Answers
Finding the composition for 1st option:
[tex](fof)(x) = f(f(x))= \frac{ \frac{x-1}{x+5}-1 }{ \frac{x-1}{x+5}+5 } \\ \\ = \frac{ \frac{x-1-x-5}{x+5} }{ \frac{x-1+5x+25}{x+5} } \\ \\ = \frac{-6}{6x+24} \\ \\ = \frac{1}{x+4} [/tex]
Since the composition of the function with itself is not x, the function and its inverse are not the same.
Similarly, we can find the compositions of next 3 functions with themselves. The results of compositions are listed below:
(gog)(x)=g(g(x)) = x
(hoh)(x)=h(h(x))=[tex] \frac{4x-3}{7-x} [/tex]
(kok)(x)=k(k(x))= x
Thus the option 2 and 4 are the correct answers i.e. these functions are the same as their inverse functions.
Related Questions
plz help with this ill give you brainlist
Answers
54 + 3x = 126
3x = 72
x = 24
3x = 72 . . . . . . . . subtract 54
x = 24 . . . . . . . . . divide by 3
The value of x is 24.
One side of a regular hexagon is 4 cm. What is the length of one other side?
a. 4 cm
b. 5 cm
c. 6 cm
d. can't be determined.
Answers
the answer is a, 4 cm
Answer:
Your Answer is 4 CM
Step-by-step explanation:
Which transformation gives the same result as a reflection over the y-axis followed by a reflection over the x-axis?
a.A rotation of 180° around the origin
b.A rotation of 270° around the origin
c.A translation to the left and then down
d.A rotation of 90° around the origin
Answers
Answer:
a. A rotation of 180° around the origin.
Step-by-step explanation:
A rotation of 180° around the origin would give us the same result as a reflection over the y-axis followed by a reflection over the x-axis. When we perform this rotation, we take each of its points through the transformation (x,y) ---> (-x, -y). This means that we would multiply the coordinates of each of the points on the shape by a negative. This is equivalent to reflecting a shape over the x-axis and the y-axis.
Quick help!! If you not sure of the answer PLEASE DON'T COMMENT
Answers
Answer is B
What is the probability that of two randomly selected women, one is 68 inches or shorter and the other is 68 inches or taller?
Answers
1.A natural law of growth is of the form y= [tex]5e^{0.2x}[/tex]. Draw a graph for this law for values of x from x = -3 to x = 3. From the graph:
A)Find the gradient of the curve at x = -2 and x = 1 by differentiation and by drawing a tangent to the curve.
B)Compare your two solution for these gradients
Answers
.. y' = e^(0.2x)
so the gradients are
.. at x=-2, e^-0.4 ≈ 0.67
.. at x=1, e^0.2 ≈ 1.22
It is difficult to get a good estimate of the gradient by drawing a tangent line. (If you want to try, the second picture is the same graph with the tangent lines turned off. You can print it out and draw your tangent line--or use your favorite picture markup program.)
B) They will likely be within "experimental error", accurate to within a couple of degrees of rotation. (Higher slopes are more difficult to approximate accurately.)
The equation of the circle whose center is at (3, 7) and whose radius is 6 is a. (x + 3)² + (y + 7)² = 6 b. (x + 3)² + (y + 7)² = 36 c. (x - 3)² + (y - 7)² = 36
Answers
What is the median for the data set?
252, 210, 264, 278, 208, 295, 248, 257, 284, 271
Express your answer as a decimal to the nearest tenth.
Enter your answer in the box.
Answers
Here there are total ten numbers (even)
So these are the steps we follow:
Step 1:
Arrange the numbers in ascending order.
252, 210, 264, 278, 208, 295, 248, 257, 284, 271
Ascending order is : 208, 210, 248, 252, 257, 264, 271, 278, 284, 295
Step 2:
Find the middle two numbers.
The middle two numbers are 257 and 264.
Step 3:
Find average of these two numbers.
Average = (257+264)/2 = 260.5
Answer : Median is 260.5
Which expression can be used to find the quotient of 15 and ?
Answers
Which expression can be used to find the quotient of 15 and y?
to find the quotient of 15 and y let's divide the value of 15 between the value of y
(15/y)
the answer is
the expression is (15/y)
if the graph of a quadratic function intersects with the x axis two times, how many solutions are there to the equation when set equal to zero
Answers
This is a conceptual question about quadratic functions.
