Answers
Answer:
[tex]\huge\boxed{D) \ f^{-1}(x) = (x-3)^2+2}[/tex]
Step-by-step explanation:
[tex]f(x) = \sqrt{x-2} + 3[/tex]
Replace f(x) by y
[tex]y = \sqrt{x-2} + 3[/tex]
Interchange x and y
[tex]x = \sqrt{y-2} + 3[/tex]
Solve for y
[tex]x = \sqrt{y-2} + 3[/tex]
Subtracting 3 to both sides
[tex]x - 3 = \sqrt{y-2}[/tex]
Taking square on both sides
[tex](x-3)^2 = y-2[/tex]
Adding 2 to both sides
[tex]y = (x-3)^2 + 2[/tex]
Replace [tex]y = f^{-1}(x)[/tex]
[tex]f^{-1}(x) = (x-3)^2+2[/tex]
Related Questions
Verify that ϕ(x)=2(1−cex), where cis an arbitrary constant, is a one-parameter family of solutions to dydx=y(y−2)2.Graph the solution curves corresponding to c=0,±1,±2using the same coordinate axes.
Answers
Answer:
Following are the solution:
Step-by-step explanation:
Given equation:
[tex]\frac{dx}{dy}= \frac{y(y-2)}{2}........(a)[/tex]
[tex]\Phi (x) = \frac{2}{1-ce^x}[/tex]
In the question [tex]\Phi (x)[/tex], is a solution of the equation (a) only if when [tex]\Phi (x)[/tex]satisfies equation (a):
let us find [tex]\Phi' (x)[/tex]:-
[tex]\Phi(x) =\frac{d}{dx} \Phi (x)=\frac{d}{dx}(\frac{2}{1-ce^x})[/tex]
[tex]= 2 \frac{d}{dx}({1-ce^x}^-1)\\\\= 2 (-1) ({1-ce^x})^{-2} \frac{d}{dx}({1-ce^x})\\\\= -2 ({1-ce^x})^{-2} (-ce^x})\\\\= 2(-ce^x) ({1-ce^x})^{-2} \\\\[/tex]
Now:
[tex]\frac{dy}{dx}=\frac{y(y-2)}{2}\\\\\frac{d}{dx}\Phi (x) =\frac{\Phi (x) (\Phi (x)-2)}{2}\\[/tex]
by subtracting the value of [tex]\Phi (x)[/tex]and [tex]\frac{d}{dx}[/tex][tex]\Phi (x)[/tex],we get:
[tex]\to[/tex][tex]2ce^x(1-ce^x)^-2= \frac{(\frac{2}{1-ce^x})(\frac{2}{1-ce^x})^{-2}}{2}[/tex]
[tex]=2ce^x (1-ce^x)^{-2}=\frac{1}{2}[\frac{2}{1-ce^x}(\frac{2-2(1-ce^x)}{1-ce^x)}]\\\\= \frac{1}{1-ce^x} \times \frac{2ce^x}{1-ce^x}\\\\=\frac{2ce^x}{(1-ce^x)^2}\\\\=2ce^x (1-ce^x)^-2[/tex]
[tex]\bold{2ce^x(1-ce^x)^-2=2ce^x(1-ce^x)^-2}[/tex]
[tex]\Phi (x)[/tex] the solution of the given equation. [tex]\Phi (x)[/tex] has one Parameter Family of
[tex]\frac{dy}{dx}=\frac{y(y-2)}{2}[/tex]
[tex]\Phi (x) =\frac{2}{1-ce^x}\\\\_{when} \ \ \ c= 0 \to \Phi (x) =\frac{2}{1-0\times e^x}=2\\\\_{when} \ \ \ c= 1 \to \Phi (x) =\frac{2}{1-1\times e^x}=\frac{2}{1-e^x}\\\\_{when} \ \ \ c= -1 \to \Phi (x) =\frac{2}{1-(-1)\times e^x}=\frac{2}{1+e^x}\\\\_{when} \ \ \ c= 2 \to \Phi (x) =\frac{2}{1-(-2)\times e^x}=\frac{2}{1-2e^x}\\\\_{when} \ \ \ c= -2 \to \Phi (x) =\frac{2}{1-(-2)\times e^x}=\frac{2}{1+2e^x}\\\\[/tex]
2a+4b-a+2b=???
Where do I start
Answers
the number in each block is the sum of the numbers in the two blocks beneath it. Some of the numbers are hidden. What is the value of y - x
Answers
Answer:
y - x = 69
Step-by-step explanation:
From the figure attached,
Number in each block is the sum of the numbers in the block beneath it.
