The value of f-¹(x) for the function f(x) = (x + 2)/x is y = 2/(x-1).
The inverse of a function f is denoted by f-¹ and it exists only when f is both one-one and onto function. An inverse function in mathematics is function which "reverses" the another function.
For example, If function f which is applied to input a gives result b and then applying inverse of the function g to b, it gives result a and vice versa.
It can be written as:
f(a) = b if and only if g(b) = a or, f⁻¹ (b) = a
In order to calculate the inverse of function f(x) = (x + 2)/x just simply swap the x and y, and solve the resulting equation for the x.
So, we have f(x) = (x + 2)/x, swap the variable x by y, we get
f(x) = (y + 2)/y ............(1)
Now, solving the above equation x = y+2/y for y.
⇒y = 2/(x-1)
∴ The value of f-¹(x) for the function f(x) = (x + 2)/x is y = 2/(x-1).
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Amount of Amy's pocket money each day is 3 times as much as the pocket money of Flora's. And the amount of Paul's pocket money is $7 more than Amy's. If they have $980 of pocket money each week, how much pocket money does Paul have each day?
Answer:-
Paul has $64 pocket money each day.
Explanantion:-
Let amy ,flora and Paul 's pocket money be x,y and z respectively.
So,
By the question :
x = 3y
So, y = x/3 - eqn i
z = 7 + x - eqn ii
7(x + y + z) = 980
x + y + z = 140
Now,
x + y+ z = 140
x + x/3 + 7 + x = 140
or, 2x + x/3 = 133
or, 6x + x = 399
so, x = 399/7
so, x = $57
Now,
z = 7 + x
= 7 + $57
= $64
what is the sum of the number k and the number before it and the number after it?
Answer:
3k
Step-by-step explanation:
k+(k-1)+(k+1)=3k
Points S, T, and P lie on a number line. Their coordinates
are 0, 1, and x, respectively. Given SP = PT, what is the value of x?
The value of x associated with the point P on a number line is 0.5.
How to find the locations of a point on a number line
In accordance with the statement, the condition SP = PT means that the locations of points S, T and P on the number line are 0, 1, x, so that S < P < T and that point P is equidistant of points S and T. Then, the location of the missing point is determined by the midpoint formula:
P = 0.5 · S + 0.5 · T
P = 0.5 · 0 + 0.5 · 1
P = x = 0.5
The value of x associated with the point P on a number line is 0.5.
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the ice rink sold 95 tickets for a total of 828.00. general admission tickets are $10.00 each and youth tickets are $8.00 each. how many of each did they sell
Answer:
GA =34
Y = 61
Step-by-step explanation:
GA= GENERAL ADMISSION =$10
Y= YOUTH =$8
GA+Y= 95
GA=95-Y
10GA+8Y=828
10(95-Y)+8Y=828
950-10Y+8Y=828
-2Y= 122 MULTIPLY BY (-1)
2Y= 122
Y= 61
GA= 34
There were 61 youth tickets sold and 34 general admission tickets
What is the opposite of the number located at point d.
Answer:
-7
Step-by-step explanation:
The number located at point D is 7, And the opposite of 7 is -7.
Determine whether the relation is a function. Explain. { ( 2 , 5 ) , ( 4 , − 2 ) , ( 3 , 3 ) , ( 5 , 4 ) , ( − 2 , 5 ) } Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the elements –2, 3, 4, and 5 are in both the domain and the range. cross out D) No; the element 5 occurs twice in the range.
Yes; for each element of the domain, there is only one element of the range.
Function and relationsFor a relation in coordinate form to be a function, there is must nor be repetition in the value of its coordinate.
Given the following relation as shown { ( 2 , 5 ) , ( 4 , − 2 ) , ( 3 , 3 ) , ( 5 , 4 ) , ( − 2 , 5 ) }, since there is no repetition in its domain values, hence the relation is a function.
We can conclude therefore that Yes; for each element of the domain, there is only one element of the range.
