Answer:
A
Step-by-step explanation:
Select the correct answer
What is the inverse of the function f(x)=x+1/x
Answer:
\(\boxed{\mathrm{B}}\)
Step-by-step explanation:
\(f(x)=\frac{x+1}{x}\)
\(y=\frac{x+1}{x}\)
Make x as subject.
Multiply both sides by x.
\(yx=x+1\)
Subtract both sides by x.
\(yx-x=1\)
Factor out x.
\(x(y-1)=1\)
Divide both sides by y-1.
\(x=\frac{1}{y-1}\)
Switch variables.
\(y=\frac{1}{x-1}\)
Answer:
\( {f}^{ - 1} (x) = \frac{1}{x - 1} \)Option B is the correct option.
Step-by-step explanation:
Let y = f ( x )
\(y = \frac{x + 1}{x} \)
Apply cross product property
\(xy = x + 1\)
Move 'x' to L.H.S and change it's sign
\(xy - x = 1\)
Take x as common
\(x(y - 1) = 1\)
\(x = \frac{1}{y - 1} \)
Replace x by f ⁻¹(x) and y by x
\( {f}^{ - 1} (x) = \frac{1}{x - 1} \)
Hence, Option B is the correct option.
Hope this helps..
Best regards!!
Last week, Rio bought 11 shirts and 11 hats for a total of $154.
Today, Rio bought 11 shirts and 20 hats for a total of $181.
Assuming neither item has changed in price, what is the cost of a shirt in dollars?
Answer:
shirt = $11 ; hat = $3
Step-by-step explanation:
shirt = s
hats = h
11s + 11h = 154 ...(1)
11s + 20h =181 ....(2)
(2)-(1) : 9h = 27
h= 27/9
h = 3
11s + 11h = 154
11s + 11(3) = 154
11s = 154 - 33
11s = 121
s=11
what is \(\frac{-8 + \sqrt{-20} }{24}\)?
Answer:
\(\displaystyle \frac{-4 + i\sqrt{5}}{12}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FactoringAlgebra II
Imaginary Numbers: √-1 = iStep-by-step explanation:
Step 1: Define
\(\displaystyle \frac{-8 + \sqrt{-20}}{24}\)
Step 2: Simplify
[Fraction] [√Radical] Factor: \(\displaystyle \frac{-8 + \sqrt{-1}\sqrt{20}}{24}\)[Fraction] [√Radical] Evaluate: \(\displaystyle \frac{-8 + i\sqrt{20}}{24}\)[Fraction] [√Radical] Simplify: \(\displaystyle \frac{-8 + 2i\sqrt{5}}{24}\)[Fraction] Factor numerator: \(\displaystyle \frac{2(-4 + i\sqrt{5})}{24}\)[Fraction] Simplify: \(\displaystyle \frac{-4 + i\sqrt{5}}{12}\)if a is a set of real numbers which is bounded above and b is a set of real numbers which is bounded below then there is at most one real number in both a and b?
If a is a set of real numbers that is bounded above and b is a set of real numbers that is bounded below, there is at most one real number that can exist in both sets.
A real number is any number that can be expressed as a decimal or fraction and exists on the number line.
If a set of real numbers, represented by a, is bounded above, it means that there exists a real number, represented by M, such that all the numbers in the set are less than or equal to M. Similarly, if a set of real numbers, represented by b, is bounded below, it means that there exists a real number, represented by m, such that all the numbers in the set are greater than or equal to m.
Now, let's consider a real number, represented by x, that exists in both sets a and b. If x exists in a, it must be less than or equal to M and if x exists in b, it must be greater than or equal to m. Hence, x must satisfy both conditions: M >= x >= m.
From these conditions, it can be deduced that M and m must be equal to x. In other words, there can only be one real number that is simultaneously the greatest value in a and the smallest value in b.
