Answer:
the inverse of the function f^-1(x)=(x-3)/(4+5x)
Step-by-step explanation:
( 3+4x)/(1-5x)
y=4x+3/1-5x swap the variables
x=4y+3/1-5y solve for y
y=x-3/4+5x
The inverse of a function is :y=x-3/4+5x
What is inverse of a function?
The inverse function returns the original value for which a function gave the output.
If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.
Steps are:
How do you solve inverse functions step by step?Finding the Inverse of a FunctionFirst, replace f(x) with y . Replace every x with a y and replace every y with an x .Solve the equation from Step 2 for y . Replace y with f−1(x) f − 1 ( x ) . Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.for example:
Suppose, f(x) = 2x + 3 is a function.
Let f(x) = 2x+3 = y
y = 2x+3
x = (y-3)/2 = f-1(y)
This is the inverse of f(x).
Given function:
f(x)= ( 3+4x)/(1-5x)
now, swap the variables x and y.
y=4x+3/1-5x
Now solving for y
x=4y+3/1-5y
y=x-3/4+5x
Hence, the inverse of the function f^-1(x)=(x-3)/(4+5x).
Learn more about inverse of a function here:
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StartLayout enlarged left-brace 1st row 4 x minus 5 y = 5 2nd row negative 0.08 x + 0.10 y = 0.10 EndLayout
Answer:
[tex]x = 1.25[/tex]
[tex]y = 0[/tex]
Step-by-step explanation:
Given
[tex]4x - 5y = 5[/tex]
[tex]0.08x + 0.10y = 0.10[/tex]
Required
Determine the solution
Make x the subject of formula in: [tex]4x - 5y = 5[/tex]
[tex]4x = 5 + 5y[/tex]
Divide both sides by 4
[tex]\frac{4x}{4} = \frac{5 + 5y}{4}[/tex]
[tex]x = \frac{5 + 5y}{4}[/tex]
Substitute [tex]x = \frac{5 + 5y}{4}[/tex] in [tex]0.08x + 0.10y = 0.10[/tex]
[tex]0.08(\frac{5 + 5y}{4}) + 0.10y = 0.10[/tex]
Solve the fraction
[tex]0.02(5 + 5y) + 0.10y = 0.10[/tex]
Open the bracket
[tex]0.1 + 0.1y + 0.10y = 0.10[/tex]
[tex]0.1 + 0.2y = 0.10[/tex]
Subtract 0.1 from both sides
[tex]0.1-0.1 + 0.2y = 0.10 - 0.1[/tex]
[tex]0.2y = 0[/tex]
Divide both sides by 0.2
[tex]y =0[/tex]
Substitute 0 for y in [tex]x = \frac{5 + 5y}{4}[/tex]
[tex]x = \frac{5 + 5*0}{4}[/tex]
[tex]x = \frac{5 + 0}{4}[/tex]
[tex]x = \frac{5 }{4}[/tex]
[tex]x = 1.25[/tex]
What is the measure of each interior angle of a regular nonagon (nine-sided polygon) ? 2 points 60° 120° 140° 40°
Answer:
the answer is to your question is 140
Answer:
140°
Step-by-step explanation:
9 - 2 = 7
7 x 180= 1260° (sum of all interior angles)
1260 ÷ 9= 140° (measure of one interior angle)
4. The difference between twice a number and
half the number is 30. What is the number?
Help me please
Answer:
20
Step-by-step explanation:
let the number be n then twice the number is 2n and half the number is [tex]\frac{1}{2}[/tex] n
Then the difference is
2n - [tex]\frac{1}{2}[/tex] n = 30 ( multiply through by 2 to clear the fraction )
4n - n = 60, that is
3n = 60 ( divide both sides by 3 )
n = 20
At a fun park, the cost of a rollercoaster ride and a ferris wheel ride is $10. The cost of a Gravitron ride and a Ferris wheel ride is $12. The cost of a rollercoaster ride and a Gravitron ride is $14. What is the cost of each ride?