Therefore, A + 21 = 32 ⇒ A = 11
A + 5 = B ⇒ B = 16
C = 5 + x
D = 32 + B ⇒ D = 32 + 16 = 48
E = B + C ⇒ E = 16 + (5 + x)
⇒ E = 21 + x
y = D + E ⇒ y = 48 + (21 + x)
y = 48 + 21 + x
y = 69 + x
y - x = 69
Therefore, y - x = 69 will be the answer.
divide 4,000,000 in the ratio 2 is to 3 is to 4 is to 5 is to 6
Answers
Answer:
Step-by-step explanation:
2+3+4+5+6=20
20/20=4,000,000
2/20=?
2/20×4,000,000÷20/20=400,000
20/20=4,000,00
3/20
3/20×4000000÷20/20=600,000
20/20=4,000,000
4/20
4/20×4,000,000÷20/20=800,000
20/20=4,000,000
5/20
5/20×4,000,000÷20/20=1,000,000
20/20=4,000,000
6/20
6/20×4,000,000÷20/20= 1,200,000
2:3:4:5:6=400,000 :600,000: 800,000 : 1,000,000: 1,200,000
What is expression is equivalent to 210,704? Is it 20,000+10,000+700+4. 200,000+10,000+700+4. Or 200,000+10,000+700+40??
Answers
Answer:
200,000+10,000+700+4
Step-by-step explanation:
identify the method that will be used to solve for x for each equation. 4x = 20 5x + 6x = 22
Answers
Step-by-step explanation:
Identify the method that will be used to solve for x for each equation.
4x=20 division property fo equality
x-11=9 addition property of eqaulity
5x+6x=22 Combining Like terms
5(x-2)=30 distibute property
Answer:
ello
Step-by-step explanation:
Identify the method that will be used to solve for x for each equation.
4x=20 division property fo equality
x-11=9 addition property of eqaulity
5x+6x=22 Combining Like terms
5(x-2)=30 distibute property
6+4m-1=21
PLEASE HELP! I’m stuck on this question :/
Answers
Answer:
m=4
best of luck!
Step-by-step explanation:
Answer:
m=4
Step-by-step explanation:
6+4m-1=21
(6-1=) 5+4m=21
21-5=16
16÷4m = 4
I need help please! I really need this fast
Answers
What is the angle between the given vector and the positive direction of the x-axis?8i + 6j.
Answers
Answer:
The between the given vector and the positive direction of the x-axis is approximately 41.186º.
Step-by-step explanation:
Let be [tex]\vec u = 8\,i + 7\,j[/tex] and [tex]\vec v = i[/tex] (Positive direction of the x-axis), the angle between both vectors can be determined from definition of dot product:
[tex]\vec u \bullet \vec v = \|\vec u\|\cdot \|\vec v\| \cdot \cos \theta[/tex]
Angle is cleared:
[tex]\cos \theta = \frac{\vec u\bullet \vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex]
[tex]\theta = \cos^{-1}\left(\frac{\vec u \bullet \vec v}{\|\vec u\|\cdot \|\vec v\|} \right)[/tex]
The norms of [tex]\vec u[/tex] and [tex]\vec v[/tex] are found by Pythagorean Theorem:
[tex]\|\vec u\| = \sqrt{8^{2}+7^{2}}[/tex]
[tex]\|\vec u\| \approx \sqrt{113}[/tex]
[tex]\|\vec v\| = 1[/tex]
The dot product between both vectors is:
[tex]\vec u \bullet \vec v = (8)\cdot (1) + (6)\cdot (0)[/tex]
[tex]\vec u \bullet \vec v = 8[/tex]
The angle is now calculated:
[tex]\theta = \cos^{-1}\left(\frac{8}{\sqrt{113}} \right)[/tex]
[tex]\theta \approx 41.186^{\circ}[/tex]
The between the given vector and the positive direction of the x-axis is approximately 41.186º.
Which features describe the graph? Select all that apply
Answers
Answer:
- Decreasing
Step-by-step explanation:
im not sure of the last two but the others are for sure a no
Can you assume intersection of lines from a diagram
Answers
Answer:
No
Step-by-step explanation:
t the two equations for the lines into slope-intercept form. ...
Set the two equations for y equal to each other.
Solve for x. ...
Use this x-coordinate and plug it into either of the original equations for the lines and solve for y.
is y+2=8 an expression
Answers
Answer:
no
Step-by-step explanation:
hope this helps
plzzz help A model train is on a track 100 cm from its starting point. Turning a switch displaces the train either forward or backward 25 cm along the track depending on which way the switch is turned. Which equation models the position of the train along the track after you turn the switch? A. |x − 25| = 100 B. |x − 100| = 25 C. |x + 25| = 100 D. |x + 100| = 25
Answers
Answer: B. |x-100| = 25
Explanation:
Draw out a number line. Mark 75, 100 and 125 on the number line as points A, B, and C in that order. Don't worry about the spacing.
