25 POINTS PLZ HELP ASAP!!!
Match the functions with their inverse functions.
Answers
1)
y=(2x-3)/5
5y=2x-3
5y+3=2x
(5y+3)/2=x
-> f(x)=(5x+3)/2
2)
y=(x+8)/2
2y=x+8
2y-8=x
-> f(x)=2x-8
3)
y=(x+2)/7
7y=x+2
7y-2=x
-> f(x)=7x-2
4)
y=(1-2x)/x
y=(1/x)-2
y+2=1/x
x=1/(y+2)
-> f(x)=1/(x+2)
We know that when we are given a inverse function as: [tex]f^{-1}(x)[/tex]
Then we find the function by the method:
Put [tex]f^{-1}(x)=y[/tex]
Then we switch the places of x and y and solve for y.
1)
[tex]f^{-1}(x)=\dfrac{2x-3}{5}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{2x-3}{5}=y[/tex]
Then we switch for x and y
[tex]\dfrac{2y-3}{5}=x\\\\\\i.e.\\\\2y-3=5x\\\\\\i.e.\\\\\\2y=5x+3\\\\\\i.e.\\\\\\y=\dfrac{5x+3}{2}[/tex]
Hence, inverse function is:
[tex]f(x)=\dfrac{5x+3}{2}[/tex]
2)
[tex]f^{-1}(x)=\dfrac{x+8}{2}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{x+8}{2}=y[/tex]
Then we switch for x and y
[tex]\dfrac{y+8}{2}=x[/tex]
[tex]y=2x-8[/tex]
Hence, inverse function is:
[tex]f(x)=2x-8[/tex]
3)
[tex]f^{-1}(x)=\dfrac{x+2}{7}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{x+2}{7}=y[/tex]
Then we switch for x and y
[tex]\dfrac{y+2}{7}=x[/tex]
[tex]y=7x-2[/tex]
Hence, inverse function is:
[tex]f(x)=7x-2[/tex]
4)
[tex]f^{-1}(x)=\dfrac{1-2x}{x}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{1-2x}{x}=y[/tex]
Then we switch for x and y
[tex]\dfrac{1-2y}{y}=x[/tex]
i.e.
[tex]1-2y=xy\\\\xy+2y=1\\\\i.e.\\\\y(x+2)=1\\\\y=\dfrac{1}{x+2}[/tex]
Hence, inverse function is:
[tex]f(x)=\dfrac{1}{x+2}[/tex]
Related Questions
How to algebraically find the limit of a function as x approaches infinity?
Answers
Well... One way you can do this is by testing a set of arrays and see the trend. If I chose to find what y1 is in (100, y1) and what y2 is in (101, y2), I would find the difference between y2 and y1. If y2 - y1 is positive, this means there is a positive relationship and y is also approaching POSITIVE infinity. A negative relation means that it is approaching NEGATIVE infinity. However, it could be approaching a single number like "4" for instance, and you just need to plug in the right number of data sets to make that educated guess.
Formula Example:
5 + 1 / (x + 1) will always approach 5 because "1 / (x + 1) will approach 0".
Hope this helps.
To algebraically find limit of a function as "x" approaches infinity, identify highest degree term, divide by "x", and evaluate the resulting expression.
To algebraically find the limit of a function as x approaches infinity, we can follow the below steps :
(i) Identify the highest degree term: Determine the term with the highest power of x in the function.
(ii) Ignore lower degree terms: If the highest degree term is dominant, ignore lower degree terms and constants.
(iii) Divide by x: Divide every term in the function by x raised to the power of the highest degree.
(iv) Evaluate the limit: Examine the resulting expression as x approaches infinity. If the expression tends to a finite value, that is the limit. If the expression diverges (goes to infinity or negative infinity), then the limit does not exist.
By simplifying the function and observing the behavior of the resulting expression, we can algebraically determine the limit of the function as x approaches infinity.
