Answers
Answer:
[tex] \huge f ^{-1}(x) = -\frac{ 2}{3 - x} [/tex]Step-by-step explanation:
to understand thisyou need to know about:inverse functionPEMDASgiven:[tex]f(x) = \frac{3x + 2}{x} [/tex]to find:[tex] {f}^{ - 1} (x)[/tex]tips and formulas:inverses of common function
[tex] + < = > - [/tex][tex] \times < = > \div [/tex][tex] \frac{1}{x} < = > \frac{1}{y} [/tex][tex]x ^{n} < = > \sqrt[n]{y} [/tex]let's solve:[tex]step - 1 : define[/tex][tex]f(x) = \frac{3x + 2}{x} [/tex][tex]step - 2 : solve[/tex][tex]substitute \: y \: for \: f(x) \\ y = \frac{3x + 2}{x} [/tex][tex]interchange \: x \: and \: y \: and \: swap \: the \: sides \: of \: the \: equation\\ \frac{3y + 2}{y} = x[/tex][tex]multiply \: both \: sides \: of \: the \: equation \: by \: y \\ \frac{3y + 2}{y} \times y = x \times y \\ 3y + 2 = xy[/tex][tex]move \: the \: constant \: and \: the \: expression \: to \: the \: right \: and \: left \: hand \: sides \: and \: change \: its \: sign \: respectively \\ 3y - xy = - 2[/tex][tex]factor \: out \: y \: from \: the \: expression \\ (3 - x)y = - 2[/tex][tex]divide \: both \: sides \: by \: 3 - x \\ \frac{(3 - x)y}{(3 - x)} = \frac{ - 2}{3 - x} [/tex][tex] y = \frac{ - 2}{3 - x} [/tex][tex] \therefore \: f ^{-1}(x) = -\frac{ 2}{3 - x} [/tex]
Related Questions
Makayla reads 18 pages of her book on Monday, 36 pages on Tuesday, 42 pages on Wednesday, and 88 pages of Thursday. Neil reads four times as many pages as Makayla’s total. How many pages did Neil read?
Answers
List the sides of the triangle in order from shortest to longest.
Answers
Answer:
FH, GF, GH
hmmmmmmmmmmm
PLEASE HELP ME
Emma invested $19,000 in an account paying an interest rate of 4.2% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest year, for the value of the account to reach $40,000?
Answers
Answer: 18
Step-by-step explanation:
Solve x2 – 18x + 81 = 4 by completing the square. Select any solutions that apply.
A. x = –11
B. x = –7
C. x = 7
D. x = 11
Answers
Answer:
7 and 11
Step-by-step explanation:
The product of two consecutive positive integers is 812. What is the value of the lesser integer? a. 7 b. 28 c. 58 d. 203
Answers
Answer:
The value of the lesser integer is [tex]28[/tex]
Step-by-step explanation:
Let two consecutive positive integers be [tex]x,x+1[/tex].
Product of two consecutive positive integers = [tex]x(x+1)=x^2+x[/tex]
Also, product of two consecutive positive integers is 812
So,
[tex]x^2+x=812\\x^2+x-812=0\\x^2+29x-28x-812=0\\x(x+29)-28(x+29)=0\\(x-28)(x+29)=0\\x=28,-29[/tex]
As [tex]x[/tex] is a positive integer,
[tex]x=-29[/tex] is rejected.
So,
[tex]x=28\\x+1=28+1=29[/tex]
Two positive integers are [tex]28,29[/tex]
The value of the lesser integer is [tex]28[/tex]
Answer:
B
Step-by-step explanation:
If O is an angle in standard position and its terminal side passes through the point
(8,5), find the exact value of cot 0 in simplest radical form.
Answers
Answer:
8/5
Step-by-step explanation:
Since the angle passes through 8,5. The horizontal side length is 8. The vertical length is 5 so now we must find the hypotenuse or radius side. Using the pythagorean theorem, that can be accomplished.
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
[tex] {8}^{2} + {5}^{2} = {r}^{2} [/tex]
[tex]64 + 25 = {r}^{2} [/tex]
[tex] \sqrt{89} [/tex]
So know me gonna to find our trig functions. Cot or cotangent is x/y so we plug that as x=8, y=5.
