Answer:
Not inverse of each other
Domain : [-∞,0) U (0,5) U (5,∞]
Step-by-step explanation:
Given in the question two functions
f(x)=1/x-5
g(x)=5x-1/x
To find that each of them are inverse of each other we will use composition
f(g(x))[tex]\frac{1}{\frac{5x-1}{x}-5 }[/tex]
take LCM
[tex]\frac{1}{\frac{5x-1-5x}{x}}[/tex]
5x will be cancel
[tex]\frac{1}{\frac{-1}{x}}[/tex]
1 ÷ (-1/x)
1 × (-x/1)
-x
Now,
g(f(x))[tex]\frac{5\frac{1}{x-5} -1}{\frac{1}{x-5}}[/tex]
[tex]\frac{5}{x-5} -1}[/tex] × [tex]5-x[/tex]
[tex]\frac{5-x+5}{x-5} * (x-5)[/tex]
10-x
As it ended up with different answers, so f(x) and g(x) are not inverse of each other
The domain are all the possible x-values of function except x ≠ 0 and x ≠ 5
We can conclude that the domain of the composition function is
Domain : [-∞,0) U (0,5) U (5,∞]
To prove whether or not the functions f(x) = 1/(x-5) and g(x) = (5x-1)/x are inverses of each other, we need to show that their compositions result in the identity function. We also need to find the domain of the compositions f(g(x)) and g(f(x)).
Explanation:To prove whether or not the functions f(x) = 1/(x-5) and g(x) = (5x-1)/x are inverses of each other, we need to show that their compositions result in the identity function. Let's start by finding the composition f(g(x)):
Plug in g(x) into f(x): f(g(x)) = f((5x-1)/x)Simplify f(g(x)) by substituting (5x-1)/x into the expression for f(x)Simplify further to obtain the composition f(g(x)) as a function of xNow, we need to find the composition g(f(x)): g(f(x)) = g(1/(x-5))
Follow the same steps as above to simplify g(f(x)) as a function of x. If the compositions f(g(x)) and g(f(x)) both result in the identity function, then the functions f(x) and g(x) are inverses of each other.
To express the domain of the compositions f(g(x)) and g(f(x)), we need to consider the restrictions on the domains of the individual functions. The domain of f(g(x)) will be the values of x for which (5x-1)/x is defined, and the domain of g(f(x)) will be the values of x for which 1/(x-5) is defined.
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Sasha bought 3 and 1/2 pints of blueberries to make jelly she ate 3/4 of a pint of varies on her way home how many pints of berries does she have left to make jelly
3 1/2 pints - 3/4 pints
3 1/2 = 3 2/4
3 2/4 = 2 6/4
2 6/4 - 3/4
2 3/4
Answer: 2 3/4 pints of berries
Sasha bought 3 and 1/2 pints of blueberries, ate 3/4 of a pint, and after calculating, she has 2 and 3/4 pints left for making jelly.
The student, Sasha, initially bought 3 and 1/2 pints of blueberries and then ate 3/4 of a pint. To find out how many pints of berries she has left, we need to subtract the amount eaten from the amount bought.
We calculate:
Convert the mixed fraction to an improper fraction:Converting 11/4 pints back to a mixed number, we get 2 and 3/4 pints. Therefore, Sasha has 2 and 3/4 pints of blueberries left to make jelly.
Help me accidentally checked it in !!!!!!!!!
Answer: 16
Step-by-step explanation:
[tex]64^{\frac{2}{3}}=(2^6)^{\frac{2}{3}}=2^{\frac{12}{3}}=2^4=\boxed{16}[/tex]
2. The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards. What function models the amount of fertilizer in cubic yards left after w weeks?
Exponential Growth: y=a*b^x where a initial amount and b is the growth factor.
Sarah identified the initial amount as 78000 and the rate as 3%. She wrote her equation as: y=78,000 〖(3)〗^x.
Error:
Correct solution:
The error is the way she wrote 3%
3% = 0.03
The correct equation should be y = 78,000(0.03)^x
Suppose you buy an appliance costing $2450 at a store charging 9% add-on interest, you make a down payment of $ 600, and you agree to monthly payments over 4 years.
Find the total cost for the appliance plus interest.
Answer:
$3116
Step-by-step explanation:
First off, we need to find the value of the appliance after the down payment.
$2450 - $600 = $1850
This then makes our principal $1850.
P = $1850
r = 9% or 0.09
t = 4 years
To find the total cost of the appliance plus interest, we need to look for our accrued amount first.