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The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14 for pie . Round to the nearest tenth of a cubic inch
Answers
volume = 4/3 x PI x r^3
r = 10/2 =5
V = 4/3 x 3.14 x 5^3 = 523.333
523.3 cubic inches
find multiplicative inverse of 2+3i / 3-2i
Answers
( 2 + 3 i ) / ( 3 - 2 i ) * ( 3 + 2 i ) / ( 3 + 2 i ) =
= ( 2 + 3 i ) * ( 3 + 2 i ) / ( 9 - 4 i² ) = → we use difference of squares
= ( 6 + 4 i + 9 i + 6 i² ) / ( 9 + 4 ) = → because : i² = - 1
= ( 6 + 13 i - 6 ) / 13 =
= 13 i / 13 = i
Answer: i.
PLEASE HELP!! 25 POINTS
A rectangle has an area of 102 cm2. The length of the rectangle is 17 cm.
What is the perimeter of the rectangle?
Answers
L*W = 102
L = 17
17W = 102
W = 6
P = 2L + 2W = 2*17 + 2*6 = 46
Openstudy using synthetic division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)?
Answers
Find the volume of each figure to the nearest tenth. Show your work.
Answers
V = (4/3) * 3.14 * 6³ ≈ 904.3 m³
b. Сone. V = (1/3)πr²h [π≈3.14; r=5]
By the Pythagorean theorem:
h = √(13²-5²) = √144 = 12 m
V = (1/3) * 3.14 * 5² * 12 ≈ 314 m³
c. Rectangular parallelepiped. V = lwh [l=11, w=5, h=6]
V = 11 * 5 * 6 = 330 cm³
what is the reciprocal of 8-3i
Answers
The reciprocal of the complex number 8-3i is found by dividing its complex conjugate (8+3i) by the modulus squared of 8-3i, which is 73. The result is 8/73 + 3i/73.
Explanation:The reciprocal of a complex number is the complex conjugate of that number divided by the modulus squared of the original number. In the case of the complex number 8-3i, its complex conjugate is 8+3i. To find the reciprocal of 8-3i, you would divide this complex conjugate by the modulus squared of 8-3i.
First, calculate the modulus squared of 8-3i:
Modulus of 8-3i = sqrt(82 + (-3)2) = sqrt(64 + 9) = sqrt(73).Modulus squared = (sqrt(73))2 = 73.Then, divide the complex conjugate by this modulus squared to get the reciprocal:
Reciprocal of 8-3i = (8+3i) / 73 = 8/73 + 3i/73.
Hillary rolls 2 number cubes numbered 1 through 6 while playing her favorite board game. She will get a second turn if she rolls a sum that is an odd number greater than 10. What are Hillary's chances of getting a second turn when she rolls the number cubes?
Answers
P(11)=(2/6)(1/6)
P(11)=2/36
P(11)=1/18
Te odd sum greater than 10 is:
either 5 + 6 = 11 or 6 + 5 =11
to get 5 & 6, P= 1/36
OR to get 6 & 5, P = 1/36
In "either or" you will add the probabilities"
P(to get a chance of getting a second turn)=1/36+1/36 = 2/36 = 1/18=0.0555
the area of a rectangle with width x and length 7x is 7x^2 what does the coefficient 7 mean in terms of the problem
Answers
Width = x
Length = 7x
Area = x(7x) = 7x^2
The coefficient 7 would mean that the length is 7 times longer than the width, x.
What is the measure of ABC?
Answers
You have to divide 130 by 2 because it is the interior angle of arc AC
130/2=65
hope this helps:)
Answer: Measure of <ABC=65°.
Step-by-step explanation:
The intercepted arc Theorem says :Angle made on circumference if half the measure of the intercepted arc.
In the given circle measure of arc is 130° The angle intercepted by arc AC is <ABC.
m<ABCwill be equal to Half of measure of arc AC
M<ABC=[tex]\frac{1}{2} of 130=65[/tex]
A circle is drawn in the xy-coordinate plane. if there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are
Answers
either x, or y or both must be 0.
So we consider the points of the form (x, 0), (0, y) and (0, 0). These are the x and y intercepts.
