Answers
Answer:
A
Step-by-step explanation:
f(x) = 1/(x-3)+7
f(x)-7=1/(x-3)
x=1/(f(x)-7)+3
f^-1(x)=1/(x-7)+3, where x≠7
The correct answer is option (a) [tex]f^{-1}(x)= \frac{1}{x-7} +3[/tex] where [tex]x\neq 7[/tex].
DomainThe domain of a function is the complete set of possible values of the independent variable
How to find domain?Given [tex]f^{}(x)= \frac{1}{x-3} +7[/tex]
Let
[tex]y= \frac{1}{x-3} +7[/tex]
⇒y-7= 1/x-3
⇒x-3 =1/y- 7
⇒ [tex]x= \frac{1}{y-7} +3[/tex]
hence option a is correct
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Related Questions
what are the exponent and coefficient of the expression 4b-^3
Answers
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Answer:
exponent: -3coefficient: 4Step-by-step explanation:
The coefficient of a term is its constant multiplier. The exponent is the power to which the base is raised.
The term 4·b^(-3) has an exponent of -3, a base of b and a coefficient of 4.
The exponent is -3; the coefficient is 4.
Answer:
exponent = -3 coefficent = 4
Step-by-step explanation:
guys pls tell me this answer as soon as possible
Answers
que es un cuadrilatero
look at the image for the question?
Answers
Answer:
396 in ^3
Step-by-step explanation:
The volume of a rectangular prism is
V = l*w*h where l is the length, w is the width, and h is the height
V = 12 * 3 * 11
V = 396 in ^3
find the LCM of 220,440,660 by common division method
Answers
Answer: LCM = 1320
Step-by-step explanation:
2 | 220, 440, 660
2 | 110, 220, 330
2 | 55, 110, 165
3 | 55, 55,165
5 | 55, 55 , 55
11 | 11, 11, 11
| 1, 1, 1
= 2 × 2 × 2 × 3 × 5 × 11
= 1320
Therefore the LCM is 1320
Must click thanks and mark brainliest
what is Collatz conjecture?
Is Collatz conjecture always true?
What so special about 3x+1 ?
Answers
Answer:
Step-by-step explanation:
The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.
Simply put it says
if a number is even, divide by 2If a number is odd, multiply by 3 and add1. or 3x + 1The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.Try 5
It's odd so triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2. You get 22 is even. Divide by 2. You get 11 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.
Take 15It's odd. Triple it and add 1. That gives 46.46 is even. Divide by 223 which is odd. Triple it and add 1 = 7070 is even. Divide by 2. 3535 is odd. Triple and add 1. 106 which is even53 which is odd. Triple it and add 1. You get 160160 is even. Divide by 2. You get 8080 is even Divide by 2. You get 4040 is even. Divide by 2. You get 2020 is even. Divide by 2. You get 1010 is even. Divide by 2. You get 55 is odd. Triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2.. You get 2.2 is even. Divide by 2. You get 11 is odd and you are in the loop because you get 4 which you have already done.Which is the best definition for the term "segment bisector"?
Answers
Answer:
a line that cuts a segment into two pieces of equal length.
A random sample of 1005 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" of the
1005 adults surveyed, 522 indicated that televisions are a luxury they could do without Complete parts (a) through (d) below.
Click Here for StatCrunch
(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without
pe
(Round to three decimal places as needed)
(b) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do
without Select the correct choice below and fill in any answer boxes within your choice
(Type Integers or decimals rounded to three decimal places as needed. Use ascending order)
O A. We are
% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between and
B. There is a
% chance the proportion of adults in the country who believe that televishans are a luxury they could do without is between
(c) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is
that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence
interval
and
Click to select your answer(s) and then click Check Answer
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Answers
From the information given in the exercise, we build the confidence interval and solve this question. First, we have to find the point estimate for the population proportion, then using this point estimate, and sample size, we build the confidence interval. According to the built confidence interval, question c is answered.
Item a:
522 out of 1005 indicated that television is a luxury that they could do without, so:
[tex]\pi = \frac{522}{1005} = 0.5194[/tex]
Thus, the point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without is 0.5194.
