Answer:
To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and [tex]f^{-1}(x)= \frac{ln\ x+4}{2}[/tex]
Step-by-step explanation:
Data provided in the question
f(x) = e^2x - 4
Now
to find the inverse let
So,
y = e^2x - 4
Now
Replace x and y
Therefore
x = e^2y - 4
Now compute the value of y
So,
x + 4 = e^2y
Now take ln on both sides:
The equation is
ln(x+4) = ln(e^2y)
ln(x+4) = 2y
y = ln(x+4) ÷ 2
[tex]f^{-1}(x)= \frac{ln\ x+4}{2}[/tex]
Therefore, To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and [tex]f^{-1}(x)= \frac{ln\ x+4}{2}[/tex]
Answer:
Put them in this order in the fill in the blanks, X,Y, 4, 2
Step-by-step explanation:
Which of the following equations have exactly one solutions 19x + 18 = -19x +18
Answer:
there's only one equation listed, and it has one solution, which is 0
Step-by-step explanation:
Answer: There is only one equation here...
Anyway it's ans is 0
Step-by-step explanation:
Feel pleasure to help u
a private opinion poll is conA private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed to be 92% confident that the sample proportion will not differ from the true proportion by more than 2% ducted for a politician to determine
Answer: 1,914
Step-by-step explanation:
first we take down the information given to us
For 92% confidence, z = 1.75
Error of margin E = 2% = 0.02
Since no estimate of population proportion has been given, we will assume:
p = q = 0.50
Hence,
Sample size required n
n = ( z/E)² × p × q
n = ( 1.75/0.02)² × 0.5 × 0.5
n = (87.5)² × 0.5 ×0.5
n = 1914
What does the graph of f(x)=3x^2-2x+1 look like
Answer:
Below.
Step-by-step explanation:
This is a parabola.
As the coefficient of x^2 is positive it will open upwards ( shaped like a 'U').
If we convert to vertex form we can find the line of symmetry and the coordinates of the vertex:
f(x) = 3x^2 - 2x + 1
f(x) = 3(x^2 - 2/3 x) + 1
f(x) = 3[(x - 1/3)^2 - (1/3)^2] + 1
f(x) = 3(x - 1/3)^2 - 1/3 + 1
f(x) = 3(x - 1/3)^2 + 2/3
So the line of symmetry is x = 1/3 and
the vertex ( the minimum of the curve) is at (1/3, 2/3).
A coordinate plane with a line passing through (negative 3, negative 5), (0, 1), and (2, 5). A function f(x) is graphed. What is the slope of the function? m = What is the y-intercept of the function? b = Which equation represents the graph of the function?
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Functions.
so after plotting the graphs, we get as,
==> m = 2.5
==> b = 0
==> y = mx+c
a straight line
Answer:
your answer is, because i got it right your welcome
Step-by-step explanation:
Which function has the greatest rate of exponential growth? Multiple choice options below.
Answer:
Option (3).(Bottom left)
Step-by-step explanation:
Formula for the exponential growth is,
h(x) = [tex]a(1+\frac{r}{100} )^{t}[/tex]
where r = rate of exponential growth
a = initial amount
t = duration or time
Option (1) (Top left)
h(t) = [tex](1+0.18)^{\frac{t}{6}}[/tex]
= [tex](1+\frac{18}{100})^t[/tex]
Rate of exponential growth will be,
r = 18%
Option (2) (Top right)
k(t) = [tex](\frac{3}{8})^t[/tex]
= [tex](1-\frac{5}{8})^t[/tex]
= [tex](1-0.625)^t[/tex]
= [tex](1-\frac{62.5}{100})^t[/tex]
r = -62.5%
This function shows the exponential decay rate of 62.5%.
Option (3) (Bottom left)
f(t) = [tex]1.36^t[/tex]
= [tex](1+0.36)^t[/tex]
= [tex](1+\frac{36}{100})^t[/tex]
r = 36%
Option (4) (Bottom right)
g(t) = [tex]0.86^t[/tex]
= [tex](1-0.14)^t[/tex]
= [tex](1-\frac{14}{100})^t[/tex]
r = -14%
This function shows the decay rate of 14%.
Therefore, Option (3). (Bottom left) shows the greatest exponential growth.