A circle can touch the axes at 1, 2, 3 or 4 points but not more.
Check the picture for examples of all the cases.
Answer: n∈{1, 2, 3, 4}
If the probability of an event is 0.7 repeating, what are the odds against the event
Answers
the polynomial (x - 2) is a factor of the polynomial 3x2 - 8x + 2.
Answers
First, let's factor 3x²-8x+2
Looking at wee can see that the first term is and the last term is where the coefficients are 3 and 2 respectively.
Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? Let's list all of the factors of 6:
Factors of 6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)
note: remember two negative numbers multiplied together make a positive number
Now, which of these pairs add to -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8
None of these pairs of factors add to -8.
So the expression 3x²-8x+2 cannot be factored.
So (x - 2) is NOT a factor of 3x²-8x+2
So the statement is false
Answer:
B.false
Step-by-step explanation:
apexs
Which of the following are arithmetic sequences? Check all that apply.
A. 1, 1, 2, 5, 8, 13
B. 5, 5, 5, 5, 5
C. 3, 6, 9, 12, 15
D. 2, 4, 8, 16, 32
Answers
Answer:
The correct option is B) 5, 5, 5, 5, 5 and C) 3, 6, 9, 12, 15 are arithmetic sequences
Step-by-step explanation:
Arithmetic sequence is: a, a+r, a+2r, a+3r, a+4r, ....... where r is common difference
Check part A) 1, 1, 2, 5, 8, 13
In which [tex]a_1=1,\, a_2=1,\,a_3=2,\,a_4=5[/tex]
common difference [tex]d=a_n+1 -a_n[/tex]
[tex]d=a_2 -a_1 =1-1=0 [/tex]
[tex]d=a_3 -a_2 =2-1=1 [/tex]
since common difference is not same
so, sequence 1, 1, 2, 5, 8, 13 is not arithmetic sequences.
Check part B) 5, 5, 5, 5, 5
In which [tex]a_1=5,\, a_2=5,\,a_3=5,\,a_4=5[/tex]
common difference [tex]d=a_n+1 -a_n[/tex]
[tex]d=a_2 -a_1 =5-5=0 [/tex]
[tex]d=a_3 -a_2 =5-5=0 [/tex]
since common difference is same
so, sequence 5, 5, 5, 5, 5 is arithmetic sequences.
Check part C) 3, 6, 9, 12, 15
In which [tex]a_1=3,\, a_2=6,\,a_3=9,\,a_4=12[/tex]
common difference [tex]d=a_n+1 -a_n[/tex]
[tex]d=a_2 -a_1 =6-3=3 [/tex]
[tex]d=a_3 -a_2 =9-6=3 [/tex]
since common difference is same
so, sequence 3, 6, 9, 12, 15 is arithmetic sequences.
Check part D) 2, 4, 8, 16, 32
In which [tex]a_1=2,\, a_2=4,\,a_3=8,\,a_4=16[/tex]
common difference [tex]d=a_n+1 -a_n[/tex]
[tex]d=a_2 -a_1 =4-2=2 [/tex]
[tex]d=a_3 -a_2 =8-4=4 [/tex]
since common difference is not same
so, sequence 2, 4, 8, 16, 32 is not arithmetic sequences.
Therefore, the correct option is B) 5, 5, 5, 5, 5 and C) 3, 6, 9, 12, 15 are arithmetic sequences
Find the value of X and Y. Show your work.
Answers
7x = 31 + 4
7x = 35
x = 35/7
x = 5
4y + 8 = 24
4y = 24 - 8
4y = 16
y = 16/4
y = 4
If x = 3 is a zero of the polynomial function f(x) = 2x3 + x2 − 25x + 12, which of the following is another zero of f(x)? ASAP
Answers
The other zeros of the polynomial if 3 is a zero is -4 and 1/2
If x = 3 is a zero of the polynomial function f(x) = 2x3 + x2 − 25x + 12, then x - 3 is a factor.