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An object is moving at a speed of 360 kilometers per hour. Express this speed in miles per day. Round your answer to the nearest whole number.
Question
Graph the line passing through (3, 4) whose slope is m = -1.
Answer: See attached
Step-by-step explanation:
See attached
Suppose the line tangent to the graph of fat x=3 is y= 4x+2 and suppose y=6x-1 is the line tangent to the graph of g at x = 3. Find the line tangent to the following curves at x = 3.
a. y = f(x)g(x)
b.y = f(x)/g(x)
The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point
a)y=24x²+8x-2 at x=3.
b) y=(4x+2)/(6x-1) at x=3.
What is tangent?The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point
Given
f at x=3 is y= 4x+2
g at x=3 is y=6x-1
f(3)= 4x+2 and g(3)=6x-1
y=f(x)g(x)
at x=3,
Solution for a:
y=f(3)g(3)
=(4x+2)(6x-1)
=24x²-4x+12x-2
=24x²+8x-2
So y=24x²+8x-2 at x=3.
Solution for b:
y=f(3)/g(3)
=(4x+2)/(6x-1)
So y=(4x+2)/(6x-1) at x=3.
Therefore y=24x²+8x-2 at x=3 for y = f(x)g(x) and y=(4x+2)/(6x-1) at x=3 for y = f(x)/g(x).
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Write 0.45 kg in g, mg and ng
Answer:
450g
450,000mg
450,000,000,000ng
Explaination:
Kg to g (x1,000)
Kg to mg (x1,000,000)
kg to ng (x1,000,000,000,000)
Suppose Albers Elementary School has 76 teachers and Bothel Elementary School has 24 teachers. If 3 teachers teach at both Albers and Bothel, compute the total number of teachers employed at Albers and Bothel combined.
The number of teachers that work in both schools is 97.
What is an addition?The addition is a way of combining things and counting them together as one large group.
We have,
Number of teachers in Alberts Elementary school = 76
Number of teachers in Bothel Elementary school = 24
Number of teachers that work in both schools = 3
The number of teachers that work in both schools:
= 76 + 24 - 3
We are subtracting 3 from the total because 3 teachers that work in both schools have been added twice.
= 100 - 3
= 97
Thus the number of teachers that work in both schools is 97.
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4m - t=m, for m
Solving for M
The solution of the given equation 4m - m - t = 0 for m is t/3.
According to the given question.
We have a linear equation in two variables i.e. 4m - t = m.
As we know that, an equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Since, we have to solve the given equation 4m - t = m for m. So, the solution of the equation 4m - t = m for m is given by
4m - t = m
⇒ 4m - m - t = 0 (subtracting m both the sides)
⇒ 3m - t = 0
⇒ 3m = t (adding t both the sides)
⇒ m = t/3.
Hence, the solution of the given equation 4m - m - t = 0 for m is t/3.
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[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
(A) (m,n) = g(n,m) for all positive integers m,n,
(B) (m,n + 1) = g(m + 1,n) for all positive integers m,n,
(D) (2m,2n) = (g(m,n))2 for all positive integers m,n
Explanation[tex] \rm f(m,n,p) = \sum \limits_{i = 0}^{p} {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]
[tex]\rm {}^{m} C_{i} \dfrac{(n + i)!}{p!(n - p + i)!} \times \dfrac{(n + p)!}{(p - i)!(n + i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!n!} \times \dfrac{n!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]
[tex] \rm f(m,n,p) = {}^{n + p} C_{p}{}^{m + n} C_{p}[/tex]
[tex] \rm \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} = {}^{m + n} C_{p}[/tex]
Now,
[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} [/tex]
[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} {}^{m + n} C_{p}[/tex]
[tex] \rm g (m,n) = {2}^{m + n} [/tex]
[tex] \rm(A) \: g(m,n) = q(n,m)[/tex]
[tex] \rm(B) \: g(m,n + 1) = {2}^{m + n + 1} [/tex]
[tex] \rm g(m + n,n ) = {2}^{m + 1 + n} [/tex]
[tex] \rm(D) \: g(2m,2n) = {2}^{2m + 2n} [/tex]
[tex] = \rm( {2}^{m + n} {)}^{2} [/tex]
[tex] = \rm(g(m,n)) {}^{2} [/tex]
what are all values of x such that 1-2/3x<=-3 is satisfied
The possible values of x will belong to the set A = [9, ∞).