EZ car rental charges $40 a day plus $0.25 per mile. Ace Rent-A-Car charges, $25 a day plus $0.45 per mile. What number of miles result in the same cost for one day?
To Finance a Vacation in 4 years, Margo saves $530 at the begenning of the every month in an account paying interest at 3.9% compounded quarterly a. What will be the balance in her ac To Finance a Vacation in 4 years, Margo saves $530 at the begenning of the every month in an account paying interest at 3.9% compounded quarterly a. What will be the balance in her account when he takes the vacation? [4 marks] b. How much of the balance will be an interest? [2 marks] c. If she waits an additional year to start her vacation, continues to save the same amount of money, how much more money does she have to spend count when he takes the vacation? [4 marks] b. How much of the balance will be an interest? [2 marks] c. If she waits an additional year to start her vacation, continues to save the same amount of money, how much more money does she have to spend
i got this question too as my homework it so hard ill let you know if i find out the answer.
what is 2 7/15 x 1 3/7
Answer:
The answer is 3 11/21
Step-by-step explanation:
Answer:
[tex]\underlie{\bold{\ 3\frac{11}{21}\ }}[/tex]
Step-by-step explanation:
[tex]2\frac7{15}\cdot1\frac37=\frac{2\cdot15+7}{15}\cdot\frac{1\cdot7+3}{7}=\frac{37}{15}\cdot\frac{10}{7}=\frac{37}{3}\cdot\frac{2}{7}=\frac{37\cdot2}{3\cdot7}=\frac{74}{21}=\frac{3\cdot21+11}{21}=3\frac{11}{21}[/tex]
Find the circumference of the circle with the given radius or diameter. (Use 3.14 for it) r=20
Answer:
C = 2πr = 2 * 3.14 * 20 = 125.6
Answer:
[tex]\huge\boxed{C\approx125.6}[/tex]
Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=d\pi=2\pi r[/tex]
d - diameter
r - radius
We have the radius r = 20.
Substitute:
[tex]C=2\pi(20)=40\pi[/tex]
use π ≈ 3.14
[tex]C\approx(40)(3.14)=125.6[/tex]
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answer:
Hey there!
We have the equation: y2-y1/x2-x1.
So, we have: 8-2/8-6.
6/2, or 3.
Hope this helps!
How many kilobytes have been downloaded so far?
Answer:
Do you have a photo or some other information to go with this?
Step-by-step explanation:
PLZ HELP Point C(3.6, -0.4) divides in the ratio 3: 2. If the coordinates of A are (-6, 5), the coordinates of point B are? If point D divides in the ratio 4: 5, the coordinates of point D are?
Answer:
In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.
To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB.
1. Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3
A (-2,-1) and B(-6, -7)The distance between A and B would be:
x= x2-x1 = -6 - (-2)= -4
y= y2-y1 = -7 - (-1)= -6
Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.
Point C(-3.6, -3.4) divides AB in the ratio 2:3
x3= x1 + AB ratio* AB distance
x3= -2 + (2/2+3)*(-4)= -3.6
y3= y1 + AB ratio* AB distance
y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4
2. Point C(0, 1) divides AB in the ratio 4:7
A(4,-3) and B(-7,8)
The distance between A and B would be:
x= x2-x1 = -7 - (4)= -11
y= y2-y1 = 8 - (-3)= 11
Since both x and y distance is 11, let's try answer with total ratio 11
Point C(0, 1) divides AB in the ratio 4:7
x3= x1 + AB ratio* AB distance
x3= 4 + (4/4+7)*(-11)= 4- 4=0
y3= y1 + AB ratio* AB distance
y3= -3 + (4/4+7)*(11)= -3 +4= 1
3. Answer: Point C(8, 9) divides AB in the ratio 5:3
A(3,4) and B(11,12)The distance between A and B would be:
x= x2-x1 = 11 - (3)= 8
y= y2-y1 = 12 - (4)= 8
Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.
Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus
Point C(-2, 5) divides AB in the ratio 2:6 -----> total ratio 8, x minus
Point C(8, 9) divides AB in the ratio 5:3 -----> total ratio 8, both x and y plus
x3= x1 + AB ratio* AB distance
x3= 3 + (5/5+3)*(8)= 3+ 5=8
y3= y1 + AB ratio* AB distance
y3= 4 + (5/5+3)*(8)= 4 +5= 9
4. Point C(-2, 5) divides AB in the ratio 2:6
A(-5,2)and B(7, 14)
The distance between A and B would be:
x= x2-x1 = 7 - (-5)= 12
y= y2-y1 = 14 - (2)= 12
Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.