To get the other factor we will take the division of the polynomial and the factor to have:
2x^3 + x^2 − 25x + 12/x - 3 = 2x² + 7x - 4
Factorize 2x² + 7x - 4
2x² + 7x - 4 = 0
2x² + 8x - x- 4 = 0
2x(x+4)-1(x+4) = 0
(x+4)(2x-1) = 0
x = -4 and 1/2
Hence the other zeros of the polynomial if 3 is a zero is -4 and 1/2
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which of the following are not necessary when proving that the diagonals of a rectangle are congruent? check all that apply
Answers
all obtuse angles are congruent
Answer:
The correct options are B and D.
Step-by-step explanation:
A quadrilateral is called rectangle if the opposite sides are congruent and parallel to each other. All interior angles are right angle and congruent.
To prove that the diagonals of a rectangle are congruent the necessary conditions are
1. Opposite sides of a rectangle are congruent.
2. All right angles are congruent.
Therefore options A and C are necessary conditions. Option A and C are incorrect.
The opposite sides of a rectangle are parallel to each other and two parallel lines never intersect each other.
Therefore the opposite sides are not perpendicular to each other. Option D is correct.
The angle whose measure is more than 90 degree is called an obtuse angle.
Since all interior angles of a rectangle are right angle and congruent, therefore there is no obtuse angle. So, condition B is unnecessary. Option B is correct.
Identify the function that best models the given data.
Answers
B) 3.125x^2 - 14.5x + 208.5
To prove this you plug 6 (which is the number of trees) instead of x
3.125x^2 - 14.5x + 208.5
3.125(6)^2 - 14.5(6) + 208.5
112.5 - 87 + 208.5
=234
Answer: W(i) = 3.125x^2 − 14.5x + 208.5
Step-by-step explanation:
There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed. Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points) Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points) Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)
Answers
To solve this problem, let us first assign variables. Let us say that:
X = number of marigold plants
Y = number of sunflower plants
n = number of months
We can see that in the given problem, X is decreasing by a percentage, this means that we have to set-up a geometric equation while for Y the decrease is linear so we set-up an arithmetic equation.
Part A.
For marigold plants X, a geometric sequence has a general form of:
X = Xo * (1 + r)^n
where r = -15% = -0.15 (negative since it is decreasing)
Xo = the initial amount of marigold plants = 150
X = 150 * (1 – 0.15)^n
X = 150 (0.85)^n
For the sunflower plants Y, an arithmetic sequence has a general form of:
Y = Yo + d * n
where d = -8 and Yo = 125
Y = 125 – 8 n
Part B. For n = 3
X = 150 (0.85)^3 = 92.12 = 92
Y = 125 – 8 (3) = 101
Part C. From Part B we see that the two values are very far from each other when n = 3, therefore they must be similar when n < 3. So we try n = 2
X = 150 (0.85)^2 = 108.38 = 108
Y = 125 – 8 (2) = 109
Therefore the two plants have approximately similar amount after 2 months.
The number of points awarded in each round of a game can be represented by f(x) = 2x, where x represents the number of the round.
What is x when f(x) = 16?
Answers
2x=16 divide both sides by 2
x=8
Answer:
x=4; in round 4, 16 points will be rewarded
If the letters a, b, c, d, e, and f are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?
Answers
Which of the following is not a way to represent the solution of the inequality 2(x − 1) less than or equal to 10? (1 point)
A. x less than or equal to 6
B. 6 greater than or equal to x
C. A number line with a closed circle on 6 and shading to the left
D. A number line with a closed circle on 6 and shading to the right
Answers
A and B are the same and C is proven wrong due to the equality sign lkeaving only D to be correct
930 miles to travel with a car that gets 22 miles per gallon. How much will it cost to travel if gas costs 2.03 a gallon?
Answers
_______________________________________________
Explanation:
_______________________________________________
(1 gal / 22 mi) * (930 mi) =
(1 gal / 22 mi) * (930 mi / 1) = {the units of "mi" ("miles" cancel out} ;
= (1 gal/ 22) * (930 / 1) = (1 gal * 930) ÷ (22 * 1) ;
= (930 gal) ÷ 22 ;
= (465 / 11) gal =
= 42 3/11 gal = 42.2727272727.... gal .