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NEED HELP!! I"LL GIVE YOU BRAINLIEST!! Find the value of b. a = 3 and c =12
Answer: b = 11.62
Step-by-step explanation:
We can use this formula to solve for b:
\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)
\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)
\(b^2= \sqrt{144-9}\)
= 11.61895004
We can round that to 11.62.
Hope this helped!
A piece of lumber 2.8 meters long weighs 24.5 kilograms. A piece 0.8 meter long is cut from
the 2.8-meter length. Determine the weight of the 0.8-meter piece.
The weight of the 0.8-meter piece is 19.6 kilograms.
We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.
Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:
W₁/2.8m = 24.5kg/1m
Solving for W₁, we get:
W₁ = (24.5kg/1m) x 2.8m = 68.6kg
Now we can use the same ratio to find W₂:
W₂/0.8m = 24.5kg/1m
Solving for W₂, we get:
W₂ = (24.5kg/1m) x 0.8m = 19.6kg
Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.
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1.94 million is what percent of 2.16 million
89.81% of 2.16 million is 1.94 million.
What percentages are there?In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. After dividing a number by its whole, multiply it by 100 to determine its percentage. As a result, the percentage refers to a component per 100. The word "percent" denotes a percentage of 100.
To calculate a group's share of the total in terms of 100, use the percentage formula. Using this method, you may represent a number as a fraction of 100. You'll see that the approach below may be used to rapidly calculate each of the the percentages:
(Value/Total Value) x 100 = %
According to the question,
(x/100) 2.16 = 1.94
x = 1.94 (100)/ 2.16
x = 194/ 2.16
x = 89.81 %
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Type the equation for the graphbelow.Pi/3 2piy = [?] sin([ ]x)
To find the equation of the graph, what we do is to recognize some characteristics of a sine function:
- Amplitude: The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In this case, the amplitude is 1.
- Period: The period of a sine function is defined as the length of one complete sine wave or one complete cycle of the curve. It can be found using the equation: P=2pi/B.
Why are these characteristics important?
Because the sine function has the following general form:
In this problem, we have A=1 and we know that the period equals 2pi/3. So,
Therefore, the equation of the graph is:
Daisy cream is sold in a bulk of 76 cups of cream. Kremlin cream is sold in a bulk of 4 1/2 gallons of cream. Marble cream is sold in a bulk of 40 pints of cream. Which one has the most cream?
Therefore , the solution of the given problem of unitary method comes out to be Daisy cream and Kremlin cream both have less cream per bulk 1 gallon and 4.5 gallons, respectively than Marble cream.
An unitary method is what?The objective can be accomplished by utilising what has already been discovered, taking advantage of this worldwide access, and including all essential components from earlier changeable study who employed a certain technique. If the anticipated claim outcome actually occurs, it will either be possible to contact the variable again or both important processes will undoubtedly miss the statement.
Here,
We must convert cups to gallons because daisy cream is sold in bulks of cups. Since a gallon of Daisy cream comprises 16 cups, one quantity of Daisy cream contains:
=> 16 cups per bulk = 1 gallon 16 cups per bulk = 1 gallon
Moscow cream is offered in bulk quantities of 4 1/2 gallons, which is one gallon.
Thus, we must convert pints to gallons. A gallon of Marble cream comprises eight pints, hence one quantity of Marble cream contains:
=> 40 pints in a bulk equal 1 gallon, 8 pints, or 5 gallons.
As a result, we can see that Marble cream, with 5 gallons per bulk, has the most cream.
Daisy cream and Kremlin cream both have less cream per bulk (1 gallon and 4.5 gallons, respectively) than Marble cream.
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Can someone please walk me through this?
3x-1=4x+8-x
3x-1=4x+8-x
3x -4x +x = 8+1
4x -4x = 9
0x =9
x= 9/0 which is undefined .
f(x)=8x+1 inverse equation
Answer:
8
Step-by-step explanation:
Si al invertir $60.000 se pierde un 8% ¿A cuánto asciende la pérdida?
Trabajando con porcentajes, concluimos que la pérdida es de $4800.
