Let [tex]f^{-1}(x)[/tex] be the inverse of
[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]
Then by definition of inverse function,
[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
Solve for the inverse :
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]
[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]
[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]
Explain plzzzzzzzzzzzzzz
Answer:
8/3
Step-by-step explanation:
x equals 8/3
7x_2_4x_6=0
3x=8 ÷3 in both sides
What are the common factors of 24 and 36?
O A. 1,2,4,6, 12
O B. 1,2,3,4,6,12
C. 1,2,3,4,6,8,12
O D. 1,3,4,9,18
Answer:
B. 1,2,3,4,6,12
Step-by-step explanation:
Factors of 24: 1, 24, 2, 12, 3, 8, 4, 6
Factors of 30: 1, 36, 2, 18, 3, 12, 4, 9, 6,
Sheila has $46 to buy graphing pads for her math class. Each pad costs $8.
How many pads can she buy? Do not include units in your answer.
Answer:
5
Step-by-step explanation:
If sheila has $46 to buy pads with, and each pad costs $8, then:
8 · 5 = 40
8 · 6 = 48
48 > 46,
So maximum amounts of pads she could is 5, and have remaining $6
Answer:
46÷8=5.75 so the answer is 5
need to evaluate integral pls help me
Answer:
[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegral NotationIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.[/tex]
[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {f(x)} \, dx + \int\limits^2_1 {f(x)} \, dx[/tex][Integrand] Substitute in function: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {9x^9} \, dx + \int\limits^2_1 {4x^3} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \int\limits^1_0 {x^9} \, dx + 4 \int\limits^2_1 {x^3} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{x^{10}}{10} \bigg) \bigg| \limits^1_0 + 4 \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^2_1[/tex]Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{1}{10} \bigg) + 4 \bigg( \frac{15}{4} \bigg)[/tex]Simplify: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
Step-by-step explanation:
[tex]\int\limits^1_0 {9x^9} \, dx +\int\limits^2_1 {4x^3} \, dx[/tex]
=[tex]\frac{9x^{10}}{10} |_0^1 + x^4|_1^2[/tex]
[tex]=\frac{9}{10}+2^4 -1 = 15\frac{9}{10}[/tex]
Tim wants to create a circle graph showing the number of physicians whose specialty is aerospace medicine. He knows the following information.53 male physicians are under 35 years of age. 8 female physicians are under 35 years of age. 155 male physicians are between 35 and 44 years of age. 17 female physicians are between 35 and 44 years of age. 145 male physicians are between 45 and 54 years of age. 10 female physicians are between 45 and 54 years of age. 98 male physicians are over 54 years of age. 2 female physicians are over 54 years of age. If he wants to include each of the eight groups in his graph, how many degrees would he use for the central angle of the "45-54 year-old Males" sector? Express your answer to the nearest whole number.
Answer:
107 :)
Step-by-step explanation:
In total there are 53+8+155+17+145+10+98+2=488 physicians of aerospace medicine. 45-54 year-old males account for 145/488 of this population, so they should account for that fraction of the central angle of the circle graph also. Since there are 360 degrees in the central angle to divide up among the groups, the 45-54 year-old male group should get 145/488 x 360 which rounds to about 107 degrees.
what is 7 plus 56 divided by 4 tims 7
Answer:
107
Step-by-step explanation:
Answer:
The answer is 105
Step-by-step explanation:
hope its help:)
What’s the y-intercept
Y-14=6(x-2.5)
Answer:
[tex]y=-1[/tex]
Step-by-step explanation:
[tex]y-14=6(x-2.5)[/tex]
[tex]y-14=6(0-2.5)[/tex]
[tex]y-14=6(-2.5)[/tex]
[tex]y-14=-15[/tex]
[tex]y=-1[/tex]
Please look for the question in the picture.
Answer:
Step-by-step explanation:
Find m
∠
J
L
K
∠JLK.
Answer:
m∠JLK° = 62°
Step-by-step explanation:
∠JLK = ∠KJL
SO
56°+2(∠JLK)° = 180°
2(∠JLK)° = 180-56
2(∠JLK)° = 124
∠JLK° = 62°
so m∠JLK° = 62°
Answer:
m∠JLK = 62°
Step-by-step explanation:
180 - 56 = 124
124 ÷ 2 = 62
DOES ANYONE KNOW PLEASE HELP ME I WILL MARK BRAINLIEST <3
Answer:
i got this i hope this is helpfulI'm sry I can't read and ans
Step-by-step explanation:
Electronic entry of medication orders through CPOE may reduce errors from poor handwriting or incorrect transcription. CPOE systems often include functionalities such as drug dosage support, alerts about harmful interactions, and clinical decision support, which may further reduce errors.
In six years Xavier will be 3 times older than Joanne is today. Joanne is 24. How old is Xavier?
Answer:
72
Step-by-step explanation:
Is the sum of 5x⁴ + x³ and 2x³ + x² a trinomial expression. If it is true, justify your answer.
Answer:
The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.
Step-by-step explanation:
(5x⁴ + x³) + (2x³ + x²) = 5x⁴ + 3x³ + x²
The sum of 5x⁴ + x³ and 2x³ + x² is a trinomial expression that is 5x⁴ + 3x³ + x²
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.