Answer:
r = cost of rollercoaster = 6
f = cost of ferris wheel=4
g = cost of graviton=8
Step-by-step explanation:
r = cost of rollercoaster
f = cost of ferris wheel
g = cost of graviton
r+f = 10
g+f = 12
r+g = 14
Take the third equation and subtract the first equation
r+g =14
-r-f = -10
-------------------
g-f = 4
Take this and add it to the second equation
g-f = 4
g+f = 12
-------------------
2g = 16
Divide by 2
g = 8
Now find f
g+f = 12
8+f = 12
f = 12-8
f=4
Now find r
r+g =14
r+8 =14
r = 14-8
r = 6
Please help Asap, will give brainiest only if answer correctly with a good explanation
Answer:
D, or the last option.
Step-by-step explanation:
See how the rotation does not say whether it is Clockwise or Counterclockwise?
Now, what that means, is that it will, default, be CCW. I don't know why, but math teachers are like that.
Now, 80* and 10* add up to 90* (because they are both unmarked and going to the same direction).
So, 90* rotation CCW. Simple! Thus, the last option should be correct.
Hope this helps!
P.S. Stay Safe!
Given each set of vertices, determine whether PQRS is a rhombus, a rectangle, or a square. List all that apply. Explain your reasoning, P(-2, -3). Q(2, - 6). R(6. - 3). S(2, 1)
Answer:
RectangleStep-by-step explanation:
Given the coordinates P(-2, -3). Q(2, - 6). R(6. - 3). S(2, 1), to determine the type of shape the quadrilateral is, we need to find the measure of the sides. To get the measure of each sides, we will take the distance between the adjacent coordinates using the formula to formula for calculating the distance between two points as shown;
D = √(x₂-x₁)²-(y₂-y₁)²
For the side PQ with the coordinate P(-2, -3). Q(2, - 6)
PQ = √(2-(-2))²-(-6-(-3))²
PQ = √(2+2)²-(-6+3)²
PQ = √4²-(-3)²
PQ = √16-9
PQ = √7
For the side QR with the coordinate Q(2, - 6) and R(6, -3)
QR = √(6-2))²-(-3-(-6))²
QR = √(4)²-(3)²
QR = √16-9
QR = √7
For the side RS with the coordinate R(6. - 3) and S(2, 1)
RS = √(2-6)²-(1-(-3))²
RS = √(-4)²-(1+3)²
RS = √16-(4)²
RS = √16-16
RS = 0
For the side PS with the coordinate P(-2, -3) and S(2, 1)
PS = √(2-(-2))²-(1-(-3))²
PS = √(4)²-(1+3)²
PS = √16-(4)²
PS = √16-16
PS = 0
For the quadrilateral to be a rectangle, then two of its sides must be equal and parallel to each other. A rectangle is a plane shape that has two of its adjacent sides equal and parallel to each other. Since two of he sides are equal i.e RS = PS and PQ = QR then the quadrilateral PQRS is a rectangle. Both rhombus and square has all of its sides equal thereby making them wrong.
The television show Lett3rs has been successful for many years. That show recently had a share of 24, meaning that among the TV sets in use, 24% were tuned to Lett3rs. Assume that an advertiser wants to verify that 24% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.
Find the probability that none of the households are tuned to Lett3rs. P(none) =
Find the probability that at least one household is tuned to Lett3rs. P(at least one) =
Find the probability that at most one household is tuned to Lett3rs. P(at most one) =
If at most one household is tuned to Lett3rs, does it appear that the 24% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?)
Answer:
(a) P(none) = 0.0488
(b) P(at least one) = 0.9512
(c) P(at most one) = 0.2186
(d) No, it doesn't appear that the 24% share value is wrong.
Step-by-step explanation:
We are given that among the TV sets in use, 24% were tuned to Lett3rs.
A pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.
Let X = Number of households that are tuned to Lett3rs
The above situation can be represented through binomial distribution;
[tex]P(X = r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]
where, n = number of samples (trials) taken = 11 households
r = number of success
p = probability of success which in our question is % of
households that were tuned to Lett3rs, i.e; 24%
So, X ~ Binom{n = 11, p = 0.24}
(a) The probability that none of the households are tuned to Lett3rs is given by = P(X = 0)
P(X = 0) = [tex]\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}[/tex]
= [tex]1\times 1 \times 0.76^{11}[/tex]
= 0.0488
(b) The probability that at least one households are tuned to Lett3rs is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.0488
= 0.9512
(b) The probability that at most one households are tuned to Lett3rs is given by = P(X [tex]\leq[/tex] 1)
P(X [tex]\leq[/tex] 1) = P(X = 0) + P(X = 1)
= [tex]\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}+\binom{11}{1}\times 0.24^{1} \times (1-0.24)^{11-1}[/tex]
= [tex]1\times 1\times 0.76^{11}+11\times 0.24^{1} \times 0.76^{10}[/tex]
= 0.2186
No, it doesn't appear that the 24% share value is wrong because the probability that at most one household is tuned to Lett3rs is somewhere close to 24% and this probability is also not unusual as it is way more than the criteria of more than 5%.