¿A cuánto asciende la pérdida?
Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.
Entonces la pérdida va a ser el 8% de $60000.
Podemos escribir las relaciones:
$60000 = 100%
x = 8%
Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:
x = $60000*(8%/100%) = $60000*0.08 = $4800
Así, concluimos que la pérdida es de $4800.
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What is the 24th term of -21, -14,-7,0,7,…
Answer:
140
If that's wrong, try 147
Step-by-step explanation:
With this brief sequence of numbers, we can see that the function is linear, and increases by 7 each term, with the first term at -21, and therefore, the "0th" term, or the y-intercept, at -28. With this information we can create a function in slope intercept form (y=mx+b):
\(y=7x-28\\\),
where our m (slope) is 7, and our b (y-intercept) is -28.
If this doesn't make sense, then the easiest way is to just keep adding seven to the previous number until you get to the 24th term.
Hope this helps!
I don’t understand this question someone please help
Answer:
£152.40
Step-by-step explanation:
If he made 80 cakes at a ratio of 3:2:5, then he made:
24 chocolate cakes
16 lemon cake
40 fruit cakes
He sold all of the chocolate: 24x2=48
He sold 3/4 of the lemon: 3/4 of 16=12 12x1.70=20.40
He sold 7/8 of the fruit cakes: 7/8 of 40=35 35x2.4=84
48+20.40+84=152.40
identify the x-values for which f(x)>-2
It should be noted that the expression that can be used to identify the x-values for which f(x)>-2 will be -2 <= x <= 2. This is illustrated in the graph.
How to explain the information?It should be noted that a graph is a diagram that is used to show the relationship that exists between the data presented or the information.
In this case, ut should be noted that the expression that can be used to identify the x-values for which f(x)>-2 will be -2 <= x <= 2. This is illustrated in the graph.
The graph is attached below.
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Help
Find a if A = 8a
Answer:
a(A) = 0
Step-by-step explanation:
On a standardized exam, the scores are normally distributed with a mean of
195 and a standard deviation of 50. Find the z-score of a person who scored
330 on the exam.
The z-score of a person who scored 330 on the exam is approximately 2.7.
To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where:
z is the z-score
x is the raw score (330 in this case)
μ is the mean (195 in this case)
σ is the standard deviation (50 in this case)
Substituting the values into the formula, we get:
z = (330 - 195) / 50
z = 135 / 50
z = 2.7
The z-score of a person who scored 330 on the exam is 2.7.
The z-score measures the number of standard deviations a particular data point is away from the mean.
In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.
The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.
A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.
In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.
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Solve the question below:
Answer:
x = 15
Step-by-step explanation:
3x+1+4x-3 = 103
7x = 105
x = 15
Express as a difference: a+5
The expression expressed as a difference is (a - 2) - (-7).
We have,
We can express a + 5 as a difference by subtracting a suitable term from it.
One way to do this is to subtract 2 and add 2, like this:
a + 5 = a + 5 - 2 + 2 (adding and subtracting 2)
= (a - 2) + 7 (rearranging)
Now,
We can express a + 5 as the difference between a - 2 and -7, like this:
a + 5 = (a - 2) - (-7)
Thus,
The expression expressed as a difference is (a - 2) - (-7).
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The lines y=-2 and y=-7 are they parallel, perpendicular, or neither?
Answer:
parallel
Step-by-step explanation:
An equation of the form
y = k
where k is a number is a horizontal line.
Since both lines have the form y = k, with two different values of k, -2 and -7, these are two different horizontal lines, so they are parallel.
Answer: parallel
Answer:
Parallel -inf to inf
Step-by-step explanation:
there is no x value so they never cross
Which equation is equivalent to 7-2(3x+4)=8x
A -6x+15=8x
B-6x-1=8x
C15x+20=8x
The equation that is equivalent to the expression 7-2(3x+4)=8x is
-6x - 1 = 8x.
Option B is the correct answer.