[tex] \frac{8}{5} [/tex]
so the answer. is 8/5
2
Select the correct answer.
Which number is the same as
s(4-1)(23-4-2);
OA. -2
OB.
OC. 2
OD. 32
OE. 512
Reset
Next
Answers
Answer:
32
Step-by-step explanation:
The number that has the same value as [tex](4^{-1})(2^3 \div 4^{-2})[/tex] is 32
The numeric expression is given as:
[tex](4^{-1})(2^3 \div 4^{-2})[/tex]
Evaluate the exponents
[tex](4^{-1})(2^3 \div 4^{-2}) = \frac 14 * 8 \div \frac 1{16}[/tex]
Express as products
[tex](4^{-1})(2^3 \div 4^{-2}) = \frac 14 * 8 * 16[/tex]
Evaluate the products
[tex](4^{-1})(2^3 \div 4^{-2}) =32[/tex]
Hence, the number that has the same value as [tex](4^{-1})(2^3 \div 4^{-2})[/tex] is 32
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Norma and Albert both clean pools. Each charges a flat fee to clean a pool. Norma cleans 12 pools in 8 hours and earns $270. Albert cleans 9 pools in 7.5 hours and earns $195.75.
Answers
Answer:
Step-by-step explanation:
Noma cleans 12 pools in 8 hours
How many pools in how many minutes?
8 x 60= 480
He cleans 12 pools in 480 minutes
How many minutes does he take to clean a pool?
480/12 = 40
He cleans a pool in 40 minutes.
How much does he earn to clean a pool?
since he cleans 12 pools to earns $270
then 270/12 =22.5
Therefore, he charges $22.5 to clean a pool in 40 minutes.
Albert 9 pools in 7.5 hours
How many pools in how many minutes?
7.5 x 60= 450
He cleans 9 pools in 450 minutes
How many minutes does he take to clean a pool?
450/9 = 50
He cleans a pool in 50 minutes.
How much does he earn to clean a pool?
since he cleans 9 pools to earns $195.75
then 195.75/9 =21.75
Therefore, he charges $21.75 to clean a pool in 50 minutes.
MATEMATICAS II
APRENIZAJE ESPERADO: Resuelve problemas de potencias con exponente entero y aproxima raíces cuadradas.
VER VIDEO DE DANIEL CARREON: RAIZ CUADRADA Súper fácil. DURACION 4:34 min
ACTIVIDAD: Encuentra por ensayo y error y por aproximaciones las raíces cuadradas de los siguientes números:
√ 100
√ 25
√ 64
√ 16
√ 9
√ 4
ACTIVIDAD: Resuelve los siguientes problemas, aplicando la raíz cuadrada. (PUEDEN USAR CALCULADORA)
A) Mi papá va a construir una bodega de forma cuadrangular (cuadrado) que tenga un área de 256 m2. ¿Cuánto deberá medir en cada lado?
B) En la escuela vamos a hacer un periódico mural y la maestra pidió que el diseño fuera cuadrado. Como los demás grupos también van a presentar el suyo, a nosotros nos tocó un espacio de 36 m2. ¿Cuánto medirá el lado de nuestro periódico?
Página 1
MATEMATICAS II
APRENIZAJE ESPERADO: Resuelve problemas de potencias con exponente entero y aproxima raíces cuadradas.
Partes de una potenciación:
La base es la cantidad que se multiplica por sí misma tantas veces como lo indique el exponente, en este caso la base es el número 6.
El exponente indica la cantidad de veces que la base se tiene que multiplicar por sí misma, en este ejemplo el exponente es el 3, el cual indica que el número 2 se tiene que multiplicar 3 veces por sí mismo, es decir 2 x 2 x 2. (Ojo: multiplicar 2 x 3 es un procedimiento equivocado en este caso de la potenciación).
La potencia es el 8; es el resultado de multiplicar 2 x 2 x 2
ACTIVIDAD: Con base a lo anterior, completa la tabla siguiente.
Página 2
Observa esta otra multiplicación de potencias de la misma base:
44 x 43 x 4 = 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 48
44+3+1 = 48 = 65536
Página 3
POTENCIA DE POTENCIA.