We have the following inequality -
1 - 2x/3 ≤ -3
We have to determine all values of x.
What is Inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question, we have the following inequality -
1 - 2x/3 ≤ -3
Subtract 1 from both sides -
-2x/3 ≤ -4
Multiply by -1 on both sides -
2x/3 ≥ 4
Multiply by 3/2 on both sides -
x ≥ 9
Hence, the possible values of x will belong to the set A = [9, ∞).
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Please help! Thank you
solve the following: The quotient of c and −19 is 38.
Answer:
your quotient should be 57
so you would start with 38 and you gotta think hmm
C+(-19)=38
okay so you would change -19 to positive 19
and then add that to 38
and then you would get 57
so therefore C=57
so
57+(-19)=38
Answer:
57
Step-by-step explanation:
Which expression is equivalent to the quotient of x and 8 times the difference of 19 and x?
Answer:
(x/8)(19 - x)
Step-by-step explanation:
The quotient is the answer to a division problem.
The difference is the answer to a subtraction problem.
"Times" indicates multiplication, which you could look at it as a link between the two functions, or quantities (them being the constants and variables sectioned off into parenthesis).
Write and solve an equation to answer the question.
How many people must attend the third show so that the average attendance per show is 3000?
Write an equation.
Write an equation
write one
Equation:_ =3000
An equation to answer the question of how many people must attend the third show to have an average attendance of 3,000 when the other show attendance numbers are 2580, and 2920 is 9,000 = 2,580 + 2,920 + x.
What is an equation?An equation is a mathematical expression or statement that shows that two values are equal.
An equation uses the equation mark (=).
Data and Calculation:To have an average attendance per show of 3,000 for three shows, a total of 9,000 people must attend the three shows (3,000 x 3).
Attendance for the first show = 2,580
Attendance for the second show = 2,920
Total attendance for the two shows = 5,500
Required attendance for the third show, x = 9,000 = 2,580 + 2,920 + x
x = 9,000 - 5,500
x - 3,500
Thus, the equation for the third show attendance is 9,000 = 2,580 + 2,920 + x where x = 3,500.
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Question Completion:And the other show attendance numbers are 2580 and 2920.
Which number sentence is not true?
A.|-20|<20
B.|9|=9
C.|-20|>|9|
D.|9|<|20|
Answer:
A
Step-by-step explanation:
that should be an equal sign
Let f(x) = x3 + 10, g(x) = x2 - 8, and h(x) = 5x + 4. Find the rule for the function.
The rule f ( x ) - g ( x ) is given as x^3 - x^2 + 18
Given data
f(x) = x3 + 10, g(x) = x2 - 8, and h(x) = 5x + 4
How to find f(x) - g(x)f(x) - g(x) = ( x3 + 10 ) - ( x2 - 8 )
= ( x3 + 10 ) - ( x2 - 8 )
opening the parenthesis gives
= x3 + 10 - x2 + 8
collecting like terms gives
= x3 - x2 + 18
Hence we can say that f(x) - g(x) = x3 - x2 + 18
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complete question
The complete question is attached
Determine which of the numbers below is a possible order of magnitude estimate of the
quantity described.
The weight of a grain of rice.
Select one:
O a. 0.000001 ounces
O b. 0.0006 ounces
OC.0.006 ounces
O d. 0.01 ounces
3
Un camión está cargado con 10 pies cúbicos de pajote. El chofer entrega 25
C
3
pies cúbicos de pajote en la primera parada y 3 pies cúbicos de pajote en la
segunda parada. En la tercera parada recoge 11½ pies cúbicos de pajote que no
quiere el cliente. ¿Cuánto pajote queda en el camión después de la tercera
parada?