Remember that a solution of ANY function is where it intersects the x-axis, so if the quadratic function intersects the x-axis TWO times, this means that there are TWO real solutions.
Here's a list of things to remember that will help you out for quadratic functions...
•if a quadratic function intersects the x-axis twice, it has two real solutions.
•if a quadratic function intersects the x-axis once, it has one real solution and one imaginary solution.
•if a quadratic function intersects the x-axis zero times, it has zero deal solutions and two imaginary solutions.
Please NOTE: If you want to know how many solutions a polynomial function has, look at it's highest exponent. If it is 2, then it has 2 solutions whether they be real or imaginary. If it is 3, then it has 3 solutions.
Also, if one of the factors are the same for a polynomial function, the way it hits the x-axis changes! This is just some extra information to help you in the long run!
I hope this helps!
Best wishes :)
Final answer:
A quadratic function intersecting the x-axis two times means there are two distinct real solutions to the equation when it is set to zero.
Explanation:
When a quadratic function intersects the x-axis two times, it indicates that the corresponding quadratic equation has two distinct real solutions.
This is because the points where the graph intersects the x-axis are the zeros of the function, which are the solutions to the equation when set equal to zero.
To find the solutions to a quadratic equation of the form ax² + bx + c = 0, one can use the quadratic formula, which is:
[tex]x = (-b \pm (b^2 - 4ac)) / (2a)[/tex]
If the discriminant (b² - 4ac) is greater than zero, this indicates two distinct real solutions.
Jalla's hourly wage is $11.791. Round her salary to the nearest cent
Answers
Jalla's hourly wage, when rounded to the nearest cent, is $11.79.
Explanation:To round Jalla's wage to the nearest cent, we must look at the numbers following the decimal. In this case, Jalla's hourly wage is $11.791. Decimal rounding rules tell us that if the number following the decimal is equal to 5 or more, round up; otherwise, round down. In this case, the number after the decimal is 9, more than 5, so we round the second decimal place up. Therefore, rounding to the nearest cent, Jalla earns $11.79 per hour, her rounded wage.
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Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?
Answers
To find the increasing intervals for this graph just based on the equation, we should find the turning points first.
Take the derivative of f(x)...
f(x)=-x²+3x+8
f'(x)=-2x+3
Set f'(x) equal to 0...
0=-2x+3
-3=-2x
3/2=x
This means that the x-value of our turning point is 3/2. Now we need to analyze the equation to figure out the end behavior of this graph as x approaches infinity and negative infinity.
Since the leading coefficient is -1, as x approaches ∞, f(x) approaches -∞ Because the exponent of the leading term is even, the end behavior of f(x) as x approaches -∞ is also -∞.
This means that the interval by which this parabola is increasing is...
(-∞,3/2)
PLEASE DON'T include 3/2 on the increasing interval because it's a turning point. The slope of the tangent line to the turning point is 0 so the graph isn't increasing OR decreasing at this point.
I really hope this helps!
Best wishes :)
Brian is playing a video game. He earns the same number of points for each star he picks up. He earns 2400 points for 6 stars, 4000 points for 10 stars, and 5,200 points for 13 stars. What is the independent and dependent value?
Answers
Write the first four terms in the multiplication pattern given by the formula 10*5n
(The n is exponent)
Answers
10*5^1, 10*5^2 , 10*5^3, 10*5^4
= 50, 250, 1250 and 6250 answer
four photographers are taking pictures at a school dance. Photographer A takes 25 of the pictures, Photographer B takes 4% , Photographer C takes 0.29 hey , and Photographer D takes 27/100 . Which choice lists the photographers in order from least to greatest by the amount of pictures they take?
Answers
x----------> number total of pictures
we know that
A------>25
B------> 4%----> 4/100------> 0.04x
C-----> 0.29------> 29%-------------------> 0.29x
D------> 27/100 --------> 27%--------------> 0.27x
[B+C+D]=4%+29%+27%--------> 60%
that means
A=100%-60%---------> 40%
so
A-------------> 0.40x
A------>0.40 x
B------> 0.04x
C-----> 0.29x
D------> 0.27x
the answer is
the photographers list in order from least to greatest by the amount of pictures they take is
B------> 0.04x
D------> 0.27x
C------> 0.29x
A------> 0.40x
What is the value of x in simplest radical form?
