
a is the first term = 12
r is the common ratio = -5/8
Substitute
S∞ = 12/1-(-5/8)
S∞ = 12/1+5/8
S∞ = 12/(13/8)
S∞ =12 *8/13
S∞ = 96/13
Hence the sum to infinity of the sequence is 96/13
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if a piece of ribbon is 4 3/4 feet long, how long is it in inches?
A nation can produce two products: tanks and autos. The table below is the nation's production possibilities schedule.
Production Possibilities
Product
Tanks
The total opportunity cost of three unit(s) of tanks is
A
0
1000
B
1
950
C
2
850
D
3
650
E
4
350
F
5
0
Using the it's formula, the total opportunity cost of three unit(s) of tanks is of 350 autos.
What is the opportunity cost formula?The opportunity cost formula is given by:
C = F - A.
In which:
F is the best return.A is the actual return.For this problem, we have that:
When no tanks are produced, 1000 autos can be produced, hence F = 1000.When 3 tanks are produced, 650 autos can be produced, hence F = 650.Thus:
F = 1000 - 650 = 350.
The total opportunity cost of three unit(s) of tanks is of 350 autos.
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solve the equation secx=2 on interval[0,2pie)
The threes solutions to the given equation sec²x - secx = 2 are:
[tex]x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ; \ x_3=\pi[/tex]What exactly are equations?An equation is a statement composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To solve: sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])
When we set t = sec x, we get the quadratic equation:
[tex]t^2-t-2=0[/tex]Which has the solutions: [tex]t_1=2 ; \quad t_2=-1[/tex]As a result, we must seek solutions to the equations:
[tex][1] \sec x=2: \quad \cos x=\frac{1}{2} \rightarrow x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ;$\\\text { [2] } \sec x=-1: \quad \cos x=-1 \rightarrow x_3=\pi ;[/tex]
Therefore, the three solutions are:
[tex]x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ; \ x_3=\pi[/tex]Know more about equations here:
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The correct question is given below:
solve the equation sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])
Coordinates: (-4, 4), (5, -1)
midpoint:
slope:
distance:
Answer:
Step-by-step explanation:
Compute the midpoint of the line segment with endpoints:
p_1 = (-4, 4) and p_2 = (5, -1)
The midpoint between (x_1, y_1) and (x_2, y_2) is their componentwise average:
((x_1 + x_2)/2, (y_1 + y_2)/2)
Substitute (x_1, y_1) = (-4, 4) and (x_2, y_2) = (5, -1):
= ((-4 + 5)/2, (4 - 1)/2)
-4 + 5 = 1:
= (1/2, (4 - 1)/2)
4 - 1 = 3:
Answer: = (1/2, 3/2)
Question 4
Tricia wants to install a decorative wall paper border around the top of the wall in he
master bedroom. The room measures 18ft by 14ft. How many feet of the border will
will she need?
Provide a numeric answer only. Do not include a unit of measure with your response
For the installation of a decorative wall paper Tricia will need 70 ft of the border to decorate the wall of her master bedroom.
The measures of the room is 18 ft by 14 ft.
So, the length of the room (l) = 18 ft
The width of the room(w) = 15 t
As we know that, perimeter of rectangle is 2(l×w).
We will get perimeter of he room = 2l × 2w
= 2(18) × 2(14)
= 70 ft.
What is the selling price if cost is $18.00 and the mark up is 70% ??
show your work
The selling price if cost is $18.00 and the mark up is 70% is $30.60
What is mark up?
The mark up means profit earned as percentage of the cost price, whereas margin means the profit is a percentage of the selling price, in other words, the profit element to add to the cost price to derive the selling price in this case is 70% of the cost price of $18.00
profit(mark up)=70%*$18.00
profit(mark up)=$12.60
selling price=cost price+ profit(mark up)
selling price=$18.00+$12.60
selling price=$30.60
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QUICK IM TIMED PLS HELP
Re arrange equation to make x the subject
X-3=4y
Answer:
Re arrange equation to make x the subject
X-3=4y
-3 will be moved to the other side of equal sign
in doing so, its sign will be be switched
so
x=4y+3
If the end behavior is decreasing to the left ,what might be true about the function
Answer:
As the input gets smaller, the output gets smaller.
Step-by-step explanation:
Absolute value of 2 is
Step-by-step explanation:
|2|=2
Hope this helps !!!!
Answer:
The absolute value is 2
Step-by-step explanation:
The absolute value is defined by how far a value is from zero and it is represented by a / /
/2/ = 2
Given || m
m || n, find the value of x.
Answer:
x=142°
Step-by-step explanation:
hope it helps ⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄
refer to the image please!!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Value of g (x) is -2, when :
[tex]\qquad \sf \dashrightarrow \: - 2.5 < x \leqslant - 1.5[/tex]
And since -2 lies in this range of x,
[tex]\qquad \sf \dashrightarrow \:g( - 2) = - 2[/tex]
Value of x is -1, when :
[tex]\qquad \sf \dashrightarrow \: - 1.5 < x \leqslant - 0.5[/tex]
And -0.5 falls in this range, hence
[tex]\qquad \sf \dashrightarrow \:g( - 0.5 ) = - 1[/tex]
Next, The value of x is 0 when :
[tex]\qquad \sf \dashrightarrow \: - 0.5 < x < 0.5 [/tex]
But, it isnt equal to 0.5, since there is open interval at both extremes.
Next, Value of x is 1, when :
[tex]\qquad \sf \dashrightarrow \:0.5 \leqslant x < 1.5[/tex]
And since it also has the value 0.5 included in it,
[tex]\qquad \sf \dashrightarrow \:g(0.5) = 1[/tex]
PLEASE HELP!