Item b:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of .
For this problem, we have that:
[tex]n = 1005,\pi = 0.5194[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5194 - 1.96\sqrt{\frac{0.5194*0.4806}{1005}} = 0.4885[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5194 + 1.96\sqrt{\frac{0.5194*0.4806}{1005}} = 0.5503[/tex]
Thus, the 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without is (0.4885,0.5503). The interpretation is that:
We are 95% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4885 and 0.5503.
Item c:
It is possible, but unlikely that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval does not contain 60%.
For another example of a confidence interval for a proportion, you can check https://brainly.com/question/16807970
Given the following situation:
A cell phone company offers a data package by charging $20 a month plus $12 per gigabyte of data used. Write a linear equation
that relates the cost C, in dollars, to the amount of data used. Use it to determine the amount of data used if they charge you
$116.
Answers
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Answer:
C = 20 +12g8 gigabytesStep-by-step explanation:
At $12 per gigabyte, the data charge will be 12g where g is the number of gigabytes. Then the total charge is ...
C = 12g +20
__
If C = 116, the value of g is found from ...
116 = 12g +20
96 = 12g . . . . . . . subtract 20
8 = g . . . . . . . . . . divide by 12
The amount of data used is 8 gigabytes if the charge is $116.
1. Determine whether the function f(x)= x³ from i to i is one to one. Explain.
2. Is the function f (x)= 3x+ 4 from the set of integers to integers one to one? Why? 48
Answers
Answer:
The function [tex]f:\mathbb Z\to\mathbb Z,~f(x)=3x+4[/tex] is injective (one-to-one).
Step-by-step explanation:
The definition of an injective function follows.
Let [tex]X,Y[/tex] be sets. Let [tex]f:X\to Y[/tex] be a function. We say [tex]f[/tex] is injective if, for all [tex]x,y\in X[/tex], [tex]f(x)=f(y)[/tex] implies [tex]x=y[/tex].
This is the proof that [tex]f:\mathbb Z\to\mathbb Z,~f(x)=3x+4[/tex] is injective.
Let [tex]x,y\in\mathbb Z[/tex] and assume [tex]f(x)=f(y)[/tex]. This means [tex]3x+4=3y+4[/tex]. Subtracting [tex]4[/tex] gives [tex]3x=3y[/tex], then dividing by [tex]3[/tex] gives [tex]x=y[/tex]. Thus [tex]f[/tex] is injective.
Find the point of intersection for the pair of linear equations.
x +y = 0.3
y=3x + 16.7
Answers
Answer:
B
Step-by-step explanation:
You should find the solution for this system of equations (The value of x is the first coordinate for the point of intersection, the value of y is the second coordinate for the point of intersection)
X+y=0.3
y=3x+16.7
use 3x+16.7 instead of y in the first equation(do it to get only x in the first equation)
x+3x+16.7=0.3
4x+16.4=0
4x=-16.4
x=-4.1
y=0.3+4.1=4.4
B
Question 13 plz show ALL STEPS
Answers
Step-by-step explanation:
Here are some of the graphs:
Blue is g(x) and Green is f(x). The 2nd graph is for the 13b. It shows our graph after 1 transformation. The 3rd graph is after both transformations.
13a. Let use the following values in
[tex]f(x) = \frac{2}{x} [/tex]
We know by definition of rational function x cannot be zero.
Let find some values across interval 2 through 4.
[tex]f(2) = \frac{2}{2} = 1[/tex]
[tex]f(3) = \frac{2}{3} [/tex]
[tex]f(4) = \frac{2}{4} = \frac{1}{2} [/tex]
Let use the following values in
[tex]g(x) = \frac{3x - 1}{x - 1} [/tex]
By definition of rational function, x cannot be 1 because it will make the denominator zero. Let use some values across the interval 0 through 4.
[tex]g(0) = \frac{0 - 1}{0 - 1} = 1[/tex]
[tex]g(2) = \frac{3(2) - 1}{2 - 1} = {5} [/tex]
[tex]g(3) = \frac{8}{2} = 4[/tex]
[tex]g(4) = \frac{11}{3} [/tex]
So graph this in a table of values. I'll post a picture of the table of values on the top.