Point C(4, 1.6) divides AB in the ratio 3:2 -----> x more than y
Point C(-2, 5) divides AB in the ratio 2:6 -------> y plus, y more than xx3= x1 + AB ratio* AB distance
x3= -5 + (2/2+6)*(12)= -5+ 3=-2
y3= y1 + AB ratio* AB distance
y3= 2 + (2/2+6)*(12)= 2 +3= 5
Step-by-step explanation:
Solve for x, given a=117. Round your answer to one decimal place.
Answer:
x = 63
Step-by-step explanation:
We can find the value of x by multiplying the difference of large arc to small arc with 1/2
if a = 117° then the large arc would be 243
1/2 × (243 - 117) = 63
Please Help I will give out brainliest
Answer:
when y=1 then x=0.5
Step-by-step explanation:
The graph is provided.
The equation y=4x-1 can be graphed by first graphing the -1 which is the y-intercept in the y=mx+b form. 4=m that is our slope. you can find the lines second point by moving 4 up and 1 to the right. rise/run =4/1. So when you move 4 up and 1 right you get another point on the line (1,3).
You can find out x=0.5 when y=1 by just tracing your finger over the graph and the point when y equals 1 the line intercepts x=0.5. Another screenshot is given.
I hope this helps!
a regular pentagon-based pyramid has 5 faces which are equilateral triangles the perimeter of it's net is 70cm what is the perimeter of the base?
Answer:
35cm
Step-by-step explanation:
The net of a regular pentagon has 10 sides.
Since each of the faces are equilateral triangles, the side lengths are equal.
Therefore:
Length of each side of the net = 70/10 =7cm
Therefore, the base is a regular pentagon of side length 7cm.
The perimeter of the base of the pyramid = 5 X 7
=35cm
The perimeter of the base of the pyramid is 35cm.
The coefficient of x in the expansion of the following is (x+3)^3 a) 1 b) 3 c) 18 d) 27 e) 9
Answer:
d) 27
Step-by-step explanation:
The expanded form of (a+b)³ is ...
(a +b)³ = a³ +3a²b +3ab² +b³
When we are expanding (x +3)³, the x-term is ...
3(x)(3²) = 27x
The coefficient of x in the expansion is 27.
Function of a Function
Answer:
B. 8
Step-by-step explanation:
Step 1: Find g(-2)
g(-2) = (-2)² + 1
g(-2) = 4 + 1
g(-2) = 5
Step 2: Find f(5)
f(5) = 2(5) - 2
f(5) = 10 - 2
f(5) = 8
Consider the function. f(x)= -2/3x-24 Which conclusions can be drawn about f–1(x)? Select two options. f–1(x) has a slope of -2/3 . f–1(x) has a restricted domain. f–1(x) has a y-intercept of (0, –36). f–1(x) has an x-intercept of (–36, 0). f–1(x) has a range of all real numbers.
Answer:
(D) [tex]f^{-1}{(x$) has an x-intercept of (-36, 0).[/tex]
(E)[tex]f^{-1}{(x)[/tex] has a range of all real numbers.
Step-by-step explanation:
Given the function: [tex]f(x)= -\dfrac23x-24[/tex]
[tex]f(x)+24= -\dfrac23x\\$Multiply both sides by $ -\dfrac32\\x=-\dfrac32(f(x)+24)\\f^{-1}(x)=-\dfrac32f(x)-36[/tex]
When y=f(x)=0
[tex]f^{-1}(x)=-\dfrac32(0)-36\\f^{-1}(x)=-36[/tex]
Therefore, [tex]f^{-1}(x)$ has a x-intercept of -36[/tex]
Also, [tex]f^{-1}(x)[/tex] has a range of all real numbers.
Therefore, Options D and E are correct.
Answer:
4 and 5
Step-by-step explanation:
EDGE
Small library contains 700 novels. how many ways can You check out three novels
The first book you select can be any one of 700.
. . . For each of those ...
The second book can be any one of the other 699.
. . . For each of those ...
The third book can be any one of the remining 698.
The total number of ways to gather three books from the shelves into your hands is (700 · 699 · 698) = 341,531,400 ways .