The value of x represents where the train is. So if we had say x = 85, then it would be at location 85 on the number line. Writing |x-100| is the distance from x to 100. The absolute value ensures the distance is never negative. We want this distance to be 25 because after traveling 25 cm, the switch is turned, and the train goes the other way.
The equation which models the movement of the train is represented by |x − 100| = 25. The correct option is B.
What is an equation?One-variable linear equation The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
The train's location is indicated by the value of x. Therefore, if x were to equal, let's say, 85, it would be at position 85 on the number line.
The distance between x and 100 is expressed as |x-100|. The distance will never be negative thanks to the absolute value. Because the switch is switched after the train has traveled 25 cm in one direction, we need this distance to be 25 cm.
Therefore, the equation which models the movement of the train is represented by |x − 100| = 25. The correct option is B.
To know more about an equation follow
https://brainly.com/question/1640242
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Can you solve 2g - 13 = 3.
g=
Answers
Steps to solve:
2g - 13 = 3
~Add 13 to both sides
2g = 16
~Divide 2 to both sides
g = 8
Best of Luck!
The solution to the equation 2g - 13 = 3 is g = 8.
To solve the equation 2g - 13 = 3 for g, we'll perform the necessary steps to isolate the variable g on one side of the equation.
Starting with the given equation:
2g - 13 = 3
First, we'll add 13 to both sides to eliminate the -13 term on the left side:
2g - 13 + 13 = 3 + 13
2g = 16
Next, to isolate the variable g, we divide both sides by 2:
(2g)/2 = 16/2
g = 8
Therefore, the solution to the equation 2g - 13 = 3 is g = 8.
In this equation, we initially have a linear expression involving the variable g and a constant term. By performing algebraic operations, we rearrange the equation to have g on one side and the constant value on the other side. This isolates the variable and provides us with a specific value for g that satisfies the equation. In this case, the value of g is determined to be 8, which can be verified by substituting it back into the original equation to see if it holds true.
To learn more about the linear equation;
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14 + 3c = 35 la respuesta de esta también porfa se los agradezco que sea con el trabajo completo gracias oh
Answers
14 + 3c = 35
Reste 14 de los dos lados
14 + 3c = 35
-14 -14
Es igual a 3c = 21
Después se divide los dos lados por 3
3c = 31
3 3
Respuesta: C=7
2/3+1/3x=2x
x=1/2
x=5/2
x=2
x=2/5
Answers
Answer:
x = 2/5
Step-by-step explanation:
Solve for x:
x/3 + 2/3 = 2 x
Hint: | Combine x/3 + 2/3 into a single fraction.
x/3 + 2/3 = (x + 2)/3:
(x + 2)/3 = 2 x
Hint: | Make (x + 2)/3 = 2 x simpler by multiplying both sides by a constant.
Multiply both sides by 3:
(3 (x + 2))/3 = 3×2 x
Hint: | Cancel common terms in the numerator and denominator of (3 (x + 2))/3.
(3 (x + 2))/3 = 3/3×(x + 2) = x + 2:
x + 2 = 3×2 x
Hint: | Multiply 3 and 2 together.
3×2 = 6:
x + 2 = 6 x
Hint: | Move terms with x to the left hand side.
Subtract 6 x from both sides:
(x - 6 x) + 2 = 6 x - 6 x
Hint: | Combine like terms in x - 6 x.
x - 6 x = -5 x:
-5 x + 2 = 6 x - 6 x
Hint: | Look for the difference of two identical terms.
6 x - 6 x = 0:
2 - 5 x = 0
Hint: | Isolate terms with x to the left hand side.
Subtract 2 from both sides:
(2 - 2) - 5 x = -2
Hint: | Look for the difference of two identical terms.
2 - 2 = 0:
-5 x = -2
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -5 x = -2 by -5:
(-5 x)/(-5) = (-2)/(-5)
Hint: | Any nonzero number divided by itself is one.
(-5)/(-5) = 1:
x = (-2)/(-5)
Hint: | Simplify the sign of (-2)/(-5).
