Determine f –1(x) if f of x is equal to the quantity x plus 3 end quantity over the quantity x minus 4 end quantity where x 4.
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 4 times x plus 3 end quantity
f inverse of x is equal to the quantity 4 times x plus 3 end quantity over the quantity x minus 1 end quantity
f inverse of x is equal to the quantity x minus 4 end quantity over the quantity x plus 3 end quantity
f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 4 end quantity
Answers
Answer:
Option BStep-by-step explanation:
Given function:
f(x) = (x + 3)/(x - 4)Find its inverse, take f(x) as y and swap x with y
x = (y + 3)/(y - 4)x = (y - 4 + 7) / (y - 4)x = 1 + 7/(y - 4)x - 1 = 7 / (y - 4)y - 4 = 7 / (x - 1)y = 4 + 7 / (x - 1)y = (4x - 4 + 7)/ (x - 1)y = (4x + 3) / (x - 1)Replace y with f⁻¹(x):
f⁻¹(x) = (4x + 3) / (x - 1)Correct choice is B
A x is equal to the quantity x plus 3 end quantity over the quantity x minus 4 end quantity where x 4. at x = 0.5, the inverse function f²(-1)(x) f²(-1)(x) = 0.5
To determine the inverse of the function f(x) = (x + 3) / (x - 4), to follow these steps:
Replace f(x) with -1, since you're looking for the inverse at the point where f(x) = -1:
-1 = (x + 3) / (x - 4)
Solve for x in terms of -1:
Multiply both sides by (x - 4):
-1 ×(x - 4) = x + 3
Distribute the -1:
-x + 4 = x + 3
Solve for x:
Subtract x from both sides:
4 = 2x + 3
Subtract 3 from both sides:
1 = 2x
Divide by 2:
x = 0.5
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Related Questions
One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. If P represents the number of female insects in a population, S the number of sterile males introduced each generation, and r the population's natural growth rate, then the female population is related to time t by
t =
P+S
P[(r−1)P − S]
dP
Suppose an insect population with 10,000 females grows at a rate of r = 0.10 and 900 sterile males are added in each generation. Evaluate the integral to give an equation relating the female population to time. (Note that the resulting equation cannot be solved explicitly for P.)
Answers
now, to do partial fraction decomposition, consider
(P+S)/P((r-1)P-S) = A/P + B/((r-1)P-S)
P + S = A((r-1)P -S) + PB
if P = 0, then:
A = -1
If (r-1)P - S = 0
=> p = S/(r-1)
B = 1 + r - 1
B = r
Therefore
t = integral(-1/P + (r-1+1)/((r-1)P - S))dP
t = -ln|P| + ln|(r-1)P-S| + 1/r-1 * integral((r-1)/[(r-1)P-S])
t = -ln|P| + ln|(r-1)P-S| + ln|(r-1)P-S|/(r-1)
t = -ln|P| + (r/r-1)ln|(r-1)P-S|
substituting known constants, we get:
t = -ln|P|-1/9(ln|-0.9P - 900|)
t = -ln|P| - 1/9(ln|-0.9P -900|)
t = -ln|P| - 1/9(ln(|(-9/10)(P + 1000)|))
t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
as P >= 0, ln(P) and ln(P + 1000) doesn’t need abs value
Note that our expression for t doesn’t account for P=0 as ln(P) is undefined at P = 0.
The expression for t is also undefined at P = -1000, but that falls outside our domain P >= 0, so we don’t really need to worry about that.
The equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the female population is related to time t by;
[tex]t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP[/tex]
Now, to do partial fraction;
(P+S)/P((r-1)P-S) = A/P + B/((r-1)P-S)
P + S = A((r-1)P -S) + PB
if P = 0, then:
A = -1
If (r-1)P - S = 0
p = S/(r-1)
B = 1 + r - 1
B = r
Therefore,
[tex]t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP[/tex]
t = -ln|P| + ln|(r-1)P-S| + 1/r-1 x integral((r-1)/[(r-1)P-S])
t = -ln|P| + ln|(r-1)P-S| + ln|(r-1)P-S|/(r-1)
t = -ln|P| + (r/r-1)ln|(r-1)P-S|
Now substituting known constants then;
t = -ln|P|-1/9(ln|-0.9P - 900|)
t = -ln|P| - 1/9(ln|-0.9P -900|)
t = -ln|P| - 1/9(ln(|(-9/10)(P + 1000)|))
t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
as P >= 0, ln(P) and ln(P + 1000) doesn’t need abs value
Therefore, the equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
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Which function has an inverse this is a function?