BUT ...
When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves. You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.
So, even though there are 341,531,400 ways to gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.
What’s are the answers for both?
Answer:
d = 8g = 2Step-by-step explanation:
8d + 4 = 5d + 28
Group like terms
That's
8d - 5d = 28 - 4
3d = 24
Divide both sides by 3
d = 8
[tex] \frac{7(7g + 8)}{4} = 38.5[/tex]
Cross multiply
we have
7(7g + 8) = 38.5(4)
49g + 56 = 154
49g = 154 - 56
49g = 98
Divide both sides by 49
g = 2
Hope this helps you
What is the value of x?
Answer:
x=12
Step-by-step explanation:
Intersecting Chords Formula:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
10 * x = ( 3+x) *8
10x = 24+8x
Subtract 8x
10x-8x = 24+8x-8x
2x= 24
Divide by 2
2x/2 =24/2
x = 12
sketch the graph for the following quadratic function.
[tex] - x ^{2} + 4x + 12[/tex]
it's ok if it's wrong.i just wanna see how the work done to do this
Answer:
Please refer to the attached image for the graph of given function.
Step-by-step explanation:
Given the equation:
[tex]-x^{2} +4x+12[/tex]
Let us rewrite by letting it equal to [tex]y[/tex].
[tex]y=-x^{2} +4x+12[/tex]
Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.
Let us compare the given equation with standard quadratic equation:
[tex]y=ax^{2} +bx+c[/tex]
we get:
[tex]a = -1\\b = 4\\c = 12[/tex]
Coefficient of [tex]x^{2}[/tex] is negative 1, so the parabola will open downwards.
Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.
Formula for axis of symmetry is:
[tex]x = -\dfrac{b}{2a}[/tex]
[tex]x = -\dfrac{4}{2(-1)}\\\Rightarrow x=2[/tex]
It is shown as dotted line in the image attached in the answer area.
Axis of symmetry will also contain the vertex of the parabola.
It is a downward parabola so vertex will be the highest point on this parabola.
Putting x = 2 in the equation of parabola:
[tex]y=-2^{2} +4\times 2+12\\\Rightarrow y =16[/tex]
So, vertex will be at P(2, 16).
Now, let us find points of parabola to sketch graph:
put x = 0, [tex]y=-0^{2} +4\times 0+12=12[/tex]
Another point is Y(0,12)
Now, let us put y = 0, it will give us two points because the equation is quadratic in x.
[tex]0=-x^{2} +4x+12\\\Rightarrow -x^{2} +6x-2x+12=0\\\Rightarrow -x(x -6)-2(x-6)=0\\\Rightarrow (-x-2)(x-6)=0\\\Rightarrow x = -2, 6[/tex]
So, other two points are X1(-2, 0) and X2(6,0).
If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.
what is pythagorus theorum?
Answer:
when the square on the hypotenuse of a right-angled triangle is equal in to the sum of the squares on the other two sides
Step-by-step explanation:
let's say......
h = ?
o = 4
a = 4
a^2+o^2=32
square root 32
5.65685424949
that is the value for h
Answer:
A^2+B^2=C^2
you use it the find any length of a right angled triangle
PLZ HELP QUICK............
Answer:
[tex]4^m[/tex]
Step-by-step explanation:
When you exponent an exponent, you multiply the powers together.
When you divide exponents, you subtract the powers.
Step 1: Convert to same base
log₄64 = 3
Step 2: Rewrite equation
[tex]\frac{(4^3)^{0.5m}}{4^{0.5m}}[/tex]
Step 3: Simplify
[tex]\frac{4^{1.5m}}{4^{0.5m}}[/tex]
Step 4: Simplify
[tex]4^m[/tex]
Eli chooses two shirts from a group of five to pack for a weekend trip. Let each shirt be represented by A, B, C, D, and E. Which statements about the situation are true?
Answer:
A, B and E statements are true
Step-by-step explanation:
Since in the question, it is mentioned that Eli selected two shirts out of pack 5 for a weekend trip
Classify each shirt as A, B, C, D, and E.
Now we have to go through the options
In the first statement it is mentioned that AB and BA are the similar. This is true as it contains in same bag.
Since Eli select two shirts so the second statement is also correct
And, the last statement is also true as he selects shirt B so there are four possible ways to second the second shirt as there are four remaining shirts are left after select one shirt
Hence, A, B and E statements are true
Answer: A, B, and E.