Answer is 140
According to the question,
Given that,
111 + 10 + 25 - 2 × 3
calculate the term
121 + 25 - 6
121 + 19
140
Una solicitud de licencia de manejar comercial
(DL 44C). Al firmar este formulario significa
que usted se compromete a hacerse un análisis
químico para determinar el contenido de alcohol
o drogas en su sangre. Si se niega a firmarlo, el
Departmento de Vehículos Motorizados (DMV)
no expedirá o renovará su licencia de manejar.
• Su nombre verdadero y completo.
• Un reporte de examen médico aprobado Medical Examination Report (MER). El formulario
federal válido (orginal o copia) del reporte del
examen médico Medical Examination Report
(MER) (MCSA-5875) y el formulario del certificado del examinador médico Medical Examiner’s Certificate Form (MEC) MCSA-5876
al solicitar la licencia de manejar o el permiso;
tal reporte debe ser expedido por un doctor en
los Estados Unidos que esté licenciado en medicina (M.D.), un doctor licenciado en osteopatía
(D.O.), un médico asistente con licencia (P.A.),
un enfermero practicante avanzado y registrado
(APN) o un doctor quiropráctico autorizado. Los
conductores que tengan certificados para manejar autobuses escolares, autobuses de actividades
estudiantiles School Pupil Activity Bus Certificate (SPAB), autobuses de jóvenes, vehículos
paratránsito para el público en general General
Public Paratransit Vehicle (GPPV) o co certificados para manejar vehículos de labores agrícolas
deben tener un examen médico expedido por
un doctor en medicina, un médico asistente con
licencia, un enfermero practicante avanzado y
registrado o un quiropráctico que esté autorizado en el registro nacional de examinadores médicos certificados National Registry of Certified
Medical Examiners (§12517.2 del CVC).
Se requiere un reporte médico fechado en los 2
últimos años para cualquier tipo de solicitud de
licencia CDL y luego cada 2 años.
Nota: No envíe por correo su reporte médico
a la patrulla de caminos California Highway
Patrol (CHP). El formulario MER y el formulario
del certificado MEC pueden presentarse en una
oficina del DMV o ser enviados por correo directamente al DMV para actualizarlos. Envíe por
correo sus formularios MER y MEC a la siguientedirección por lo menos 4 semanas antes que se
venza su reporte médico anterior o su privilegio
para manejar vehículos CMV puede invalidarse.
Envíe el reporte médico a:
Department of Motor Vehicles
CDL/PDPS Unit, MS G204
PO Box 942890
Sacramento, CA 94290-0001
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PLEASE HELP SIMPLIFY 4(m + ( -2) + 15
Answer:
[tex] \sf \large \: 4m+52[/tex]
Step-by-step explanation:
4(m−2+15)
=(4)(m+−2+15)
=(4)(m)+(4)(−2)+(4)(15)
=4m−8+60
=4m+52
Answer:
4m+52
Step-by-step explanation:
A shredding machine can shred 20 sheets of paper in 14 seconds. The bin has room
for 1000 sheets of shredded paper.
How long will it take to fill the bin if the machine has to stop for 3 minutes after every
200 sheets to prevent overheating?
Answer:
See below
Step-by-step explanation:
Rate = 20 sheets / 14 seconds = 10/7 sheet / sec
every 200 sheets is 4 rest periods = 12 minutes
1000 sheets / (10/7 sheet/ sec) + 12 min
700 seconds + 12 minutes
= 700 seconds + 720 seconds = 1420 seconds = 23 min 40 sec
The numbers of students in the 8 schools in a district are given below.
(Note that these are already ordered from least to greatest.)