Tiene que ser la misma base y se multiplican los exponentes
EJEMPLO: (��3)4=
Expresión expandida (��3)(��3)(��3)(��3)= se suman sus exponentes ��3+3+3+3=��12 También se puede multiplicar sus exponentes. Entonces la potencia de (��3)4 es ��12 (��3)4 = ��12
Página 4
MATEMATICAS II
APRENIZAJE ESPERADO: Resuelve problemas de proporcionalidad directa e inversa y de reparto proporcional.
ACTIVIDAD: Ve y analiza el video “Tablas de proporcionalidad”
ACTIVIDAD: Analiza las siguientes tablas e indica si es un problema de proporcionalidad directa o inversa.
_______________________ _______________________
Usa la regla de tres para encontrar
los valores en cada tabla.
EJEMPLO:
SE MULTIPLICAN LOS DATOS
ENCONTRADOS
86 x 45 =38.7
100
X = 38.7
Página 5
EJEMPLO:
90 x 200 = 257.14
70
X = 257.14
TABLA 1 (SE MULTIPLICA 82 x 9) ENTRE 12 = 61.5) x = 61.5Página 6
Answers
marlee drove 60 miles using 2 gallons of gas.Which is the unit rate in fraction form?
Answers
Answer:
30 mile per gallon
Step-by-step explanation:
60/2=30
Answer:
30 miles/ 1 gallon
i need help asap i’ll be giving a brainliest to the person with the correct answer
Answers
Answer:
A newborn weighs 8 pounds at birth and gains 1.5 pounds each month for the next 3 months.
They all mostly seem right, but when a baby is first born the year is 0, so therefore it most likely seems like the first one! :)
^^ hope this helps :)
2x + y < 15
x + y < 10
Answers
Answer:
y<15-2x
y<10-x
Step-by-step explanation:
Which of the following are like terms
y and -3y
2x2 and 3x3
k4 and 8k4
2x and x
Answers
y and -3y
k⁴ and 8k⁴
2x and x
These are like terms
Washington Middle School is painting a circle on their playground with a radius of 12 feet. What will be the total area of the circle, in square feet?
Answers
Answer: circle
A=452.39ft2
R radius 12
A=πr 2=π. 12 ‘2=452.38934ft’2
Is this true or false?
Answers
Answer:
True
Step-by-step explanation:
Use the rule of fractional exponent: The denominator becomes the root index and the numerator becomes the power.
(0,-9)after a rotation of 180 counterclockwise about the origin
Answers
Since a rotation from the origin by 180 converts (x,y) to (-x,-y)
The coordinate after a rotation of 180° counterclockwise about the origin is (0, 9).
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
The given coordinate is (0, -9).
Rotation rule:
Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (-x,-y).
Now, (0, -9) → (0, -(-9))
(0, -9) → (0, 9)
Therefore, the coordinate after a rotation of 180° counterclockwise about the origin is (0, 9).
Learn more about the rotation here:
brainly.com/question/1571997.
#SPJ2
Transversal relations
Answers
Answer:
The answer is 75
Step-by-step explanation:
By way of parallelism
[tex]x + 15 = 90 \\ x = 75[/tex]
equivalent Find the number that makes the ratio equivalent to 1:7. 4:
Answers
Answer:
28
Step-by-step explanation:
Ratios are like fractions. Since you're finding an equivalent ratio, u can set them up like equivalent fractions and put an x where the missing number would go:
[tex]\frac{1}{7} = \frac{4}{x}[/tex]
You can either cross multiply and then solve for x, but it's easier to just think about it. The fractions are equivalent, right? So for them to be the same you'd have to do to the bottom what u do to the top.
To get from 1 to 4, you multiply by 4. By that logic, to get from 7 to x you'd have to multiply by 4 as well. Therefore x = 7x4, which is 28.
So x = 28
Question Help
3.3 PS-14
A salesperson at a jewelry store earns 4% commission each week. Last week, Jarrod sold $750
worth of jewelry. How much did he make in commission? How much did the jewelry store make
from his sales?
Answers
BRAINLIEST TO WHOEVER CAN GET THIS RIGHT FIRST!
If 3x−y=12, what is the value of 8x / 2y ?