Step-by-step explanation:
A is correct: the combination of AB and BA are the same because they both contain the same letters, just a different order.
B is correct: each shirt can be paired with any one of the other remaining shirts because she will be choosing 2 shirts.
E is correct: If he chooses shirt B, there are 4 possible outcomes for choosing the 2nd shirt. This is true because there is only one B in a group of 5 shirts, so 5-1 = 4 possible outcomes.
Hope this helped.
Have a nice day. :)
Plz help, and it's easy, 3D shapes ASAP
Answer:
9. A cylinder
10. A cone
Step-by-step explanation:
You sketched the shapes right
Answer:
Please look below for your answer
Step-by-step explanation:
The first is a cylinder and the second is a cone. Those are amazing drawings B.T.W. I love them
I hope I helped
Please mark me as brainliest
Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable.
Complete question:
Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?
Answer:
Here,
Independent variable (IV) is: the color of the light produced by the lamp (red, orange, yellow, green, or blue)
We are also told only 10 participants are available.
All 10 participants are being exposed to all five levels of the color variable in the same order.
Counterbalancing is said to be a technique used when establishing task order. It helps prevent introduction if cofounding variables.
Dr. Lyte will need to use counterbalancing technique in this scenario because some of the participants may be unable to understand difference in similar colours. Example some participants may not be able to differentiate between orange and red when the red colour comes after orange.
But using counterbalancing technique, Dr. Lyte can avoid such an error.
Lori is making 3 mugs of hot chocolate. Each mug holds 1/2 a pint. How many cups of hot chocolate does Lori pour?
Answer:
3 CUPS pints
Step-by-step explanation:
Multiple to get it by doing this (1/2) US pint x 3 = 1.5 US pints *2= 3 cups
Help please urgently❤️ With atleast some Plz
Answer:
2. -3, 1.
3. -2, 0.
4. 6, 8.
5. 20.
Step-by-step explanation:
2. x - 3y + 6 = 0
-3y = -x -6
y = 1/3x + 2
y + 4 = -5/4(x - 1)
y + 4 = -5/4x + 5/4
y = -5/4x + 5/4 - 16/4
y = -5/4x - 11/4
If you sketch these two lines on paper (or draw them on a graphing calculator), you will find that they intersect at (-3, 1).
So, the values you enter on the response would be -3, 1.
3. x + 3y = -2
x = -3y - 2
-3x + 5y = 6
-3(-3y - 2) + 5y = 6
9y + 6 + 5y = 6
14y + 6 = 6
14y = 0
y = 0
x + 3 * 0 = -2
x + 0 = -2
x = -2
-3 * -2 + 5 * 0 = 6
Since everything works out, the solution to the two equations is (-2, 0).
So, the values you enter on the response would be -2, 0.
4. 3x - 4y = -14
2x + 5y = 52
2(3x - 4y = -14)
3(2x + 5y = 52)
6x - 8y = -28
6x + 15y = 156
6x + 15y = 156
-6x + 8y = 28
23y = 184
y = 8
3x - 4 * 8 = -14
3x - 32 = -14
3x = 18
x = 6
2 * 6 + 5 * 8 = 12 + 40 = 52
Everything works out, so your solution is (6, 8).
Your answer will be (6, 8).
5. For a system of equations to have no solution, the y's and the x's must have the same coefficients.
5x - Ky - 10 = 0
y = 1/4x + 6
-Ky = -5x + 10
Ky = 5x - 10
1/5Ky = x - 2
1/20Ky = 1/4x - 1/2
1/20K = 1
K = 20
y = 1/4x - 1/2
y = 1/4x + 6
1/4x - 1/2 = 1/4x + 6
1/4x - 1/4x = 6 + 1/2
0 = 6.5
There is no solution, so K = 20.
Hope this helps!!
Which expression is equal to StartAbsoluteValue negative 12 EndAbsoluteValue minus StartAbsoluteValue Negative 3 EndAbsoluteValue? –15 –9 9 15
Answer:
9.
Step-by-step explanation:
When there is an absolute value, anything within the absolute value becomes positive. Things outside the absolute values stay as they are.
|-12| - |-3| = 12 - 3 = 9.
Hope this helps!
Answer:
The answer is C
Step-by-step explanation:
hope it helps