b(x)=x^2 + 2x
d(x)=-4x
m(x)=-3
p(x)=|x|
Answers
Answer :-
Option 2
Step by step explanation :-
d (x) = -4x has an inverse .
Where do I put the parenthesis to make it true?
5 – 6w – 5 – 95 + 2w = –48w – 70
Answers
Answer:
i just stole your points thank you
Step-by-step explanation:
5 – 6w – 5 – 95 + 2w = –48w – 70
-6w + 2w + 48w = -70 -5 + 5 +95
44w = 25
w=25/44
in what value of b makes y= 2x + b the same as y= 2x what does that value mean
Answers
Answer:
B = 0
Step-by-step explanation:
If you have y = 2x + b and are trying to get to y = 2x
Then just remove the B itself meaning it's value would be 0 so it is as if that variable was never in the actual equation.
Basing ourselves off of the formula "y = mx + b"
B = 0 would mean that the y-intercept of the line is 0
Answer:
0
Step-by-step explanation:
if y=2x and y=2x+b is the same then b must be 0.
1. You are interested in recycling behavior and whether it varies between urban and
rural residents. You know that the statewide recycling rate is 48.89%, and you
survey 140 rural residents and 310 urban residents to find out if they recycle.
180 urban residents respond that yes, they recycle. 130 do not. 40
rural residents recycle, and 100 do not.
a) Construct an expected frequencies crosstab, based on the sample size and the
statewide recycling rate.
b) Construct an observed frequencies crosstab, based on your actual data.
(NOTE for 1a and 16: Be sure to include both percentages and frequency values, in
Answers
Answer:
65
Step-by-step explanation:
A scientist needs 180 milliliters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many milliliters of the 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution
Answers
9514 1404 393
Answer:
120 mL of 25% solution60 mL of 10% solutionStep-by-step explanation:
Let q represent the quantity of 25% solution in the mix. Then 180-q is the quantity of 10% solution. The quantity of acid in the mix is ...
0.10(180 -q) +0.25(q) = 0.20(180)
18 +0.15q = 36 . . . . simplify
0.15q = 18 . . . . . . . . subtract 18
q = 18/0.15 = 120 . . . . divide by the coefficient of q
180-q = 60
The scientist should mix 120 mL of 25% solution with 60 mL of 10% solution.
Jerome makes and sells his own energy drinks. He mixes a liquid drink mix with water to create his own special blend. Jerome usually uses 8 cups of water and 3 cups of drink mix. Tomorrow, there is a road race in town, however, and Jerome thinks he’ll be able to sell a lot more of his energy drinks than usual. Jerome’s brother told him to add one cup of water for every one cup of drink mix he added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink. Jerome’s sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio the same and still increase the total amount of energy drink. Who is correct: Jerome’s brother or Jerome’s sister? As you complete the task, keep this question in mind: Based on what you know about ratios, what do you think the answer will be? Directions: Complete each task, reading the directions carefully as you do. You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and on the completeness and accuracy of your explanations. Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy. Now let’s get started! Step 1: Finding the part-to-part and part-to-whole ratios To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix. What is the ratio of water to drink mix? (2 points) What is the ratio of drink mix to water? (2 points) What is the ratio of drink mix to mixed energy drink? (2 points) What is the ratio of water to mixed energy drink? (2 points) Step 2: Testing Jerome’s brother’s approach Jerome’s brother told him to add one cup of water for every one cup of drink mix he add
Answers
Answer:
not well explained??
Step-by-step explanation:
?? explain it better bro.
hen Max was a puppy, he weighed 512 pounds. At his 1-year check-up with the vet, Max weighed 15.8 pounds.
How much weight did Max gain between the time he was a puppy and his 1-year check-up?
