What i the invere of f(x) = 3/(x 1) f ^ - 1 * (x) = (3 - 1)/x f ^ - 1 * (x) = 3 x f ^ - 1 * (x) = x^ 1 2 f ^ - 1 * (z) = 3/x - 1
The inverse of f(x) = 3/(x-1) is f^-1(x) = 3/x - 1.
So the correct answer is f ^ - 1 * (x) = 3/x - 1
The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. To find the inverse of a function, we need to switch the roles of x and y and then solve for x.
Given the function f(x) = 3/(x + 1), we can find its inverse by:
y = 3/ (x + 1)
Multiply with (x + 1) and divide by y
y(x + 1)/ y = (3/ (x + 1))×(x + 1)/ y
x + 1 = 3/ y
x = 3/ y - 1
Switching the roles of x and y:
y = 3/ x - 1
Thus f^(-1)(x) = 3/ x - 1
It's worth noting that in order for a function to have an inverse function it must be a one-to-one function. This means that for every y value there is only one x value.
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HELP DUE IN 15 MINS!
Quadrilateral ABCD is an isosceles trapezoid. Find the values of x and y.
x =?? degrees
° y =?? degrees
Answer:
Isosceles trapezoid has congruent base angles:
∠A ≅ ∠D and ∠B ≅ ∠C
5x = 80x = 164y - 12 = 1004y = 112y = 28Answer:
x = 16 degrees
y = 28 degrees
Step-by-step explanation:
1.) ∠A ≈ ∠D since they are base angles: so;
5x = 80
=> divide 5 on both sides:
x = 16 degrees
2.) Now Substitute 16 in for the x-value
5x ⇒ 5(16) = 80,
3.) Since we know the measure of the sum of interior angles is 360° we can say that:
(4y - 12) + 100 + 5(16) + 80 = 360
=> 4y - 12 + 100 + 80 + 80 = 360
=> 4y + 248 = 360
Subtract 248 on both sides of "="
=> 4y = 112
Divide 4 on both sides of "="
=> y = 28
Hope this helps!
The diameter of a circle is 16 in. Find its circumference in terms of \piπ.
Answer:
50.24
Step-by-step explanation:
The formula for solving circumference is 2 x pi x r
first the radius is 8 (divide 16 by 2 and get radius)
( pi can be 22/7 or 3.14. but I’m taking 3.14 )
second, we have all values, now we just have to substitute them!
Pi = 3.14
R = 8
so when we do 2x 3.14 x 8 = 50.24
I hope this helped!
Answer: The area of the circle is 64π cm
Step-by-step explanation:
d=16→r=8
A= π⋅8 ^2
A= π⋅64
A=64π
Audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (–1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)
The reasonable solutions for this situation is (1, 3.5) and (2, 2)
What is Graph?A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.
Audrey has x pounds of red grapes and y pounds of green grapes.
She has less than 5 pounds of grapes in all, hence:
x + y < 5
Also, x ≥ 0, y ≥ 0
a) The option (–1, 2) is wrong because x = -1 < 0
b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5
c) The option (2, 2) is correct because 2 + 2 = 4 < 5
d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.
e) The option (5, 0) is wrong because 5 + 0 is not less than 5
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Which of the following is equivalent to x/x^2-1 + 4/x^2-6x-7?
a. x(x-7)+4(x-1)/(x+1)^2(x-7)
b. x+4/(x+1)^2(x-7)
c. x(x-7)+4(x-1)/(x+1)(x-1)(x-7)
d. x+4/(x+1)(x-1)(x-7)
Answer:
x(x-7)+4(x-1)/(x-1)(x+1)(x-7)
Step-by-step explanation:
Given the expression x/x²-1 + 4/x²-6x-7
Factorize x²-6x-7
x²-6x-7
= x²-7x+x-7
= x(x-7)+1(x-7)
= (x+1)(x-7)
Replace back into the expression given
x/x²-1 + 4/x²-6x-7
= x/x²-1 + 4/ (x+1)(x-7)
= x/(x+1)(x-1) + 4/(x+1)(x-7)
Find the LCM
= x(x-7)+4(x-1)/(x-1)(x+1)(x-7)
This gives the required expression
a rectangular computer screen has an area o A square inches. The width of the computer is 7 inches. Which equation rpresents x the length of the computer screen in inches
Answer:
x = A/7
Step-by-step explanation:
Given that the screen is rectangular, recall that the area A of a rectangle whose length is L and width is W is given as
A = L * W
Hence if the width is 7 inches and the length is x inches then the area which is A square inches is connected to both sides as
A = x * 7
Divide both sides by 7
x = A/7 inches
Radicals help please
Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.