________________________________________________________
(456 /11) gal * ($ 2.03 / gal) =
$85.813636363636363581 -------> round to: $85.81 .
__________________________________________________________
A key code must contain 6 numerals. There are 10 numerals available. Using these numerals, how many different key codes may be created? A. 151,200 B. 340 C. 210 D. 3,480
Answers
Answer: Option A, 151,200 possible combinations.
Explanation:
The code must contain 6 numbers, and there are a total of 10 numbers avaible. Here we must assume that the numbers must be different, because of the word "avaible" and the options avaible.
This means that for the first number, we have 10 options, for the second number, we have 9 options (because we already took 1), in the third number, we have 8 options, and so on.
The total number of combinations is equal to the product between the number of options for each number in the code.
10*9*8*7*6*5 = 151,200
Then the right option is A.
Which is an equation of a circle with center (2, -1) that passes through the point (3, 4)?
1. (x + 2)2 + (y - 1)2 = 26
2. (x + 2)2 + (y - 1)2 = 13
3. (x - 2)2 + (y + 1)2 = 26
4. (x - 2)2 + (y + 1)2 = 13
Answers
A captain of a fishing boat pays each member of his crew $20, plus $3 per fish caught. How much would a crew member earn for catching 40 fish?
Answers
Answer: C) $140
20 times 3 plus 20
A crew member would earn $140 for catching 40 fish, calculated by adding the base pay of $20 to the additional pay of $3 per fish caught for the total number of fish.
To calculate how much a crew member would earn for catching 40 fish, given that the captain of the fishing boat pays each crew member a base amount of $20 plus an additional $3 per fish caught. To find the total earnings, we use the formula:
Total earnings = Base pay + (Pay per fish × Number of fish caught)
Plugging the given numbers into the formula, we get:
Total earnings = $20 + ($3 × 40)
Total earnings = $20 + $120
Total earnings = $140
Therefore, a crew member would earn $140 for catching 40 fish.
The trees at a national park have been increasing in numbers. There were 1,000 trees in the first year that the park started tracking them. Since then, there has been one fifth as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible.
1 1000
2 200
3 40
Answers
Term 1: 1000
Term 2: 200
Term 3: 40
From term 1 to term 2, there's a decrease by [tex] \frac{1}{5} [/tex]
From term 2 to term 3, there's a decrease also by [tex] \frac{1}{5} [/tex]
The rule to find the [tex]n^{th} [/tex] term in a sequence is
[tex]n^{th}=a r^{n-1} [/tex], where [tex]a[/tex] is the first term in the sequence and [tex]r[/tex] is the ratio
So, the formula for the sequence in question is
[tex]n_{th} [/tex] term = [tex]1000( \frac{1}{5} ^{n-1} )[/tex]
The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.
We can find a partial sum of the sequence using the formula
[tex]S_{∞} = \frac{a}{1-r} [/tex] for -1<r<1
Substituting [tex]a=1000[/tex] and [tex]r= \frac{1}{5} [/tex] we have
[tex] S_{∞} [/tex] = [tex] \frac{1000}{1- \frac{1}{5} } [/tex] = 1250
Hence, the correct option is option number 1
Answer:
A
Step-by-step explanation:
A bag contains 21 red marbles, 22 green marbles, 24 orange marbles, and 10 yellow marbles. You choose a marble randomly from the bag.
What is the approximate probability that you will choose a green or yellow marble?
A. 0.358
B. 0.435
C. 0.416
D. 0.538
Answers
21 +22+24+10 = 77 total marbles
22 +10 =32 green and yellow marbles
32/77 probability of choosing a green or yellow one
32/77 = 0.416
answer is C. 0.416
What is the equation of the blue graph?
Answers
G(x) = (x - 5)^2 ....move F(x) = x^2 to the right 5 units
Hope it helps
f-7 over g equals h, sole for f