We are given the expression as;
5x⁴ + x³ and 2x³ + x²
We need to find of the sum of the expression as;
(5x⁴ + x³) + (2x³ + x²)
= 5x⁴ + 3x³ + x²
The sum of 5x⁴ + x³ and 2x³ + x² is 5x⁴ + 3x³ + x²
To know more about an expression follow;
brainly.com/question/19876186
#SPJ2
Description of a turn for those who have never done math / for a child
Answer:
Step-by-step explanation:
1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move. What are the possible outcomes of your first roll? 3 green spaces, 2 star spaces, 1 question mark space2 green spaces, 2 star spaces, 2 question mark spaces2 green spaces, 2 star spaces, 3 question mark spaces6 green spaces
Answer:
The answer is B.) 2 green spaces, 2 star spaces, 2 question mark spaces
Step-by-step explanation:
Just a "calculation," or rather, I did this question before.
Hope this helps!
(Can you mark me brainliest?)
Have a great day/night/afternoon!
- ❤ 7272033Alt ❤
What is the slope of the linear equation that has the values shown in the table
Answer:We noted above that a linear function has the form f(x)= mx+b, f ( x) = m x + b, where m m is the slope of the line, and b b is the y y -intercept. Since m m and b b can take on various values
Step-by-step explanation:
5. Jolene made 8 pink bracelets using
b beads on each bracelet and 7 blue
bracelets with b beads on each
bracelet. Which expression gives the
total number of beads she used?
Answer:
so she made 8 so
8*what ever the rest is
then she has b
8b plus what ever
then each one has 7 blue beads on each one
8(b+7)or 8b+56
Hope This Helps!!!
Answer:
Step-by-step explanation:
8b + 7b = Total Beads for the Pink(8) and Blue(7) bracelets
15b = Total beads
Factor the following expression. Type x^2 for 22 as needed. If it is not factorable, type unfactorable.
22-8x+16
Answer:
63
Step-by-step explanation:
you divide and add then subtract
If A is the center of the circle which of these is/are radii
Answer:
it could be
A to B
A to E
or A to F
all of them would work
Answer:
segments EA, AB, FA
Step-by-step explanation:
These points are all from the circumference, connecting to the radii, A.
subtract the polynomials (4x^2-9x-7)-(3x^2-5x-6)
Answer:
x^2 - 4x - 1
Step-by-step explanation:
Please help me I don’t want to fail
Answer:
c
Step-by-step explanation:
Determine whether a triangle with the given side lengths is a right triangle.
Answer:
See answer below.
Step-by-step explanation:
This is true for all right triangle a² + b² = c² were c = the largest number
9, 12, 15 A right triangle
21, 28, 35 A right triangle
9, 13, 16 Not a right triangle
10, 11, 15 Not a right triangle
can someone please tell me these answers
Answer:
4/5
Step-by-step explanation:
To find the rate of change, you are finding the slope of the chart.
Using the equation, △y/△x can be rewritten as [tex]\frac{y2-y1}{x2-x1}[/tex].
Plug in 2 coordinate points in the chart to find the rate of change.
[tex]\frac{8-4}{10-5} =\frac{4}{5}[/tex]
The rate of change is 4/5.
Solve the following formula for x y = 7 m x − 8 b
Answer: It depends on which variable you're solving for.
Step-by-step explanation:
Solving for b: b=7/8mx + -1/8xy
Solving for m: m=xy+8b
______
7x
Solving for x: x=-8b
___
-7m+y
Solving for y: y=7mx-8b
______
x
I need some help plsssss
Answer:
(6, - 5 )
Step-by-step explanation:
The parabola is symmetrical about x = 4
The point (2, - 5 ) is 2 units to the left of x = 4 ,then
the point 2 units to the right of x = 4 is (6, - 5 )
Approximately what portion of the box is shaded blue?
A.2/3. B.9/10
C.3/5
are 6/12 and 12/24 equavilent
Answer:
yes because they're both half of each other
Answer:
Yes
Step-by-step explanation:
A permanent magnet d.c. motor has an armature resistance of 0.5 Ω and when a voltage of 120 V is applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power loss in the armature, (c) the torque generated at that speed
Answer:
applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power loss in the armature, (c) the torque generated at that speed
voltage of 120 V is applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power
Last week, the price of oranges at the farmers market was $1.75 per pound. This week, the price has decreased by 15%. What is the price of
oranges this week?
Answer:
11.6 (6 is repeating)
Step-by-step explanation:
1.75 divided by 15% of 75
Jane needs to memorize words on a vocabulary list for German class. She has memorized 8 of the words, which is one-fourth of the list. How many words
are on the list?
Answer:
x = 32 words
Step-by-step explanation:
Okay...let's get solving! :D Firstly, we
let the word list be x and convert the long paragraph into an equation that we can use.
one-fourth = 1/4
Memroized = 8 words
[tex]x * \frac{1}{4} = 8[/tex]
Thus, we solve the equation.
x = 32 words
Determine the value of x for the following equation: 9(x + 2) = 72
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
So, first we divide the equation by 9 on both sides to get: [tex]\frac{9\left(x+2\right)}{9}=\frac{72}{9}[/tex]
Then, we simplify to get [tex]x+2=8[/tex]
Now, to leave x alone we subtract 2 from both sides ([tex]x+2-2=8-2[/tex]) to get our final answer of [tex]x=6[/tex]
brainliest pls