We have,
To find the equation that is equivalent to 7-2(3x+4)=8x, simplify the given equation by applying the distributive property and combining like terms.
7 - 2(3x + 4) = 8x
First, distribute the -2 to the terms inside the parentheses:
7 - 6x - 8 = 8x
Combine like terms:
-6x - 1 = 8x
Thus,
The equation that is equivalent to the expression 7-2(3x+4)=8x is
-6x - 1 = 8x.
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Look at this data set. 6, 8, ?, 15, 18, 14, 16, 8 The data set has 8 data points. The missing data point is a whole number. The median of the data set is 12. What is the value of the missing data point from the data set? A. 20 B. 15 C. 10 D. 5
The value of the missing data point is 10. Option C
How find the value of the missing data pointThe data set has 8 data points, and the median is given as 12. The median is the middle value when the data points are arranged in ascending or descending order.
Let's arrange the data set in ascending order:
6, 8, ?, 8, 14, 15, 16, 18
Since the median is 12, it should be the fourth data point when arranged in ascending order. Therefore, the missing data point must be the fourth value in the sorted data set.
From the given options, the only whole number that could fit as the fourth value in the data set is 10.
Thus, the value of the missing data point is C. 10.
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The figures below are similar. What is the missing side length?
helppppp kkkasnnansnejsjs
Answer: “6b”
Step-by-step explanation:
Please help me for 15 points
Three percent of the students at Midwood High School are left-handed. There are 700 students at Midwood High School. How many students at Midwood High School are left-handed?
A.21 students
B.210 students
C.140 students
D.12 students
Answer:
21 students because 3% = 0.03 . When you multiply 0.03 by 700, you get 21.
Answer:
\( \frac{3}{100} \times 700\)\(3 \times 7\)\(21\)there are total 21 left handed students in the school.
Autumn buys 5 hats at $8.99 each. How much does she spend?
Answer:
Autumn spends $44.95 On hats. Why would she need 5 hats? I don’t know.
Step-by-step explanation:
5 hats, all costing $8.99
You do 5*8.99, and this gives you $44.95
Answer:
5 x 8.99 = 44.95
Step-by-step explanation:
Please help i need it done asap
Thank you have a great day
there were 3 coins and they were tossed 200 times total. 23 times, 3 of them showed heads, 72 times, 2 of them showed heads, 77 times, 1 of them showed heads, 28 times, 0 showed heads. whats probability for each of the events?
Answer:
Step-by-step explanation:
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.Solution:Probability of an event, P(E) = Number of occurrences where the event takes place / Total number of occurrencesThe probability of 2 heads coming up when three coins are tossed simultaneously is given by the ratio of the number of times a particular outcome occurs to the total number of tosses.Total number of tosses = 200Number of 2 heads outcomes = 72Probability of 2 heads outcomes = Number of 2 heads outcomes / Total number of tosses= 72/200= 9/25
The length of a rectangle is 5 cm less than 3 times its width. If the perimeter is 54 cm, find its length.
Answer:
W = 8cm
L = 19cm
Step-by-step explanation:
The first step to solving these problems is always writing the information that is given into 2 equations.
Piece of info #1: Length is 5cm less than 3 times the width
Piece of info #2: Perimeter (of the rectangle, which has 4 sides) is 54cm
Turing these into equations...
Equation 1) L = 3*W - 5
Equation 2a) L+L+W+W = 54
Let's simplify that second equation:
Equation 2b) 2L+2W = 54
Now, we just solve the system of two equations by substitution. Take the known value of L from equation 1 and substitute it in for the value of L in equation 2b:
2*(3*W-5)+2W = 54
Now we solve for W:
6W - 10 + 2W = 54
8W - 10 = 54
8W = 64
W = 64/8
W = 8 cm
Now that we know W, we can substitute its value into either equation 1 or equation 2 to find L. Here, I'll randomly choose equation 1.
Equation 1) L = 3*W - 5
L = 3*8 - 5
L = 24-5
L = 19 cm