13b. We need to write g(x) as a transformation of f(x). If we look at the graphs, g(x) has a asymptote at x=1 while f(x) has a asymptote of 0. This means that we need to move f(x) to the right one unit or move (x-1) units.
We will upgrade the graph.
Now we can just add 3 to f(x) to get to g(x).
In the 3rd graph, notice how both graphs coincide. Our transformations is complete.
The answer is
[tex]g(x) = f(x - 1) + 3[/tex]
13c. We can say this as we move f(x) to the right 1 unit and shift f(x) up 3 units.
What is the perimeter of the triangle?
Answers
The perimeter will be 30
Step-by-step explanation:
Perimeter = all side lengths added
Step 1. Determine the length of the triangle
Answer: 5
Step 2. Determine the width of the triangle
Answer: 12
Step 3. Determine the diagonal line across the triangle
Answer + explanation:
For it to figure it out, we must use this method called Pythagorean Theorem
Pythagorean Theorem: a^2 + b^2 = c^2
Where a = 12 b = 5 and c = the diagonal line
12^2 + 5^2 = c^2
144 + 25 = c^2
c^2 = 169
c = 13
The diagonal line measures 13 units
Step 4. Add all of the dimensions we just reviewed
Answer:
Length = 5
Width = 12
Diagonal line = 13
5 + 12 + 13 = perimeter
perimeter = 30
Therefore, the perimeter is 30
X cubed = 343^-1 find the positive value of x
Answers
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Answer:
x = 1/7
Step-by-step explanation:
x³ = 1/343
x = 1/∛343 = 1/7
The positive value of x is 1/7.
_____
Additional comment
A square root (or any even-index root) will have both positive and negative real values. A cube root (or any odd-index root) will have only one real value, whose sign will match the sign of the value being rooted.
343^(-1/3) is the cube root of a positive number, so it will be a positive real number.
Determine the domain and range of the relation. *
Answers
Speeding up velocity for 5 seconds, same speed for another 10 seconds, slows down for 10 seconds.
A cement mixture costs $33 a ton. It is composed of Grade A cement at $36 a ton and Grade B cement at
$24 a ton. How were these two cements mixed?
Answers
Converting to costs we get 36a + 24b = 33(a + b)
36a + 24b = 33a + 33b
36a - 33a = 33b - 24b
3a = 9b
a = 3b
This means the mixture contains 3 times as much of grade A than grade B
The ratio of grade A : grade B = 3 : 1
For example if we mixed 3 tons of A with 1 ton of B we would get 4 tons of mixture
The cost would be 3 x 36 + 1 x 24 = 108 + 24 = $132 for 4 tons = $33 per ton
Vehicles that get more than 40 miles per gallon can cross one county’s new bridge for free. Which graph shows the fuel-use rate of vehicles that have to pay to cross the bridge?
Answers
Answer:
D
Step-by-step explanation:
More than 40 miles per gallon
Open circle at 40 and line goes to the left
Answer: the answer is C
Step-by-step explanation:
because it is a open circle going to the left
If one foot is
equivalent to 12
inches, how many
inches are in 3 feet?
*Bonus: What is
another name for that
length?
Answers
Answer:
36 am I wright
because in this case we should always multiply
Show why (2×3×7)^4 = 2^4 × 3^4 × 7^4 show work
Answers
[tex] {a}^{m} \times {b}^{m} = ( {ab)}^{m} [/tex]
(2×3×7)⁴=(2×3)⁴×7⁴(2×3×7)⁴=(2×3×7)⁴RHS=LHSplease mark this answer as brainlist
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 242
(ii) 1280
(iii) 245
(iv)968
(v) 1728
(vi) 4851
Answers
Answer:
BELOW
Step-by-step explanation:
242: multiply it by 2 to get 484 and its square root is 22
1280: multiply it by 5 to get 6400 and its square root is 80.
245: multiply it by 5 to get 1225 and its square root is 35.
968: multiply it by 2 to get 1936 and its square root is 44.