A = P + Prt
A = $1850 + $1850(0.09)(4)
A = $1850 + $666
A = $2516
Now that we know our accrued amount, we then add our down payment to find the total cost.
Total cost = $2516 + $600
Total cost = $3116
To calculate the cost of an appliance with added interest, subtract the down payment from the purchase price to determine the amount of the loan. This is followed by the calculation of the total interest over the length of the loan. Adding these two amounts provides the total cost of the appliance plus interest, which in this case is $2516.
Explanation:The total cost of the appliance plus interest can be calculated by first determining the amount of the loan made, which is the cost of the appliance minus the down payment. This comes out to $2450 - $600 = $1850.
Then, the add-on interest over 4 years is calculated by multiplying the amount of the loan by the annual interest rate and by the number of years. For this question, that is $1850 * 0.09 * 4 = $666.
So, the total cost of the appliance with interest added is the sum of the amount of the loan and the amount of the interest. Therefore, $1850 + $666 = $2516 is the total cost for the appliance plus interest.
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SOMEONE PLEASE HELP ME!!!
if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)
Replace x in each equation with 4:
f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21
g(x) = x^2-9 = 4^2 -9 = 16-9 =7
Now you have values for f(x) and g(x) now you can solve for f/g and f+g:
f/g = 21 / 7 = 3
f+g = 21 + 7 = 28
For this case, we have that by definition:
[tex](f + g) (x) = f (x) + g (x)\\(\frac {f} {g})(x) = \frac {f (x)} {g (x)}[/tex]
We have the following functions:
[tex]f (x) = x ^ 2 + 2x-3\\g (x) = x ^ 2-9[/tex]
So:
[tex](f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28[/tex]
On the other hand:
[tex](\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4[/tex]
[tex](\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3[/tex]
Answer:
[tex](f + g) (4) = 28\\(\frac {f} {g}(4)) = 3[/tex]
Solve for the roots in the following equation. Hint: Factor both quadratic expressions. (x 4 + 5x 2 - 36)(2x 2 + 9x - 5) = 0 x = a0 a1, ± a2, - a3, ± a4 i
Answer:
The final solution is all the values that make
( x 4 + 5 x 2 − 36 ) ( 2 x 2 + 9 x − 5 ) = 0 true. x = − 2 , 2 , 3 i , − 3 i , 1 2 , − 5
Step-by-step explanation:
x 4 + 5 x 2 − 36 = 0 2 x 2 + 9 x − 5 = 0
Answer:
1,2,2,5,3
Step-by-step explanation:
it's right you idiots
Jack rolls two standard number cubes.find the probability that the sum of the roll is 5, given that one cube up even and the other came up odd
Answer:
[tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
We are given that Jack rolls two standard number cubes and we are to find the probability that the sum of the roll is 5, given that one cube up even and the other came up odd.
A sum of two from two rolls would always be one even and one odd, whatsoever is the case.
To have a sum of five, we can have (1, 4), (2,3), (3,2) or (4,1) out of a sample space of 36 so the probability will be [tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex].
Lina bought x rolls of film at $5.00 per roll and spent $25. How many rolls of film did Lina buy? (MUST SHOW WORK)
Answer:
Step-by-step explanation:
If Lina supposedly bought 10 rolls, we would show it by the following equation,5*10=50, and since 25 is half of 50, we would have 5 as our solution.
25/5=5
5 rolls of films is our solution
If Kayla babysits for 3 hours, she will earn$27. How much will she earn for 4 hours?
Answer:
kayla will earn $26
She will earn $36.00 in 4 hours.
27 divided by 3 = 9
9 x 4 = 36
Hope this makes sense and helps.
The number of students at Bedrock Middle School decreased to 90 % last year's number. Last year, there were 1,500 students. How many students are there this year?
Answer:
1,350 students
Step-by-step explanation:
The number of students this year is 90% of the number from last year. Find 90% of 1500....
90% is 0.9 as a decimal,
0.9(1500) = 1,350 students
Answer: 2i50 students
Step-by-step explanation:
Do 90% of 1,500
10% = 150
150 x 9 = 1350
We need the total amount of students
So do 1350 + 1500 = 2850 students
Which numbers are factors of 4? Select all that apply.