185, 235, 255, 266, 269, 303, 370, 381
Send data to calculator
Suppose that the number 381 from this list changes to 237. Answer the following.
(a) What happens to the median?
(b) What happens to the mean?
O It decreases by 0
O It increases by 0
O It stays the same.
O It decreases by 0
O It increases by 0
O It stays the same.
Part (a)
The middle values were nitially 266 and 269, but now they are 255 and 266. Thus, the median changes from 267.5 to 260.5, meaning it decreases by 7.
Part (b)
The sum before the change is 2264, but after, it is 2120. This means the sum decreased by 144, and thus the mean decreased by 16.
Kelly wants to find out if the townspeople would be in favor of creating a local dog park. she pulls an equal number of people from several age groups and from different areas of town. Is this study likely to yield valid results? Explain.
Answer: Yes
Step-by-step explanation: Kelly's results are likely to be correct mainly because she pulled votes from several different age groups. The fact that she asked several age groups whether or not they would be in favor of creating a local dog park shows that her results are likely to yield valid results.
Write the function whose graph is the graph of y=x³ +3, but is reflected about the y-axis.
Answer:
Reflected function is y = - x³ + 3
Step-by-step explanation:
When a function f(x) is reflected about the y-axis, the reflected function becomes g(x) = f(-x)
f(x) = x³ + 3
f(-x) = (-x)³ + 3 =-x³ + 3
To make a sand sculpture Arthur used 2 cm³ of red sand with a density of 4 g/cm³ 7 cm³ of yellow sand with a density of 5 g centimeter and 5 cm³ of brown sand with a density of 6 g cubiccm³ what is the average density of the sculpture in grams per cubic centimeter express your answer as decimal to the nearest 10th.
Answer:
5.2 g/cm³
Step-by-step explanation:
Given a sculpture consisting of 2 cm³ at 4 g/cm³, 7 cm³ at 5 g/cm³, and 5 cm³ at 6 g/cm³, you want its average density.
MassThe total mass of the sculpture is the sum of the masses of the components. Each of those is the product of its volume and density.
red sand: (2 cm³)(4 g/cm³) = 8 g
yellow sand: (7 cm³)(5 g/cm³) = 35 g
brown sand: (5 cm³)(6 g/cm³) = 30 g
The total mass of the sculpture is ...
total mass = 8 g + 35 g + 30 g = 73 g
VolumeThe total volume of the sculpture is the sum of the volumes of its parts:
total volume = 2 cm³ +7 cm³ +5 cm³ = 14 cm³
Average densityThe density is the ratio of mass to volume:
ρ = (total mass)/(total volume) = (73 g)/(14 cm³) = 73/14 g/cm³
= 5 3/14 g/cm³ ≈ 5.2 g/cm³
The average density of the sculpture is about 5.2 g/cm³.
The length of a rectangle is two more than triple the width. If the perimeter is 84 inches, find the
dimensions.
The width is
The length is
Submit Question
inches.
inches.
The length and width is 32 inches and 10 inches.
Let us assume the width of rectangle be w. So, length of rectangle = 3w + 2. As per the known fact, the length and width of rectangle for perimeter is related as - Perimeter = 2 (length + width)
Keep the values in formula to find the value of width
84 = 2 (3w + 2 + w)
Performing addition in bracket
84 = 2 (4w + 2)
Performing multiplication
84 = 8w + 4
8w = 84 - 4
Performing subtraction
8w = 80
w = 80 ÷ 8
Performing division
w = 10 inches
Finding length now -
Length = 3×10 + 2
Length = 30 + 2
Length = 32 inches
Hence, the length and width is 32 inches and 10 inches.
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Evaluate |r| when r=−29.
Reason: The absolute value erases the negative sign.
Saying |-29| = 29 means that the number -29 is 29 units from 0 on the number line.
Answer: 29
Step-by-step explanation: The absolute value of -29 is 29. An absolute value is a number's distance from 0. -29 + 29 = 0, therefore the absolute value is 29.