Answers
a = 84
b = 13
c = x
[tex]\sqrt{84^2 + 13^2} = 85[/tex]
Thus, x = 85.
[tex] {x}^{2} = {13}^{2} + {84}^{2} \\ {x}^{2} = 169 + 7056 = 7225 \\ x = \sqrt{7225} = 85[/tex]
There are 84 students in the glee club there are 12 more boys than girls what is the ratio of the number of girls to the number of boys
Answers
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The midpoint of the line segment from upper p 1p1 to upper p 2p2 is left parenthesis negative 1 comma 5 right parenthesis(−1,5). if upper p 1p1equals=left parenthesis negative 4 comma 6 right parenthesis(−4,6), what is upper p 2 question mark p2?
Answers
Final answer:
To find the coordinates of point P2 when given the midpoint M(-1, 5) and point P1(-4, 6), we use the midpoint formulas, resulting in P2 having the coordinates (2, 4).
Explanation:
The midpoint of a line segment is the point that is exactly halfway between the endpoints of the line segment. By definition, the midpoint M(x, y) can be found using the endpoints P1(x1, y1) and P2(x2, y2) with the formulas:
x = (x1 + x2)/2y = (y1 + y2)/2To find P2, we solve for x2 and y2 using the midpoint M(-1, 5) and the given point P1(-4, 6):
x2 = 2x - x1 = 2(-1) - (-4) = -2 + 4 = 2y2 = 2y - y1 = 2(5) - 6 = 10 - 6 = 4Therefore, the coordinates of point P2 are (2, 4).
Final answer:
The coordinates of P2 are (6, 4).
Explanation:
The midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the two endpoints. In this case, the midpoint is (-1, 5), and one endpoint is (-4, 6). To find the other endpoint, we can use the formula:
x-coordinate of P2 = 2 * (x-coordinate of midpoint) - x-coordinate of P1 = 2 * (-1) - (-4) = 2 + 4 = 6
y-coordinate of P2 = 2 * (y-coordinate of midpoint) - y-coordinate of P1 = 2 * (5) - 6 = 10 - 6 = 4
Therefore, the coordinates of P2 are (6, 4).
You roll a single die numbered from 1 to 6. What is the probability of rolling a number greater than 3 and then a number less than 3?
Answers
Maya's penny bank is 3/10
full. After she adds 520
pennies, it is
4/5 full. How many pennies can Maya's bank hold?
Answers
Maya's bank can hold 1733 pennies.
Explanation:To find out how many pennies Maya's bank can hold, we can set up an equation using the given information. Let's start with the fact that Maya's bank is 3/10 full before adding 520 pennies. This means that 3/10 of the bank's capacity is equal to 520 pennies. We can use this information to find the total capacity of the bank.
Since 3/10 of the bank's capacity is equal to 520 pennies, we can set up the equation (3/10)x = 520, where x represents the total capacity of the bank in pennies.
To solve for x, we can multiply both sides of the equation by 10/3 to cancel out the fraction. This gives us x = (10/3) * 520 = 1733.33. Since we cannot have a fraction of a penny, we round down to the nearest whole number. Therefore, Maya's bank can hold 1733 pennies.
find the number of possible choices for a 4-digit (pin) if the digits cannot be repeated
find the possible choices of a 4-digit (pin) if the digits cannot be repeated
Answers
There are 10 digits to choose from for the first digit. Since the digits cannot repeat, there are 9 to choose from for the second; 8 choices for the third; and 7 choices for the fourth.
10(9)(8)(7) = 5040.
The number of possible choices for a 4-digit PIN where the digits can't repeat is 5040, coming from the product of the choices per position: 10 choices for the first digit, 9 for the second, 8 for the third, and 7 for the fourth.
Explanation:The subject of this question is combinatorics, a branch of mathematics that focuses on the counting and arrangement of objects. We want to find out the number of possible choices for a 4-digit PIN, where the same digit can't repeat. In this situation, at the first position, we have 10 choices (from 0 to 9). However, once we pick one number, it can't be repeated, so in the second, third and fourth positions, we have 9, 8, and 7 choices respectively.
So, we multiply the choices together to come up with 5040 (10*9*8*7) possible choices for a 4-digit PIN where the same digit can't be repeated. This method of counting is generally known as the multiplication principle in combinatorics.
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if you put down 15% on a $9000 car and pay monthly payments of $189.40 for 48 months , what is the total price of the car?