1
4
2
3
Answer:
1,2,4
Step-by-step explanation:
Factors are the numbers that we can multiply together to make 4
1*4 = 4
2*2 = 4
The factors are 1,2 and 4
Answer:
1, 2 and 4Step-by-step explanation:
[tex]Factors\ of\ 4:\ 1,\ 2,\ 4\\\\4=4\cdot\boxed{1}\\4=2\cdot\boxed2\\4=1\cdot\boxed4[/tex]
Asa owed $25 to his friend. He then borrowed another $14 after paying back $12 to his sister. Which expression could be used to find how much money Asa owes or has?
Answer:
Asa has $13 and owes $39
Step-by-step explanation:
25 + 14 = 39$ (amount of money he owes)
25 - 12 = 13$ (amount of money he has)
Length of the missing leg is:
Pythagorean theorem - Integers -
Find the missing leg
PLEASE HELP
(need to show work)
Im so confused!!
The lengths of the legs of each triangle are:
1) Leg = √19
2) Leg = √105
3) Leg = √60
How to use Pythagoras Theorem?
Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
a = √(c² - b²)
1) We are given that:
Hypotenuse = 10
Opposite side = 9
Thus, using Pythagoras Theorem, we have:
Leg = √(10²- 9²)
Leg = √19
2) We are given that:
Hypotenuse = 19
Opposite side = 16
Thus, using Pythagoras Theorem, we have:
Leg = √(19²- 16²)
Leg = √105
3) We are given that:
Hypotenuse = 8
Opposite side = 2
Using Pythagoras Theorem, we have:
Leg = √(8²- 2²)
Leg = √60
2pt 4 fl oz, 5 cups 39fl oz. What is the greatest amount of paint?
Answer:
5 cups 39 fl oz
Step-by-step explanation:
There are 2 cups to a pint, so 2pt 4 fl oz becomes 4 cups 4 fl oz, which is less than 5 cups 39 fl oz
Josephina is five years older than Cameron and the sum of their ages is 31. Can you write or type an equation and solve it to figure out their ages? Or, must you use the 5-D process to solve? Either way, find a way to solve it. How old are Josephina and Cameron? Show that your answer is correct.
Cameron - х years
Josephina is five years older than Cameron = х+5 years
sum of their ages is 31
х+х+5=31
2х=31-5
2х=26
х=13 Cameron
13+5=18 Josephina
The age of Josephina and Cameron is 13 and 18.
The calculation is as follows:
here Cameron be х years
And, Josephina is five years older than Cameron so х+5 years
Also,
The sum of their ages is 31
Now
х+х+5=31
2х=31-5
2х=26
х=13 Cameron
13+5=18 Josephina
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explain how to convert numbers from standard form to scientific.
Answer:
Start by moving the decimal place in the number until you have a coefficient between 1 and 10. The number of places to the left that you had to move the decimal point is the exponent. so for example, 0.000345 would be 3.45(10)^4
Step-by-step explanation:
Hope that helps!
Which function is represented by the graph
f(x)= -|x|+4
f(x)= -|x|-4
f(x)= -|x+4|
f(x)= -|x-4|
It’s the forth one
The answer is -|x-4|.
Answer:y=-|x-4|
Step-by-step explanation:
we know the graph of y=|x| touches at x=0 and opens upward towards y axis
but this graph is facing downwards therefore it should be of form
y=-|x|
but it touches the x axis at x=4
therefore the graph is represented by
y=-|x-4|
4 is added inside the mod because it intersect x axis at x=4
The graph would be y=-|x-4|+1 if it shifts 1 unit upwards.
Which number line shows the solution set for |m| = 4
Answer:
Last choice that shows points on +4 and -4 is the correct graph.
Step-by-step explanation:
We have been given equation [tex]|m|=4[/tex]. Now we need to find out which of the given number lines shows the corret solution set for [tex]|m|=4[/tex].
We know that [tex]|x|=a[/tex] can be broken into two parts as:
[tex]x=+a[/tex] and [tex]x=-a[/tex]
Same way we can break [tex]|m|=4[/tex] into two parts as:
[tex]m=+4[/tex] and [tex]m=-4[/tex]
Hence last choice that shows points on +4 and -4 is the correct graph.
Answer:
D is correct
Step-by-step explanation:
what is the nth term in the sequence -4/3,-1,-4/5,-2/3,-4/7 with work please
-4/3 is the nth term
Last option is none of the above
Answer:
A and B
Step-by-step explanation:
When rotating a point (or any shape around a certain point), none of the diameters of the shape will change. So for example, with this circle, when you rotate it around a point, the radius and circumference will not change because it has just rotated. It wont be on the x-axis though because point P is not on the x-axis an it is being rotated 180 degrees about point P. Just know that when you are rotating, nothing about the shape changes, all angles or measurements will be the same, it is just moving to a different place.