1728: multiply it by 3 to get 5184 and its square root is 72
4851: multiply it by 11 to get 53361 and its square root is 231.
HOPE THIS HELPED
Find the midpoint of the segment with the given endpoints.
(7,10) and (-1,- 8)
Answers
Answer:
(3,1) is the midpoint
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(7+-1)/2 = 6/2 =3
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(10+-8)/2 = 2/2 = 1
(3,1) is the midpoint
Answer:
(3, 1)
Step-by-step explanation:
We can use the formula [ (x1+x2)/2, (y1+y2/2) ] to solve for the midpoint.
7+(-1)/2, 10+(-8)/2
6/2, 2/2
3, 1
Best of Luck!
moho has 25 coins in dime , quarter and nickel . The cain have a value of 3.75 . Moho then remove five of each coin in prder to pay parking meters . How many coins does he left
Answers
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Answer:
10 coins
Step-by-step explanation:
5 of each of three kinds of coins is a total of 3×5 = 15 coins. If Moho started with 25 coins and used 15, he has ...
25 -15 = 10 . . . coins remaining
The fraction 64/72 is a
Answers
Hope this helps, If it is pls Brainliest !!
Answer:
proper fraction
Step-by-step explanation:
This is a proper fraction, which has a numerator smaller than the denominator
a mixed number has a whole number in front such as 1 3/5
An improper fraction has a numeration greater than a denominator such as 7/6
Solve 5x + 3 = -7x + 21
Answers
x = 3/2
Step-by-step explanation:
5x + 3 = -7x + 21
5x - -7x = 21 - 3
12x = 18
x = 18/12
x = 3/2
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.
Answers
Answer:
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 590 hours, standard deviation of 25 hours.
This means that [tex]\mu = 590, \sigma = 25[/tex]
Find the probability of a bulb lasting for at most 622 hours.
This is the p-value of Z when X = 622.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{622 - 590}{25}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997.
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
Which of the following equations have no solutions?
Choose all answers that apply:
-60.2 + 32 = 32x + 60
-60.X + 32 = 322 - 60
-60.2 + 32 = -60.2 + 60
-60x + 32 = -60.2 - 32
Answers
Option 3 is not possible
-60.2 + 32 = -60.2 + 60
And these are not equal
Rest all options have x and are solvable
Must click thanks and mark brainliest
........................
Which of the following will help increase productivity?
Answers
Coefficient and degree of the polynomial
Answers
Answer:
The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.
If it was just a number and no x then it would still be the coefficient.
The degree is 9 as it is the highest power shown.
Step-by-step explanation:
See attachment for examples
Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).
Answers
Answer:
0.5*sqrt33
Step-by-step explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33
Need the help thanks guys
Answers
Answer:
Option D is the correct answer.
Step-by-step explanation:
The equation of the function is in vertex form. Thus, we can analyze the equation to determine the x and y values of the vertex. We know that the template format of a vertex form equation is as follows:
f(x) = a(x – h)2 + k . The only constants we need are h and k, where 'h' is the x-value of our vertex and 'k' is the y-value of our vertex.
The value of 'k' can be found quite simply by looking at the equation: -9.
The value of 'h' is a little trickier, as we must take into account the 'subtract' sign of the template equation, meaning that the '+7' in the given equation actually means that we are subtracting negative seven. Thus, the value of 'h' is -7.
Thus, the vertex of this graph is (-7,-9).
This means that option D is correct.
Answer:
The vertex is at ( -7, -9)
Step-by-step explanation:
y = (x+7)^2 -9
This is written in vertex form
y = a( x-h)^2 +k where ( h,k) is the vertex
y = ( x - -7)^2 + -9
The vertex is at ( -7, -9)
f (x) = sqrt(x)+ 2, g(x)=x^2+ 1
find f(g(x))
and g(f(x))
Answers
Answer:
[tex]f(x) = \sqrt{x} + 2 \\ \\ g(x) = {x}^{2} + 1 \\ \\ f{g(x)} = \sqrt{ {x}^{2} + 1 } + 2 \\ \\ g{f(x)} = {( \sqrt{x} + 2 )}^{2} + 1[/tex]