Multiply numerator and denominator of (-2)/(-5) by -1:
Answer: x = 2/5
Answer: [tex]x=2/5[/tex]
Simplify both sides of the equation
[tex]1/3x+2/3=2x[/tex]
Subtract 2x from both sides
[tex]1/3x+2/3-2x=2x-2x\\-5/3x+2/3=0[/tex]
Subtract 2/3 from both sides
[tex]-5/3x=2/3-2/3=0-2/3\\-5/3x=-2/3[/tex]
Multiply both sides by 3/-5
[tex](3/-5)*(-5/3x)=(3/-5)*(-2/3)\\x=2/5[/tex]
0.2121 repeating as fraction
Answers
The area of a triangle is 11.5 square in the base is 23 in what is the height in inches
Answers
Answer:
Height = 1 inch
Step-by-step explanation:
area of triangle = 1/2 x base x height
11.5 =1/2 x 23 x height
23/23 = height
height = 1
h = 1 inches
Step-by-step explanation:The area of a triangle = formula
A = b×h/2
2A = b×h
h = 2A/b
h = 2×11.5in²/23in
= 23in²/23in
= 1 in
24x - 22 = -4 (1 - 6x)
Answers
Answer:
ffdfssss
Step-by-step explanation:
fdfdfdfd
Answer:
x is invalid.
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Remember to follow PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, distribute -4 to all terms within the parenthesis:
-4(1 - 6x) = (-4 * 1) + (-4 * -6x) = -4 + 24x
24x - 22 = -4 + 24x
Isolate the variable, x. Subtract 24x from both sides:
24x (-24x) - 22 = -4 + 24x (-24x)
0 - 22 = -4 + 0
-22 ≠ -4, therefore, this question is invalid.
~
How much is 5 divided by 3/10?
Answers
Answer:
16.6666666667
Step-by-step explanation:
Answer:
16 2/3
Step-by-step explanation:
Step 1:
5/1 ÷ 3/10
Step 2:
5/1 × 10/3
Step 3:
50/3
Answer:
16 2/3
Hope This Helps :)
What is the sum of 9+10 (;
Answers
Answer:
19 or 21.
Step-by-step explanation:
I swear.
5 + 5 = 10
10 + 5 = 15
15 + 4 = 19
________________
9 + 9 = 18
18 + 10 = 28
28 - 5 = 23
There are two nines so
23 - 2 = 21
Solve the inequality. Graph the solution
|2x+7|>23
Answers
If 2x+7>=0, x>=-3.5 then |2x+7|=2x+7.
Then the inequality becomes:
2x+7>23, 2x>16, x>8.(which is an acceptable result since we already assumed x>=-3.5)
If 2x+7<0, x<-3.5 then |2x+7|= -(2x+7).
Then the inequality becomes:
-(2x+7)>23, 2x+7<-23, 2x <-30, x<-15.
(which is an acceptable result since we already assumed x<-3.5)
Thus the answer is x<-15 or x>8.
The graph is simple. You draw the line of real numbers and "shadow" all numbers above 8 and all numbers bellow - 15.
Please answer I will make you Brainliest if it's right
Answers
Answer:
perfect square
Step-by-step explanation:
Translate and solve: 24.67 is what percent of 129? Rounded to the nearest tenth of a percent.
Answers
Answer:
31.8
Step-by-step explanation:
24.67x129
=>31.82
=>31.8
Use the simple interest formula to determine the missing value. p =$1325, r =?t=2 years I=$37.10 r=?% (Do not round until the final answer. Then round to one decimal place as needed.)
Answers
Answer:
r = 1.4 %
Step-by-step explanation:
given p(principle) is 1,375$, r(interest rate) is unknown, t(time in years) is 2, and I(Interest / final balance) is 37.10$. The simple interest formula: I = prt can be rewritten as: r = I/pt to solve for r. 37.1 / ( 1325 × 2 ) = 37.1 / 2650 = 0.014 = ( 0.014 * 100 ) % = 1.4 %
A cell phone weighs about 2.8x 10pounds. Which value of n is most reasonable?
-3
-1
0
1
Answers
Answer:0
Step-by-step explanation: took the quiz
help me I don't understand
Answers
Answer: the answer should be A
if this helps the equation format is y= mx + b your replace the with the slop and the b with the y intercept
the way to find the slope is rise over run
Step-by-step explanation:
Mark used the money from his saving account for a down payment for a car. Money in his savings account is an example of a
3
Personal finance
Answers
Answer:
Personal finance
Step-by-step explanation:
Personal finance is a technical term in which a person or group of persons pool resources together for the purpose of budgeting, saving, or spending as they deem fit.
Money in Mark's saving account that he used as a down payment for his car is an example of personal finance.
In a box plot, if there is an outlier shown in the picture below, what is considered the min? The outlier or 59?
Answers
Step-by-step explanation:
The outlier is excluded, so the minimum is 59.
Michael earns $10 per hour. He regularly works 40 hours per week.
How many overtime hours would he have to work in a week for his
overtime pay to be greater than his regular gross pay?
Answers
5. Tania earns $13.50 per hour at the Glendale Florist. She regularly works 40 hours per week. She is paid time-and-a-half for each hour of overtime work. Last week she worked. 43 hours. What was her gross pay for the ...
Missing: michael | Must include: michael