Describe fraction.Components of fractions are the numbers in the numerator and denominator (and ratios). The denominator, which is the smallest number, represents the greatest possible number of parts that can be put together to create a whole. You can tell how many parts you have by looking at the numerator, which is the greatest number. It might not be the whole thing! If the denominator is 0, that is bad. Division by zero is prohibited. If the denominator is a 1, our fraction is actually an integer.
Here,
we can rationalize a radical-containing fraction's denominator by doing the following:
Step 1: In order to eliminate the radical from the denominator, multiply the numerator and denominator by a radical.
Verify in step two that all radicals have been streamlined.
Step three is to simplify the fraction, if necessary.
Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.
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Given a bag of 5 blue, 3 green, and 8 red marbles.. What is the probability of picking a blue
and then a green with NO replacement
[tex]b = 5, \: g = 3, \: r = 8[/tex]
[tex]total = 5 + 3 + 8 = 16[/tex]
[tex]p(b) = \frac{5}{16} [/tex]
[tex]p(g |without \: replacement|) = \frac{3}{16 - 1} = \frac{3}{15} = \frac{1}{5} \\ [/tex]
[tex]p(b \: and \: g) = \frac{5}{16} \times \frac{1}{5} = \frac{1}{16} [/tex]
A circle has a diameter of 12 centimeters. A sector of the circle is 9 square centimeters. What is the measure of the central angle whose radii define the sector?
Answer:
sector area = [central angle / 360] * PI * radius²
central angle = sector area * 360 / [PI * radius²]
central angle = 9 cm² * 360 / [3.14159 * 6²]
central angle = 28.6479139544 degrees
Source: http://www.1728.org/radians.htm
Step-by-step explanation:
What is the surface area of the pyramid?
Answer:
166
Step-by-step explanation:
1) the area of triangles on the left and right sides: 2*13
2) the area of triangles on top and bottom sides: 10*12
3) the area of the rectangle in the middle: 10*2
4) Altogether: 2*13+10*12+10*2=166
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.
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Using a number line, find both the intersection and the union of the following
intervals:
(-3,∞) and (4,∞)
The answer choice which represents a number line for the intersection of the given intervals is; (4, ∞).
The answer choice which represents a number line for the union of the given intervals is; (-3, ∞).
What is the number line representation of the intersection and union of the given intervals?It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.
Since the given intervals are; (-3, ∞) and (4, ∞)
It follows that the intersection of both intervals is the interval; (4, ∞).
Also, the interval which represents the union of both intervals is; (-3, ∞).
Hence, the image which represents both scenarios is attached.
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Thirty-seven states use wind as a source of energy.
>What fraction of the states does not use wind energy?
Answer:
0.26. This is the fraction of states that do not use wind energy.
Step-by-step explanation:
There are 50 states total. If 37 use wind energy, then 50 - 37, or 13, do not.
13/50 = 0.26. This is the fraction of states that do not use wind energy.
Solve each system by graphing
I’m looking for the answer but also a explanation of how you solved it so I can solve the other 1s without help
Answer: its hard to give an answer but read explanation
Step-by-step explanation: so the first number (1/3x) is your slope and the second number is the y-intercept (5). so for example, you're going to put positive 5 on the y-axis and because you slope is a fraction, rise/run will make you go 3 to the right and 1 up. Then you do the same with the second equation except, the slop is negative and you'll have to go down.
An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. how many seats are in the 10th row?
a. 60
b. 93
c. 102
d. 110
Answer:
Step-by-step explanation:Its actually 102, not 110
Question 10: Let the graph of f(x) represent the cost in thousands of dollars to feed the zoo animals daily, where x is the number of animals measured in hundreds. What does the solution to the function (2, 12) represent?