Answers
Amount=(15/100×9000)+(189.40×48)
=1350+9091.2
=10,441.2
The total amount of money paid for the car after a period of time will be $10,441.2
How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50-foot radius?
Answers
50ft = 600in
then have to find the circumference
[tex]2\pi600 = 3769.9 [/tex]
then you would divide that by 6
[tex]6 \div 3769= 628.16[/tex]
Or 628 flowers
A circular garden with a 50-foot radius needs 628 flowers spaced every 6 inches.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that, flowers are spaced every 6 inches, are needed to surround a circular garden with a 50-foot radius.
As we know that, their is 12 inches in 1 foot.
1 foot = 12 inches
50 foot = 50 × 12 inches
50 foot = 600 inches
Circumfereeence of circle is obtained as,
C= 2πr
C=2×3.14×600
C=3768
If the floweres are spaced flowers, spaced every 6 inches, the number of are needed to surround a circular garden with a 50-foot radius,
n = C / 6
n=3768 / 6
n=628
Thus, a circular garden with a 50-foot radius needs 628 flowers spaced every 6 inches.
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Write a function named righttriangle() that accepts the lengths of two sides of a right triangle as the arguments a and
b.
Answers
A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.
What is the experimental probability of the arrow stopping over Section 1?
Section 1 Section 2 Section 3
28 36 16
Answers
Answer: [tex]\frac{7}{20}[/tex]
Step-by-step explanation:
From the given table, The number of times arrow comes results in section 1= 28
The total number of times spinner spins =80
Now, the experimental probability of the arrow stopping over Section 1 is given by:-
[tex]\text{P(Section 1)}=\frac{28}{80}=\frac{7}{20}[/tex]
Hence, the experimental probability of the arrow stopping over Section 1 is [tex]\frac{7}{20}[/tex]
Simlify the sum 4/m+9 + 5/m^2-81
Answers
9m - 76/(m + 9)(m - 9)
Hope this helps! :)
4m - 31
-------------------
(m+9)(m-9)
Explanation:
1) the given sum is:
4 5
------ + -------------
m+9 m^2 - 81
2) factor m^2 - 81
m^2 - 81 = (m + 9)(m - 9)
3) rewrite the sum
4 5
------- + ------------------
m+9 (m+9)(m-9)
4) least common denominator: (m + 9)(m - 9)
4(m-9) + 5 4m - 36 + 5 4m - 31
--------------------- = ------------------- = ----------------
(m+9)(m-9) (m+9)(m-9) (m+9)(m-9)
Compute the area of the triangle. H=8cm b=14cm
Answers
A= (b*h)/2
A=(8*14)/2=112/2=56
divide 56 in the ratio 5 3
Answers
But,
5 + 3 = 8
56/8 = 7
7*5 = 35
7*3 = 21
Hope this helps !
Photon
The given value is 56
We need to divide in the ratio 5 : 3
We can do it this way:
5x + 3x = 56
8x = 56
[tex] \frac{8x}{8} = \frac{56}{8} [/tex]
8 and 8 cancels out
x = 7
5(7) : 3(7)
35 : 21
the length of a rectanglr exceeds its width by 5 inches, and the area is 84 square inches. what are the length and width of a a rectangle
Answers
The area is the product of length and width, which is to say that the length and width are factors of the area.
Assuming the dimensions are integers, you want factors of 84 that differ by 5.
... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12
The last of these pairs differ by 5, so ...
the length is 12 inchesthe width is 7 inches.Answer:
The answer is l=12, w=7
Step-by-step explanation:
Brayden is simplifying the expression 4n – (n – 3)2. He begins by distributing the negative to the terms inside the parentheses. What should he have done instead? combine like terms square the binomial cube the binomial rewrite the expression as a fraction
Answers
The correct step is to square the binomial (n - 3)² before combining like n terms.
Brayden is working on simplifying the expression 4n – (n - 3)². The correct initial step is not to distribute the negative inside the parentheses, but rather to square the binomial. This involves applying the binomial square formula [tex](a - b)^2 = a^2 - 2ab + b^2[/tex], to the expression inside the parentheses. Therefore, simplification should start with (n - 3)² resulting in [tex]n^2 - 6n + 9[/tex]. After this, Brayden should combine like n terms by adding or subtracting them to simplify the expression further.