a football is fired upward with an initial speed of 800 feet per second. It is given that h=-12t^2+360t (h is the height of the football at any given time).what will you set h equal to in the equation to to find how many seconds it takes the football to hit the ground?
Answer:
30 s
Step-by-step explanation:
When the ball hits the ground h=0. To find the time t when this happens we must solve the equation h=0.
●h= 0
● -12t^2+360t =0
● t(-12t +360) = 0
● t = 0 or -12t +360 =0
● t=0 or -12t = -360
● t=0 or 12t =360
● t=0 or t=360/12
● t=0 or t= 30
The equation has two solutions.
The ball was fired with an initial speed of 800 feet per second so it cannot hit the ground at t=0.
So the ball hits the ground after 30 s.
Beth says that the graph of g(x)=x-5+1 is a
Translation of 5 units to the left and 1 unit up of
F(x)=x
She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x) is Beths description of the transformation correct? Explain
Answer:
(-15,3)
Step-by-step explanation:
Answer:
No, Beth is not correct. The function g(x) has an h value of 5 and a k value of 1. This would be a horizontal translation of the square root function of 5 units to the right, rather than the left. Beth was correct about the vertical translation of the square root function of 1 unit up. The point (0, 0) from the square root function would be translated to the point (5, 1) on the graph of g(x).
Step-by-step explanation:
This came right from Edg
FI = 20 IH = 19. Calculate the length of GI
Answer:
7.55
Step-by-step explanation:
3/x = x/19
x² = 57
x = 7.54983....
The function d(s) = 0.0056s squared + 0.14s models the stopping distance
of a car, d(s), in metres, and the speed, s, in kilometres per hour. What
is the speed when the stopping distance is 7 m? Use a graph to solve.
Answer:
The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.
Step-by-step explanation:
Let be [tex]d(s) = 0.0056\cdot s^{2} + 0.14\cdot s[/tex], where [tex]d[/tex] is the stopping distance measured in metres and [tex]s[/tex] is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.
The procedure to find the speed related to the given stopping distance is described below:
1) Construct the graph of [tex]d(s)[/tex].
2) Add the function [tex]d = 7\,m[/tex].
3) The point of intersection between both curves contains the speed related to given stopping distance.
In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.
what is the value of X when f(x)=g(x) ?
Answer:
x=3
Step-by-step explanation:
We want to find the value of x where the two graphs intersect
The graphs intersect at ( 3,8)
The value of x is 3
HIIIIII 2 QUESTIONS IN THE 2 PICS HELP PLS
Answer:
(1)C- Trapezoid
(2)D-20 square feet
Step-by-step explanation:
Question 1
A cross-section of a rectangular pyramid cut perpendicular to the base but not passing through the top will have two parallel sides where one of the sides will be longer. Therefore, the shape which describes the cross-section will be a trapezoid.
Question 2
The base of the Triangle = 5 feet
Height of the Triangle = 8 feet
[tex]\text{Area of a triangle}=\dfrac12 \times $Base \times Height\\=\dfrac12 \times 5 \times 8\\=20 ft^2[/tex]
Can someone help me with this problem?
━━━━━━━☆☆━━━━━━━
▹ Answer
Slope = 1
▹ Step-by-Step Explanation
y = mx + b
'm' represents the slope. since there is no number before the x, the coefficient will always be 1. therefore, the slope is 1.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
What true bearing is WSW equivalent to?
Answer:
S 67.50° W
Step-by-step explanation:
What is the solution to the system of equations?
y= 2/3x+3
x = –2
Answer:
[tex]x = -2[/tex] and [tex]y = \frac{5}{3}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{3}x + 3[/tex]
[tex]x = -2[/tex]
Required
Determine the solution to the equations
From the second equation, we have the value of x already;
The next step is to substitute -2 for x in the first equation
[tex]y = \frac{2}{3}x + 3[/tex] becomes
[tex]y = \frac{2}{3}(-2) + 3[/tex]
[tex]y = \frac{-4}{3} + 3[/tex]
[tex]y = -\frac{4}{3} + 3[/tex]
Take LCM
[tex]y = \frac{-4 + 9}{3}[/tex]
[tex]y = \frac{5}{3}[/tex]
Hence,
[tex]x = -2[/tex] and [tex]y = \frac{5}{3}[/tex]
c) Bhurashi can do 1/3 part of a work in 6 days.
(1) In how many days would she complete the whole work?
(ii) How much work does she do in 1 day?
m) How much work is left to do if she worked only for 9 days?
Answer:
i. 18 daysii.[tex] \frac{1}{18} [/tex] part of workiii. [tex] \frac{1}{2} [/tex] part of workStep-by-step explanation:
i.
[tex] \frac{1}{3} [/tex] part of work can be done in 6 days.
Days taken to complete the whole work:
= 6 * 3
= 18 days
ii. Whole work will be done in 18 days.
So, 1 day work = [tex] \frac{1}{18} [/tex]
iii. Work done in 9 days :
[tex] \frac{1}{18} \times 9 [/tex]
[tex] = \frac{1}{2} [/tex]
So, remaining work :
[tex]1 - \frac{1}{2} [/tex]
[tex] = \frac{1 \times 2 - 1}{2} [/tex]
[tex] = \frac{2 - 1}{2} [/tex]
[tex] = \frac{1}{2} [/tex] part of work
Hope this helps...
Good luck on your assignment..
you are having a pizza making party. You will need 6 ounces of dough and 4 ounces of sauce for each person at the party (including myself the host) Once you have a total count of guests you have exactly the amount needed for ingredients. the dough and sauce that I have is 130 ounces all together. How many ounces of dough did I buy? Explain How many ounces of sauce did I buy? Explain How many guests are coming to the party? Explain
Answer: 78 ounces of dough was bought.
52 ounces of sauce was bought.
There were 13 guests .
Step-by-step explanation:
Let x = Number of guests
As per given, For each person 6 ounces of dough and 4 ounces of sauce is required.
i.e. Total ounces of dough and sauce together required = 6+4=10
The dough and sauce is 130 ounces all together.
i.e. [tex]10x=130[/tex]
Divide both sides by 10 , we get
x= 13
i.e. there were 13 guests .
Total ounces of dough = 6 x ( Number of guests) = 6 x 13= 78 ounces
hence, 78 ounces of dough was bought.
Total ounces of sauce = 4 x ( Number of guests) = 4 x 13= 52 ounces
hence, 52 ounces of sauce was bought.
The total ounces of dough is 78 ounces
The total ounces of sauce is 52 ounces
The total number of guests is 13
The equation that can be used to represent the question given is:
6a + 4a = 130
Where a represents the number of guests at the party.
The above equation means that the total ounces of dough and sauce bought is a function of the number of guests at the party. These total ounces is equal to 130.
6a + 4a = 130
10a = 130
a = 130 / 10
a = total number of guests = 13
The total ounces of dough = 13 x 6 = 78 ounces
The total ounces of sauce = 13 x 4 = 52 ounces
A similar question was solved here: https://brainly.com/question/16430804?referrer=searchResults
Select the correct answer. The capacity in cubic feet of a cylindrical silo is given by the function C(x), where x is the radius of the silo in feet. The area of the circular base of the silo is given by the function A(x). C(x) = 6.28x3 + 18.84x2 A(x) = 3.14x2 Which function, H(x), represents the height of the silo? H(x) = x + 3 H(x) = 2x − 6 H(x) = 2x + 6 H(x) = x − 3
Answer:
C. H(x) = 2x+6
Step-by-step explanation:
Volume of the cylindrical silo = Area of its circular base × Height
Volume of the cylindrical silo = πr²×H
If the area of the circular base of the silo is given by the function A(x), the volume is given by C(x) and the height is given by H(x), the formula can be expressed as;
C(x) = A(x) × H(x)
The height of the cylindrical silo will be;
H(x) = C(x)/A(x)
Given C(x) = 6.28x³ + 18.84x² and
A(x) = 3.14x²
H(x) = 6.28x³ + 18.84x²/3.14x²
H(x) = x²(6.28x+18.84)/3.14x²
H(x) = (6.28x+18.84)/3.14
H(x) = 3.14(2x+6)/3.14
H(x) = 2x+6
Hence, the function, H(x) that represents the height of the silo is 2x+6.
Usando a fatoração com fator comum em evidência, fatore o seguinte polinômio: x3 + x2 + x
Answer:
x(x^2 + x + 1)
Step-by-step explanation:
x^3 + x^2 + x = x(x^2 + x + 1)
1. Calculate Q3 of the following data:
4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4
Answer:
4.75
Step-by-step explanation:
A basketball player scored 9 points in two games. What could her scores in each of the games be? This question helps children think about a problem for which there's a range of possible answers. For young children, decomposing numbers within 10 is an important reasoning strategy. There are ten possible answers, for whether the players scored 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 points in Game 1. Changing the number of points is a way to tailor the question for individual needs.
Answer:
The correct ans is...
4 and 5
Hope this helps....
Pls mark my ans as brainliestangle x and y are complementary angles . angle y measure 37 plzz help asap
Answer:
53 degrees
Step-by-step explanation:
Complementary angles add to 90 degrees
a+b = 90
a=37
37+b = 90
Subtract 37 from each side
37+b-37 = 90-37
b =53
Answer: 53 degrees
Step-by-step explanation: We can find the measure of <b by taking 90 minus the measure of <a which is 90 - 37 or 53 degrees.
NEED HELP ASAP I DONT GET THIS
Answer:
x = 60
Step-by-step explanation:
In a circle, the sum of the angles that meet at a point is 360 degrees. So now that we have the total, we can subtract all the given information in the picture. We have 84, 75, 68, and x + 73. Now let us set up and equation for this problem.
360 = 84 + 75 + 68 + x + 73
Now combine like terms.
360 = x + 300
Now subtract 300 on both sides.
x = 60
And this is the value of x.
Answer:
50 degrees
Step-by-step explanation:
84 + 75 + 68 = 227
227 - 360 = 133
133 - 73 = 50
The answer is 50 degrees.
What is 5/7 subtracted by 2/5
Answer:
11/35
Step-by-step explanation:
Valerie had a jug that contained 128 fl oz of salsa to put into bowls at a restaurant. She filled each bowl with 6 fl oz of salsa until there was not enough salsa left in the jug to completely fill another bowl. How many fluid ounces of salsa were left in the jug?
Answer: 2 fl oz
Step-by-step explanation:
Division with remainders
128/6=21.33333..
[tex]21\cdot 6=126[/tex]
128-126=2
2 fl oz was left in the jug
Please answer this question now only answer if you know the answer
Answer:
v = 10.997
Step-by-step explanation:
For this, simply use the law of cosines.
v^2 = (16)^2 + (6)^2 - 2(16)(6)cos(27)
v^2 = 256 + 36 - 171.073
v^2 = 120.927
v = 10.997
Cheers.
Answer:
[tex]\boxed{11}[/tex] unitsStep-by-step explanation:
To solve the length of UW, you can use the Law of Cosines for a SAS case:
[tex]\boxed{v^2=\sqrt{u^2+w^2-2(uw)cos(V)} }[/tex]
Substitute the values and solve with a calculator:
[tex]\boxed{\sqrt{16^2+6^2-2(16*6)cos(27)} = 10.99666983 \approxeq 11}[/tex]
The length of UW is 11 units.
Mark the absolute maximum point of the graph.
is the absolute maximum point (-3,5)?
Is (0, 3) a solution to the following system?
Y=-x+3
Y=2x-3
A No, because it does not check in either equation.
B. No, because it does not check in the first equation.
C. No, because it does not check in the second equation.
D. Yes, because it checks in both equations.
Solve each equation with (0, 3)
y = -x + 3
3 = -0 + 3
y = 3 (correct since y = 3 in (0, 3))
y = 2x - 3
3 = 2(0) - 3
3 = 0 - 3
3 = -3 (incorrect since it isn't equal)
So... No, because it does not check in the second equation.
Best of Luck!
hey loves!!! PLz help me
Answer:
Hey there!
We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.
Hope this helps :)