Enter your answer as a decimal or simplified mixed number in the box.
Answers
Answer:
10.3lbs or 10 3/10 as a mixed number
Step-by-step explanation:
i have the same question on my test so i know this is right but here's an explanation: so 5 1/2 pounds is the same as 5.5 pounds, and if you add 10 pounds to 5.5 pounds, you get 15.5 pounds, which is 3 ounces away from 15.8 pounds. so adding 3 ounces to the 10 pounds, then adding that to the 5.5 pounds, you would get 15.8. therefore, your answer is 10.3lbs.
The puppy gained 10.3 pounds of weight in 1 year.
What is subtraction?Subtraction is one of the arithmetical operations, to subtract means to take away from a group or a number of things.
Given that, Max was a puppy, he weighed [tex]5\frac{1}{2}[/tex] pounds. At his 1-year check-up with the vet, Max weighed 15.8 pounds.
[tex]5\frac{1}{2}[/tex] pounds = 5.5 pounds
Weight before 1 year = 5.5 pounds
Weight after 1 year = 15.8 pounds
Weight gained by the puppy in 1 year = 15.8-5.5 = 10.3 pounds
Hence, the puppy gained 10.3 pounds.
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WILL GIVE BRAINLIEST
These two triangles are congruent by ....
O SSS
O SAS
O HL
O ASA
O AAS
O the triangles are NOT congruent
Answers
SAS postulate states that if two sides and one angle of the two triangles are congruent then the corresponding triangles are congruent.
These two triangles are congruent by SAS postulate
Proof
Statements Reasons
In ΔNHJ ↔ ΔKHJ
mHJ≅mHJ common to both Δs∠N≅∠K right anglesmHN≅mHK givenFrom 1,2, and 3 ΔNHJ ≅ ΔKHJ SAS≅SAS
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Which graph best represents y = −x2 + 6x − 1?
Answers
Answer:
which graph best represents y = -x2 + 6x - 1?
Step-by-step explanation:
hich is the graph of the linear function that is represented by the equation y= 1/2x-2 ?
Answer:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex: ( 3 , 8 )
Focus: ( 3 , 31 /4 )
Axis of Symmetry: x = 3
Directrix: y = 33/4
x y
1 4
2 7
3 8
4 7
5 4
Step-by-step explanation:
Below is a picture of the graph
Customers at a gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the scenario.
What is the slope of the line?
Answers
Find the value of y for the given value of x.
y = x/2 + 9;x = -12
Answers
Step-by-step explanation:
x = -12
y = x/2 + 9
y = -12/2 + 9
y = -6 + 9
y = 3
A ruler 30 cm long is broken into two parts in the ratio 8:7. How long
are the two parts?
Answers
Answer:
Step-by-step explanation:
Length of each part of the ruler will be
8x and 7x
. Hence, 8x+7x=30 => 15x=30 =>x=2
Hence, the lengths will be
8x=8×2=16
7x=7×2=14
Supplies for last year cost $1,477, which was $177 over budget. Rounded to the nearest 1%, by what percent did the cost exceed the budgeted cost?
8%
11%
12%
13%
14%
Answers
Answer:
12% is the correct answer.
The simple interest charged on a 12-month loan of $82,000 is $631. Find the simple interest rate. (Round your answer to one decimal place.)
Answers
Step-by-step explanation:
631/82000×100
=0.8
MARK ME BRAINLIEST PLSS!
in an auditorium,there are 104 rows with 24 seats in each row.how many seats are available?
Answers
Answer:
2,496 seats
Step-by-step explanation:
If there are 104 rows with 24 seats in EACH row, we must multiply to find the answer. Which is gives you the equation: 104 x 24 = 2,496
hope this helps!
mark me brainliest :D
Please hurry, question in the image.
Only real answers will get positive feedback.
Answers
Answer:
The answer is D
Step-by-step explanation:
rate my answer and I hope this helps
Use point-slope from to write the equation of a line that passes through the point (10,3) with slope -5.