Cost (in thousands)
20
15
(2. 12)
10
5
Number of Animals (in hundreds)
• There are 200 animals, and the cost is $12,000 daily.
• There are 2,000 animals, and the cost is $1,200 daily.
• There are 1,200 animals, and the cost is $2,000 daily.
• There are 12,000 animals, and the cost is $200 daily.
Answer: I believe is the first one
Step-by-step explanation: It says animal in hundreds right. so looking at it 200 animals is right. But also x = 2 and y = 12
Hope this helps I'm sorry if it does not help
Work out an expression for the nth term of the quadratic sequence
2, 17, 40, 71
Give your answer in the form
an^2 + bn + c
where a, b and c are constants.
I
A high school coach wants to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 on the shares. Which inequality represents the maximum cost of each pair, s, the coach can buy
HURRY! PAST DUE MATH HOMEWORK!
Answer:
45.7 inches
Step-by-step explanation:
The perimeter uses 3 sides of the square, so 3 x 10 = 30. We'll add that later.
Then we need to find the circumference of the half-circle. We know the diameter is 10, because that's the side of a square.
Circumference = pi x diameter
C = 3.14 x 10 = 31.4
But that's for the whole circle. We only have a half.
31.4 /2 = 15.7 is the perimeter for the half circle. Add this to the 3 sides of the square
30 + 15.7 = 45.7
What is the area, in square centimeters, of the trapezoid below?
11.7 cm
5.5 cm
6.5 cm
Answer:
50.05 cm^2
Step-by-step explanation:
Ok so first lets find the area of the rectangle before finding the attached triangle. You have to imagine a line separating this shape into a triangle and rectangle.
The rectangle's size is 6.5x5.5=35.75 cm^2
The rectangle's size is 11.7-6.5 to get the base length, which is 5.2
The height is 5.5
So it's 5.2*5.5/2=14.3 cm^2
14.3+35.75=50.05 cm^2
A taxi driver filled his car petrol tank with 54 litres of petrol on Saturday. On Sunday he filled his tank with 64 litres of petrol. If the petrol costs Rs.82 per litre, how much did he spend on petrol?
Answer:
the amount spent on petrol is Rs 9,676
Step-by-step explanation:
Given that
The tax driver filled the car petrol with 54 liters on Saturday
On sunday, he filled his tank with 64 liters
And, the petrol cost is Rs 82 per liter
We need to find out the amount of money spent
SO,
= (54 liters + 64 liters) × Rs 82
= Rs 9,676
Hence, the amount spent on petrol is Rs 9,676
……………………………………………………………………………
Answer:
ITS 64 degrees
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
hope this helps:)..........
Nicole was driving down a road and after 6 hours she had traveled 90 miles. At this speed, how many miles could Nicole travel in 8 hours?
Answer:
120
Step-by-step explanation:
90÷6=15×8=120
HELP ILL GIVE BRAINLY IF ITS RIGHT
What is the volume of this composite solid?
2 m
4 m
7 m
2 m
2 m
O A. 78 cubic meters
B. 64 cubic meters
Ο Ο Ο
C. 58 cubic meters
D. 62 cubic meters
Answer:
B. 64 cubic meters
Step-by-step explanation:
The first rectangle has the dimensions 7 x 2 x 4. 2 x 4 is 8, and 8 x 7 is 56. The square has the dimensions 2 x 2 x 2, which is 8. 56 + 8 is 64, so the answer is 64.
Answer:
ITS B HOPE THIS HELPS
Step-by-step explanation:
Guliskhan plans to cover a certain distance by running and bicycling. She runs at a constant speed, and she bicycles at a speed of 7 meters per second (m/s)
Therefore, the inequality problem solution is even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.
What is inequality?Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<
Here,
R should stand for Guliskhan's running seconds, and B should stand for her bicycling seconds.
Guliskhan is said to bike at a pace of 7 meters per second, hence the distance (in meters) that he covers in B seconds will be 7B.
An inequity of 3R + 7B 1000 has been handed to us.
We can observe that 7B reflects the cycling distance covered by Gulkishan in meters in B seconds.
Guliskhan covers a distance of 3R meters in the number of seconds she runs for, where R is the number of seconds she runs for.
Guliskhan moves at a steady pace of 3 meters per second because of this.