Anand is driving on a long road trip. He currently has 10 gallons of gas in hi
car. Each hour that he drives, his car uses up 2 gallons of gas. How much ga
would be in the tank after driving for 2 hours? How much gas would be left
after t hours?
gas left after 2 hours
gas left after t hours
Answer:
8 gallons left.......
Step-by-step explanation:
10 - 2 = 8
Jan has a car worth $3500. She still owes $1000 on the loan. She also borrowed $800 on a credit card. What are her total liabilities?
Answer:
Step-by-step explanation:
By adding the laibilites together you get 1,800.
One rectangle is "framed" within another. Find the area of the shaded region if the
"frame" is 1 unit wide.
10
5
The rectangle that is shaded has an area of 18 square units.
The framed rectangle is represented by the darkened area, while the frame is shown in white.
The frame's known width is two units, and both the rectangle and the frame have the following dimensions:
width = 7 units
length = 10 units
Now, if we remove the frame, each measure will lose 2*2 units, or 4 units (because for each measure we have the frame in both sides).
As a result, the measurements for the shaded rectangle are as follows:
width = 7 units - 4 units = 3 units
length = 10 units - 4 units = 6 units.
And since the product of a rectangle's width and length determines its area, we may calculate:
A = (3 units)*(6 units) = 18 square units.
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- A certain forest covers an area of 30 square kilome-
ters. In 2018, the number of pine trees in this
particular forest was 75,000. In 2019, the number
of pine trees had decreased so that there was an
average of 2,000 pine trees per square kilometer in
the forest. What was the total percent decrease in
the number of pine trees in this forest from 2018 to
2019?
E. 20%
F.24%
G. 25%
H. 30%
Answer:
E
Step-by-step explanation:
2018 : 75 000 pines
2019 : 2000 pines / km^2 * 30 km^2 = 60 000 pines
(75 000 - 60 000) / 75 000 = .2 or 20 %
Please HELP ME I need help on this final question
Rob and Lila try to simplify 18 x 42 + (9 – 3)2. Rob simplifies the expression and gets 360. Lila simplifies it and gets 324. Which student is correct? What error did the other student make?
The result of the expression, 18 x 4² + (9 – 3)² after simplification is 324.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.
Simplifying the expression
The given expression is 18 x 4² + (9 – 3)²
Using the BODMAS rule, we get,
= 18 x 4² + (6)²
= 18 × 16 + 36
= 288 + 36
= 324
Lila estimated it right.
The mistake that Rob might have made would be that he must have not solved (9 – 3)² the right way and gained the wrong answer.
Hence, the result of the expression, 18 x 4² + (9 – 3)² after simplification is 324.
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16. The formula A = r² can be used to find the area of a circle. Solve the equation for r.
a. r=A-2n
b. r = √A - T
C. r=
d.)r =
A
A
211
-6 + (-2)? What does it meanrnjrhdbr
adding a negative is the same as subtracting a positive
the expression -6+ (-2) is the same as -6-2 which is -8
PLS HELP PLS I DON'T WANT TO FAIL PLEASE HELP PLEASE 20 POINTS
Answer:
653209
Step-by-step explanation:
Because i did this already
Model this expression on a number line
Consider the information about the economy of Pakistan. Note that the currency of Pakistan is the rupee.
The government purchases: 3.30 trillion of rupees.
Individuals consume: 9.50 trillions of rupees.
Individuals save: 5.44 trillions of rupees.
Businesses invest: 1.20 trillions of rupees.
Foreigners spend: 0.50 trillions of rupees to purchase Pakistani firms.
Pakistan imports: 2.13 trillions of rupees.
Pakistan exports: 1.40 trillions of rupees.
Calculate Pakistan's GDP. Assume that the values are all current and no conversions need to be made. Give your answer in terms of trillions of rupees, and round to two decimals.
Pakistan's GDP is 13.27 trillion rupees.
What is GDP?GDP is the total value of all products manufactured and goods provided within that territory during a specific period.
We have,
Government purchases = 3.30 trillion rupees.
Individuals consume = 9.50 trillion rupees.
Individuals save = 5.44 trillion rupees.
Businesses invest = 1.20 trillion rupees.
Foreigners spend =0.50 trillion rupees to purchase Pakistani firms.
Pakistan imports = 2.13 trillion rupees.
Pakistan exports = 1.40 trillion rupees
GDP is given by:
C + I + G + NX
Where,
C = Consumption
I - Investment
G - Government Purchases
NX - Net Exports = Export - Import
So,
C = 9.50
I = 1.20
G= 3.30
NX = ( 1.40 - 2.13 ) = -0.73
GDP = 9.50 + 1.20 + 3.30 - 0.73
GDP = 13.27 trillion rupees.
Thus Pakistan's GDP is 13.27 trillion rupees.
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Jorge sells chairs for $230 after a markup of $80. Jorge's percent of markup based on the selling price is?
Jorge's percent of markup based on the selling price is 34.78%.
The Percent markup based on Selling Price is calculating using the formula
Percent Markup = ( Markup/Selling Price )*100
In the given question
The Selling Price of chair = $230
Markup = $80
Substituting the values of Selling price and Markup in the Percent markup formula,
We get ,
Percent Markup = (80/230) * 100
=0.3478
=34.78
Therefore , the percent markup based on the selling price is 34.78%.
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14. Which expression shows the sum of 30 and 45 as the product of th and a sum of two numbers with no common factor? A) 5(6 + 9) B 15(2+3) C 15(15 +45) D 90(2+3)
What the slope of the line on the graph please help me
Answer: Slope = 7/6
Step-by-step explanation: