Answers
Answer:
[tex]f(x)=\dfrac{2x-1}{x+2}\\ \\f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]
[tex]f(x)=\dfrac{x-1}{2x+1}\\ \\f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]
[tex]f(x)=\dfrac{x+2}{-2x+1}\\ \\f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]
[tex]f(x)=\dfrac{2x+1}{2x-1}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]
[tex]f(x)=\dfrac{x+2}{x-1}\\ \\f^{-1}(x)=\dfrac{x+2}{x-1}[/tex] - extra
Step-by-step explanation:
1.
[tex]f(x)=y=\dfrac{2x-1}{x+2}\\ \\y(x+2)=2x-1\\ \\yx+2y=2x-1\\ \\yx-2x=-1-2y\\ \\x(y-2)=-1-2y\\ \\x=\dfrac{-1-2y}{y-2}\\ \\y=f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]
2.
[tex]f(x)=y=\dfrac{x-1}{2x+1}\\ \\y(2x+1)=x-1\\ \\2xy+y=x-1\\ \\2xy-x=-1-y\\ \\x(2y-1)=-1-y\\ \\x=\dfrac{-1-y}{2y-1}\\ \\y=f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]
3.
[tex]f(x)=y=\dfrac{x+2}{-2x+1}\\ \\y(-2x+1)=x+2\\ \\-2xy+y=x+2\\ \\-2xy-x=2-y\\ \\x(-2y-1)=2-y\\ \\x=\dfrac{2-y}{-2y-1}\\ \\y=f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]
4.
[tex]f(x)=y=\dfrac{2x+1}{2x-1}\\ \\y(2x-1)=2x+1\\ \\2xy-y=2x+1\\ \\2xy-2x=1+y\\ \\x(2y-2)=1+y\\ \\x=\dfrac{1+y}{2y-2}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]
5.
[tex]f(x)=y=\dfrac{x+2}{x-1}\\ \\y(x-1)=x+2\\ \\xy-y=x+2\\ \\xy-x=2+y\\ \\x(y-1)=2+y\\ \\x=\dfrac{2+y}{y-1}\\ \\y=f^{-1}(x)=\dfrac{x+2}{x-1}[/tex]
Related Questions
Find the number of ways to listen to 4 different CDs from a selection of 15 cds?
A. 1355
B. 2730
C. 360,360
D. 32,760
Answers
Answer: letter a should be the correct answer
Step-by-step explanation:
D is the answer for this question
a toy company's total payment salaries for the first two months of 2005 is $21, 894. write and solve an equation to find the salaries for the second month if the first month's salaries are $10,205.
Answers
Solution: Second month = m
The equation is
m + 10205 = 21894
m = 11689
So the second month will be $11,894. :)
To solve for the second month's salaries, subtract the first month salary from the total for two months. The solution to the equation $21,894 - $10,205 gives this salary: $11,689.
Explanation:The subject of this problem is a toy company's salary expenses over a course of two months. Let's denote the salary expenses for the second month as X. We know from the problem that the total salary expenses for the first two months (January and February) are $21,894. Furthermore, we know that the salary expenses for January are $10,205.
We can write an equation to express these facts as follows: X (which is the salary expenses for February) is equal to the total salary for the two months minus the salary for January, or in mathematical notation, X = $21,894 - $10,205.
We solve this math equation by subtracting $10,205 from $21,894, giving us X = $11,689. Therefore, the second month's salaries total $11,689.
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A rectangular prism has a volume of 2320.5 in.? a width of 12.75 inches and a height of 14 inches what is the length?
Answers
Answer:
13
Step-by-step explanation:
Volume = length x width x height
2320.5 = l x 12.75 x 14
2320.5 = l x 178.5
2320.5/178.5 = l
l = 13
Let f(x)= cos(2x) +e^(-x). for what value of x on the interval (0,3) will f have the same instantaneous rate of change as the average rate of change of f over the interval?
Answers
[tex]f(x)[/tex] is continuous on [0, 3] and differentiable on (0, 3), so the mean value theorem applies here. It says that there is some [tex]c[/tex] in the open interval (0, 3) such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]
We have
[tex]f'(x)=-2\sin2x-e^{-x}[/tex]
so
[tex]-2\sin2c-e^{-c}=\dfrac{\cos6+e^{-3}-2}3\implies c\approx1.5418[/tex]
Given the similarity statement ΔDEF ∼ ΔXYZ, which angle corresponds with ∠Z?
A. ∠F
B. ∠Y
C. ∠E
D. ∠D
Answers
Answer:
F
Step-by-step explanation:
In congruent triangles, or similar triangles, the letters in the same place will also be congruent
Answer:
the answer is A
Step-by-step explanation:
Hi I would really iike if someone helped me with this homework that I have I don't understand. an aquarium in the shape of a parallelepiped ABCDEFGH length AB = 80cm, width AD = 40cm, height DH = 50cm. a) we put HM = x cm give a frame for x b) give, according to x, the volume of water contained in the aquarium. This volume will be expressed in cm ^ 3 then in liters.
Answers
170^3 this is the answer just make sure you do you're work.
The model represents an equation. What value of x makes the equation true?
A)
3
4
B)
9
2
C) −
3
4
D) −
9
2
Answers
Answer:
B) 9/2
Step-by-step explanation:
Subtracting 5x+7 from both sides leaves 2x = 9.
Dividing the 9 into two parts, we find ...
x = 9/2
Answer: 9/2 your welcome i got a 100% on the test by the way
Step-by-step explanation:
A set of 36 cards is numbered with the positive integers from 1 to 36. If the cards are shuffled and one is chosen at random, what is the probability that the number on the card is a multiple of both 4 and 6?
Answers
Answer:
1/12.
Step-by-step explanation:
The numbers divisible by 6 are 6, 12, 18, 24, 30 and 36.
Of these 12, 24 and 36 are also divisible by 4.
So the required probability is 3/36
= 1/12.
(05.06)
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A) (−5, 2)
B) (5, −2)
C) (−5, −2)
D) (5, 2)
Answers
the answer for this question is (B) 5,-2
Please please help please
Answers
Answer:
130.5 in²
Step-by-step explanation:
The area (A) of a regular pentagon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 8.7 × 5 ← pentagon has 5 sides
= 43.5 in
A= 0.5 × 43.5 × 6 = 130.5 in²
Hannah is saving money for a car. She earns $160 each week working part time after school and on the weekends at Papa's Pizza. Hannah currently has $1,280 in savings. Her parents put $50 in her savings account each week and she saves one-half of her paycheck each week. Which expression represents the situation? (n represents the number of weeks) A) 1,280 + 130n B) 1,280 + 160n + 50n C) 1,280 + 160n 2 D) 1,280 + 160n + 50n 2
Answers
Answer:
it is A
Step-by-step explanation:
What is the degree of x 6 + 4x – 3?
Answers
Answer:
The degree of a polynomial is the highest degree of its monomials with non-zero coefficients
Step-by-step explanation:
not sure
The maximum power of the polynomial x⁶ + 4x - 3 that is degree will be 6.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
A polynomial's degree is the greatest exponent of its variable term. The variable in this example is x, and the maximum exponent of x is 6, which is the degree of the polynomial. As a result, the polynomial x⁶ + 4x - 3 has a degree of 6.
More about the polynomial link is given below.
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A box without a top is to be made from a rectangular piece of cardboard, with dimensions 11 in. by 16 in., by cutting out square corners with side length x and folding up the sides
Answers
Answer:
• V = x(11 -2x)(16 -2x)
• x ≈ 2.1 in
Step-by-step explanation:
a) The volume of the box is the product of its depth (x), width (11 -2x) and length (16 -2x). The equation can be simply ...
v(x) = x(11 -2x)(16 -2x)
__
b) A graphing calculator can plot this equation directly. All that is needed is to enter it into the appropriate space provided by the calculator. The value of x that gives the greatest volume is the value that makes the function have a local maximum between x=0 and x=5.5 (where the volume is again zero).
That value of x is about 2.1 inches.
Help Plz ASAP!!!!!
Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and check #149 on 9/14 in the amount of $240.67. No other Transactions were made
What should the balance be in Arianna register? Use this bank statement
A.-$32.63
B.$448.72
C.$587.88
D.877.82
Answers
Answer:
Step-by-step explanation:
Observe in the attached image that the final balance in your account on 9/1 is $578.30.
Then:
*On 9/6 he makes a payment of $140.30
*On 9/8, he makes a withdrawal from an ATM of $120
This means that:
$140.30 + $120 = $260.30
Then:
*On 9/18 you receive a deposit of $356.22
This means that:
$356.22
So, we have:
Beginning Balance: $578.30.
Total Withdrawals: $260.30
Total Deposits: $356.22
Final Balance = Beginning balance + Total Deposits - Total Withdrawals
Final Balance= $578.30 + $356.22 - $260.30
Final balance= $674.22
Then:
Date Description Debits(-) Credits(+) Balance
9/6 Auto Pay 140.30 438.00
9/8 ATM 120.0 318.00
9/18 Deposit 356.22 674.22
The balance in Arianna's register after the transactions will be $587.88. Then the correct option is C.
What is a bank transaction?
A monetary transfer is a record of money entering and exiting your account and is known as a bank transaction.
Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and checks #149 on 9/14 in the amount of $240.67.
No other Transactions were made.
Then the balance be in Arianna's register will be
→ $ 578.37 + $ 310.25 - $ 60 - $ 240.67
→ $ 587.88
More about the bank transaction link is given below.
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If B=26° and b=18 then find c (picture provided)
Answers
Answer:
c. 41.1
Step-by-step explanation:
To find a, we'll use the Law of Sines that says:
[tex]\frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex]
And we'll isolate c to get:
[tex]c = \frac{sin(C) * b}{sin(B)}[/tex]
Then we will plug-in the information we already have :
[tex]c = \frac{sin(90) * 18}{sin(26)} = 41.06[/tex]
So, let's round it to 41.1 to match the answer number C.
Answer:
The correct answer is option C. 41.1
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Sin θ = opposite side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of c
It is given that, B=26° and b=18
Sin26 = opposite side/Hypotenuse = b/c
c = 18/Sin26 = 41.1
Therefore the correct answer is option c. 41.1
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
An organization of berry farmers releases a study reporting that people who eat blueberries every day have a lower cholesterol level.
Which statement describes the best conclusion to draw from the study?
Answers
Answer:
C
Step-by-step explanation:
I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.
The best conclusion from the study is that the consumption of blueberries might be associated with lower cholesterol levels. However, it's important to note that correlation does not mean causation and other factors could be at play.
Explanation:The statement that comes closest to an appropriate conclusion from the study is that the possible consumption of blueberries might be associated with lower cholesterol levels. However, it is important to remember that correlation does not necessarily imply causation. While the organization of farmers showed a connection between eating blueberries and lower cholesterol, this does not necessarily mean eating blueberries directly causes lower cholesterol. Other factors could be involved. For instance, those who eat blueberries daily might generally lead healthier lifestyles, contributing to lower cholesterol levels.
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Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v ≤ π.
Answers
Compute the surface element:
[tex]\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv[/tex]
[tex]\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}[/tex]
[tex]\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}[/tex]
So the integral is
[tex]\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)[/tex]
[tex]=\dfrac23(37^{3/2}-1)[/tex]
Find the area of the shaded sector (It is 45 degrees with a radius of 7) Help!!!
Answers
Answer:
Step-by-step explanation:
The formula for the area of a sector is
[tex]A_{s} =\frac{\theta }{360}*\pi r^2[/tex]
where theta is the angle given as 45 and r is the radius (7). Plugging in we get
[tex]A_{s}=\frac{45}{360}*\pi (7)^2[/tex]
Simplify a bit to get
[tex]A_{s}=\frac{1}{8}*49\pi[/tex]
which gives you, in terms of pi:
[tex]A_{s}=\frac{49\pi }{8}[/tex]
or if you need to use the decimal form, rounded to the hundredths position:
A = 19.24
Solve the quadratic equation by factoring. 9x^2+24x+20=4
A. x=4/3
B. x=-3/4
C. x=4
D. x=-4/3
Answers
D. -4/3
Let's solve your equation step-by-step.
9x2+24x+20=4
Step 1: Subtract 4 from both sides.
9x2+24x+20−4=4−4
9x2+24x+16=0
Step 2: Factor left side of equation.
(3x+4)(3x+4)=0
Step 3: Set factors equal to 0.
3x+4=0 or 3x+4=0
x= −4 /3
Hope This helps
Answer:
D. x = [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
Step 1: Subtract 4 from both sides.
9x^2 + 24x + 20 − 4 = 4 − 4
9x^2 + 24x + 16 = 0
Step 2: Factor left side of equation.
(3x+4)(3x+4) = 0
Step 3: Set factors equal to 0.
3x+4=0 or 3x+4=0
x = [tex]-\frac{4}{3}[/tex]
I hope this helps your assignment! Anyways, have a fantastic day! :D
Determine the critical? value(s) for a? left-tailed test of a population mean at the alphaequals0.01 level of significance based on a sample size of nequals15.
Answers
Answer: 2
Step-by-step explanation:
Anna's scores for a video game are 670, 575, 400, 575, 1250, 720, and 885. Which statement about the data is correct?
Answers
Answer:
Step-by-step explanation:
what are the statements about the data?
Answer
C) The mean is greater than the median.
Step-by-step explanation:
To find the median, order the scores from LEAST to GREATEST.
400, 575, 575, 670, 720, 885, 1250.
The mean is the middle number, which is 670.
To find the mean, average the scores:
400 + 575 + 575 + 670 + 720 + 885 + 1250
7
= 725
725 > 670; therefore, the mean is greater than the median.
Please help!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
65 - Acute
72 - Acute
96 - Obtuse
Answer:
(a)
Step-by-step explanation:
Given 3 sides of a triangle a, b and c where c is the longest side, then
• If a² + b² = c² ⇒ triangle is right
• If a² + b² > c² ⇒ triangle is acute
• If a² + b² < c² ⇒ triangle is obtuse
Here a = 65, b = 72 and c = 96
65² + 72² ? 96²
4225 + 5184 ? 9216
9409 > 9216 ⇒ triangle is acute
in the triangle below what ratio is sec H
Answers
For this case we have that by definition:
[tex]Secant (A) = \frac {1} {Cosine (A)}[/tex]
Then, we find the cosine of the angle H, this will be given by the leg adjacent to H on the hypotenuse of the triangle.
[tex]Cos (H) = \frac {g} {f}[/tex]
So, the secant of H is given by:[tex]Sec {H} = \frac {1} {\frac {g} {f}}\\Sec {H} = \frac {f} {g}[/tex]
Answer:
Option C
Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the ground to the floor of the porch, which is 2 1/2
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.
What length board should Jessica buy if she uses the maximum angle of incline?
Enter your answer in the box. Round only your final answer to the nearest tenth.
Answers
The board must be about 4.4 ft long
Answer:
Length of board should Jessica buy is 4.4 feets.
Step-by-step explanation:
Height of the ramp = [tex]2\frac{1}{2} ft=\frac{5}{2} ft[/tex]
Distance of the porch from the ground = x
Inclination of the ramp,θ = 35°
In triangle ABC,
AB = [tex]\frac{5}{2} ft[/tex]
AC = x
θ = 35°
According trigonometric ratios:
[tex]\sin \theta =\frac{Perpendicular}{hypotenuse}[/tex]
[tex]\sin 35^o =\frac{AB}{AC}[/tex]
[tex]0.573576=\frac{\frac{5}{2} ft}{x}[/tex]
[tex]x=4.3586 ft\approx 4.4 ft[/tex]
Length of board should Jessica buy is 4.4 feets.
Can someone please help me on this question.
Answers
Answer:
Step-by-step explanation:
[tex]3x^{2} + 5x-12=0[/tex]
[tex]-12=-5x-3x^{2}[/tex]
[tex](-12=-5x-3x^{2} ) * -1[/tex]
[tex]\sqrt{12=5x+3x^{2}[/tex]
Graph y = | x | + 5
Answers
Answer:
(0,5) (0,-5)
Step-by-step explanation:
Answer:
Step-by-step explanation:
The basic (parent) function here is y = |X|, the absolute value function.
This function has a v-shape that opens up and has its vertex at (0, 0).
Each leg is at a 45° angle to the x - axis. Draw this.
Then translate the entire graph upward by 5 units. The result will be the graph of y = | x | + 5.
40 points PLEASE HURRY!!!
Noya needs to determine the number of books that will fit into a box. If the box has a length of 18 inches and each book is 2/9 of an inch thick, which expression can be used to determine the number of books that will fit into the box?
A. 18 divided by 2/9
B. 18 x 2/9
C.2/9 divided by 18
D.9/2 divided by 18
Answers
Answer:
A. 18 divided by 2/9
Step-by-step explanation:
To determine the number of boos that will fit into a box that is 18 inches long, we divide the length of the box by the length of the books
18 inches divided by 2/9 inches per book
This tells us how many books
copy dot flip
18 * 9/2
81 books
shelby's monthly periodic rate is 1.95%. what is the APR?
Answers
Monthly periodic rate = 1.95%
The APR is the annual periodic rate
The annual periodic rate is the monthly rate multiplied by 12, because there are 12 months in a year
APR = monthly periodic rate X number of months in a year
= 1.95% X 12
= 23.4%
By using the concept of Annual Periodic rate and Monthly periodic rate,
Annual periodic rate of Shelby = 23.4%
What is Annual Periodic Rate and Monthly periodic rate?
At first it is important to know about Periodic rate.
Periodic rate is the rate that can be charged on loans for a certain period.
If the periodic rate is calculated over a month then it is called monthly periodic rate.
If the periodic rate is calculated over a year then it is called Annual periodic rate.
Here,
Monthly periodic rate of Shelby = 1.95%
Annual periodic rate of Shelby = [tex]1.95 \times 12[/tex]
= 23.4%
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What is "theoretical probability"? What is "experimental probability"? What's the difference?
Answers
Theoretical probably is what you would expect to happen.
Example, flipping a coin has a 50% chance of landing on heads, so if you flipped a coin 100 times, theoretically the coin would land on heads 50 times ( 50%).
Experimental probablity is what actually happens. Using the coin example, flipping the coin 100 times, it could actually land on heads 100 times or any number of times from 0 to 100.
Hello There! Theoretical probability deals with events happening in theory. It is what is expected t happen.
Experimental probability is a little different. This is based on the number of repeated trials during an experiment.
The difference is Theoretical probability is what you expect to happen
Experimental probability is what actually ends up happening.
A fish tank is a cube. Its side length is 4 1/2 feet. The volume of water needed to completely fill the fish tank is ___ cubic feet.
Answers
The equation for the volume of a cube is V=s^3, where V is volume and s is side length. Plug in and solve:
V=4.5^3
V=4.5*4.5*4.5
V=91.125ft^3
Hope this helps!!