Answers
Answer:
[tex]y=-5x+5[/tex]
PLZZZ HELP MEEEeeeeeeeeeeeeeeeeeee
Answers
Answer:
I am a professional, worry not
-1.6 < -1.55 < -0.4 < 1.35 < 1.7
A sample in which each element in a population has a equal chance of being selected
Answers
Answer:
simple random sample
Step-by-step explanation:
I hope that's it
I need help with part a and b please
Answers
Answer:
The total answer should be 38 on the top
Step-by-step explanation:
a) So the first partial quotient would be equal to 30 as 31 x 30 = 930
b) Second partial quotient would be 8 as 31 x 8 = 248
Answer:
0
38
I hope it's help byeeee
what is 250% of 5
please help
Answers
Answer:
12.5
Step-by-step explanation:
You can read this problem as ...
2.5 × 5 = 12.5
__
You can think of % as meaning /100. You can think of "of" as meaning "times". Then the expression
250% of 5
can be thought of as ...
250/100 × 5
= 1250/100 = 12.5
WHAT IS 159 DIVIDED BY 3 (ITS NOT HARD PLEASE ANSWER I DON'T HAVE A CACULATER)
Answers
Answer:
Step-by-step explanation:
The asked quotient of 159 divided by 3 is the number 51.
What is divide?It is the inverse of multiplication, and it is used to find out how many times one number can be divided by another. In mathematics, the division is an arithmetic operation that involves splitting a quantity into equal parts or groups.
Here,
As mentioned in the question, we have to determine the quotient of 159 divided by 3
So let the quotient be y,
y = 159/3
y = 51
Thus, the asked quotient of 159 divided by 3 is number 51.
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What value of x would result in the numerical value of zero in the expression 7+x+(−10) ?
Answers
Answer:
x = 3
Step-by-step explanation:
So if we plug in 3 to 7+x+(-10), it simplifys to
7+3+(-10)
10+(-10)
10-10 = 0
x=3
Up arrow, right arrow, down arrow, left arrow, up arrow, right arrow, down arrow, left arrow. What's the conjecture
Answers
Answer:
The correct option is;
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, -y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-Arrow (-x, y).
Taking the result from the first reflection (x, -y) and applying the second mapping rule will result in (-x, -y), not (y, x), which reflection across the line y = x should give
Step-by-step explanation:
We have that for reflection across the x-axis, (x, y) → (x, -y)
For reflection across the y-axis, (x, y) → (-x, y)
Therefore, given that the pre-image before the reflection across the y-axis is (x, -y), we have;
For reflection across the y-axis, (x, -y) → (-x, -y)
For reflection across the line, y = x, gives (x, y) → (y, x) which is not the same as (-x, -y)
Find the volume of the following prism.
Answers
Answer:
[tex]4860[/tex] cubic units
Step-by-step explanation:
First, we use the formula of the triangle prism to solve the question
[tex]v=\frac{1}{2}b*h*l[/tex]
[tex]v=\frac{1}{2} 18*12*45[/tex]
[tex]v=4860 cm^{3}[/tex]
WILL GIVE BRAINLIEST!!
Which graph shows the following system of equations and it’s solution?
{ -2x -y = -5
{ 2x - 3y = 1
Answers
Answer:
Step-by-step explanation:
These two lines will intersect at (-4, -3). The top equation will have a slope of 1/4 and the bottom one a slope of 7/4.
I need help with my algebra.
Answers
Answer:
f(-2) =-2
Step-by-step explanation:
f(-2) means what is the output of the function when the input of the function is -2
When x =-2, y =-2
f(-2) =-2
If you randomly select a card from a well-shuffled standard deck of 52 cards, determine the probability that the card you select is not a spade.
A. Write your answer as a simplified fraction.
B. Write your answer as a decimal, rounded to the nearest thousandth.
C. Write your answer as a percent. Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Answers
Answer:
a. 1/13
b. 0.077
c. 7.7
Step-by-step explanation:
a. there are 4 of the 6 in a deck of cards so the probability of taking this cards from the deck of 52 cards is 4/52. Given you 1/13.
I have to get this done by today pls help me
Answers
Answer:
16
Step-by-step explanation:
d = 800
t = ( 1 / 500 ) d
t = ( 1 / 500 ) 800
= 800 / 500
t = 1.6 hours