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
Answers
Answer:
D
Step-by-step explanation:
answer is d
plus help me I will mark no explanation needed ❤️❤️❤️❤️
Answers
Answer:
whats the question
Step-by-step explanation:
I need some guidance on math:(
Answers
Answer:
C. -38
Step-by-step explanation:
We know that if the denominator is not given, then it is 1
So,
(-5/1) = (y-7/9)
Now, cross-multiply and set them equal
-45 = y - 7 Add both sides by 7
-38 = y
The square of one number is 23 less than the square of a second number. If the second number is 1 more than the first,
what are the two numbers?
If x represents the smaller number, then which of the following quadratic equations represents the word problem?
Answers
Austin opened a bank account. He deposited $100 on Monday and $70 on Tuesday.
Every week he deposits an additional $15. He has a total of $500 in his bank account
now. How many weeks has he been depositing $15?
Answers
Answer:
22 weeks
Step-by-step explanation:
Answer:
22 weeks
Step-by-step explanation:
500-170=330
330/15=22
22 weeks
Write the equation of a line that passes through the point (0, 3) and (-4, 11). *
Answers
Answer:
[tex] \large \boxed{y = - 2x + 3}[/tex]
Step-by-step explanation:
Goal
Write the equation of a line with given coordinate pointsGiven
Coordinate points which are (0,3) and (-4,11).Step 1
Use the slope formula also known as rise over run to calculate the slope.[tex] \large \boxed{m = \frac{y_2-y_1}{x_2-x_1} }[/tex]
Substitute coordinate points in.
[tex]m = \frac{11 - 3}{ - 4 - 0} \\ m = \frac{8}{ - 4} \longrightarrow \frac{2}{ - 1} \\ m = - 2[/tex]
Step 2
Substitute the value of slope in the slope-intercept form.[tex] \large \boxed{y = mx + b}[/tex]
where m = slope and b = y-intercept.
[tex]y = - 2x + b[/tex]
Step 3
Substitute any given coordinate points in the new equation to find the value of b.Substitute both coordinate points still give the same solution.
Step 3.1 — (0,3)
[tex]y = - 2x + b \\ 3 = - 2(0) + b \\ 3 = 0 + b \\ 3 = b[/tex]
Step 3.2 — (-4,11)
[tex]y = - 2x + b \\ 11 = - 2( - 4) + b \\ 11 - 8 = b \\ 3 = b[/tex]
Therefore, the value of b is 3.
Step 4
Substitute the value of b in the equation.[tex]y = - 2x + b \\ y = - 2x + 3[/tex]
Hence, the equation of a line is y = -2x+3.
What is the area of a rectangle with length 36 cm and width 4 cm?
Answers
Answer:
A=144cm²
Length: 36cm
Width: 4cm
Step-by-step explanation:
36 x 4 = 144 cm
f(x) = x + 5 and g(x) = 2x Find (f +g)(x)
Answers
Answer:
Step-by-step explanation:f
(
x
)
=
2
x
g
(
x
)
=
x
+
5
Set up the composite result function.
f
(
g
(
x
)
)
Evaluate
f
(
g
(
x
)
)
by substituting in the value of
g
into
f
.
f
(
x
+
5
)
=
2
(
x
+
5
)
Apply the distributive property.
f
(
x
+
5
)
=
2
x
+
2
⋅
5
Multiply
2
by
5
.
f
(
x
+
5
)
=
2
x
+
10
Can someone help me the score for TB: 3 & KC: 7
Answers
Answer:
Tampa Bay had 7 points in first quarter and Kansas City had 3.
Step-by-step explanation:
Rounded: KC - 0; TB - 10
Added: 10
Multiplied: 21
Hope it helps!
PLEASE HELP ME
You place a cup of 205°F coffee on a table in a room that is 72°F, and 10
minutes later, it is 195°F. Approximately how long will it be before the coffee
is 180°F? Use Newton's law of cooling:
Answers
Every 10 min it goes down 10 degrees.
We need it to go down 205-180=25 degrees.
Since it goes down 1 degree per min, it would take 25 min. I don't know about the law part though.
Answer:
27 minute is correct via A P E X
Step-by-step explanation:
Can some help please
Answers
Answer:
D
Step-by-step explanation:
3 months start with J, so its 9/12, meaning D is correct
JANUARY February March April May JUNE JULY Agugust September October November December