B. Since Gulkiskhan 3R plus 7B has traveled a total distance greater than or equal to 1000 meters, her minimum intended distance is 1000 meters.
C. Let's replace R=60 and B=90 in our inequality to see if Guliskhan is capable of traveling this minimum distance.
=>3*60 + 7*90 ≥ 1000
=>180 + 630 ≥ 1000
=>810 ≠> 1000
Therefore, even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.
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plss help help help can someone plss help me
~plss respect my question~
I really need this right now so please
Answer:
1) The stars are not constant in their position.
2) No. The stars aren't in original position because of apparent movement of stars in the sky.
3) Due to rotation of earth on its axis , the stars appear to move from west to east in the sky. Actually stars don't move as they are constant in their position but they appear to move with respect to earth.
4) Both the motion of stars & motion of sun are similar because both are an example of apparent motion. Both appear to change their respective positions but in reality , sun & stars are constant in their positions. But as earth is rotating , it appears like sun & stars are changing their positions.
How is the graphed system of equations classified?
Drag and drop words into the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A Response area system has at least one solution. A Response area system has an infinite number of solutions.
A system that has no solution is classified as inconsistent.
A system that has one and only one solution is classified as independent
The system of equation graphed is consistent and independent.
How to interpret the graph of linear equations?The equations given by the graph are expressed as;
3x - 4y = 32
3x + 5y = 24
Now, if we subtract eq 1 from eq 2, we will get;
5y - (-4y) = 24 - 32
9y = -8
y = -8/9
Put 8/9 for y in eq 2 to get;
3x + 5(8/9) = 24
3x = 24 - 40/9
3x = 176/9
x = 176/27
Now, to classify solution to equations, we say that;
1) When there is no solution, it is inconsistent.
2) When there is one and only one solution, it is independent
Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.
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A train travels 90 miles in 15 minutes. How many miles does it travel in 2 hours?
Answer:
360
Step-by-step explanation:
60 divided by 15=4
90 x 4 =360
Answer:
720 miles
Step-by-step explanation:
This is assuming the train continues to move at the same speed.
You can think about the problem in the following way:
The 2 hour journey is split up into x number of 15 minute segments.
2 hours = 120 minutes
120/15 = 8
Therefore, x = 8.
If the journey can be split into 8 15 minute segments, and each 15 minute segment carries it 90 miles, the total distance traveled is given by:
8 * 90 miles = 720 miles
Atlernatively, you can calculate the average speed of the train.
Speed = Distance/Time
So: Speed = 90 miles/15 minutes = 6 miles/minute.
Reusing the above formula, substituting in speed = 6 miles/minute and time = 120
HELP DESPERATE 50 POINTS AND BRAINLIEST!!!!!
Answer:
6 Passwords
Step-by-step explanation:
718, 781, 817, 871, 178, 187
(Hope this helped! Please comment any questions) :)
Answer:
The idiot that sent the link just got taken down so I'll just answer with my comment.
Step-by-step explanation:
"I believe it is 6"
Please Simplify the phrase the first two and find the last one
Answer:
1) 23x + 6y
2) 8x - 4y
3) 4x - x² + 7
Step-by-step explanation:
Simplify:
Multiply each term of (3x + 6y) by 5 and multiply each term of (2x - 6y) by 4.
5(3x + 6y) + 4 (2x - 6y) = 5*3x + 5*6y + 4*2x - 4*6y
= 15x + 30y + 8x - 24y
Now, combine like terms. Like terms have same variable with same power.
= 15x + 8x + 30y - 24y
= 23x + 6y
2) 3(4x - 2y) - 2*(2x -y) = 3*4x + 3*(-2y) + (-2)* 2x + (-2)*(-y)
= 12x - 6y - 4x + 2y
= 12x - 4x - 6y + 2y
= 8x - 4y
3) f(x) = 3x + 2
To find f(x +1), replace x with (x +1)
f(x +1) = 3*(x + 1) + 2
= 3*x + 3*1 + 2
= 3x + 3 + 2
=3x + 5
f(2x) = 3*(2x) + 2
= 6x + 2
f(2x) + h(x) = 6x + 2 - x² - 2x + 5
= 6x - 2x - x² +2 + 5
= 4x - x² + 7