Hope this helped ^-^
Hey can someone answer this ASAP
Answer:
csc θ = [tex]\sqrt{85}[/tex]/6
sec θ = [tex]\sqrt{85}[/tex]/7
tan θ = 6/7
Step-by-step explanation:
The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;
6^2 +7^2 = hypotenuse^2
hypotenuse = [tex]\sqrt{85}[/tex]
csc θ = 1/sinθ
sinθ = opposite side/hypotenuse
= 6/[tex]\sqrt{85}[/tex]
csc θ = [tex]\sqrt{85}[/tex]/6
sec θ = 1/cosθ
cosθ = adjacent side/hypotenuse
sec θ = hypotenuse/adjacent side
= [tex]\sqrt{85}[/tex]/7
tan θ = Opposite side/adjacent side
= 6/7
the sum of two numbers is 21 and their difference is 5
X+Y = 21 ---> Y = 21-x
X-y = 5
x - (21-x) = 5
2x - 21 = 5
2x = 26
x = 13
13 and 8
The two numbers are 13 and 8.
13 + 8 = 21
The difference (13 - 8) is 5.
A right triangle has coordinates A(6, 0), B(0, 0), and C(0, 8). What is the perimeter of the triangle?
A. 18 units
B. 20 units
C. 24 units
D. 28 units
Answer:
C
Step-by-step explanation:
From the given coordinates
A(6, 0), B(0, 0) then AB = 6 - 0 = 6
B(0, 0), C(0, 8) then BC = 8 - 0 = 8
To calculate AC use Pythagoras' theorem on the right triangle formed
AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100
Take the square root of both sides, hence
AC = [tex]\sqrt{100}[/tex] = 10
Perimeter = AB + BC + AC = 6 + 8 + 10 = 24 → C
The coordinates of 3 of the vertices of a parallelogram are (–7, 3), (–6, 1), and (–4, 5). What is the equation for the line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a parallelogram are parallel.)
Answer: [tex]y=-2x-3[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form, is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
By definition, parallel lines have the same slope.
Then:
- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]
- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:
[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]
Then, the equation for the line containing the side opposite the side containing the first two vertices is:
[tex]y=-2x-3[/tex]
How Find the solution set of the inequality
−4x+35>2
Answer:
[tex]x<8\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]-4x+35>2\\-4x>-33\\x<\frac{33}{4} \\x<8\frac{1}{4}[/tex]
Remember to flip the sign when you divide or multiply both sides by a negative number! You don't need to flip the sign with adding or subtracting as in the case of step one subtracting 35 from both sides.
The solution of the inequality −4x+35>2 will be x < (33 / 4).
What is inequality?The relationship between two phrases using a symbol like "not equal to," "greater than," or "less than" indicates that they are not equal.
The given inequality will be solved as below:-
−4x+35>2
−4x>- 35 + 2
−4x > - 33
−4x > - 33
x < ( 33 / 4 )
Therefore, the solution of the inequality −4x+35>2 will be x < (33 / 4).
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Simplify.
38√
3√4
6√8
24√8
6√4
Answer:
the first one i believe
Step-by-step explanation:
hope this helps
Answer:
3√4
Step-by-step explanation:
Find a linear equation in your life?
My life is not linear. Time is not constant. My life (and time included) is just a series of times that do not run parallel to each other. Instead, they drift further or closer as a function of velocity and curvature of space time.
Answer: If you are looking for a linear equation in your life, an example could be the rate of the grass growing in your lawn. The y axis could be the height and the x axis could be the time. As it grows, the line representing the grass could go up gradually; when you cut it, the line can stop. Keep doing that for however long you'd like to represent the grass growing/getting cut.
A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if it’s length is 6 feet more than it’s width?
Answer:
The Field's length is 93ft
Step-by-step explanation:
P=2L+2w
360=2(w+6)+2w
360=2w+12+2w
360=4w+12
348=4w
348/4=w
87=w
L=w+6
L=87+6
L=93
The width of a rectangular field surrounded by 360 feet of fencing is 87 feet. The length of the field, which is 6 feet more than the width, is 93 feet.
Explanation:We are dealing with a rectangular field here, and we know that the length of a rectangle is equal to the total fencing (perimeter), divided by two, minus the width. Now, the problem states that the length is 6 feet more than the width. Therefore, we can create the following equation: 2x + 2(x + 6) = 360, where x is the width.
After simplifying this equation, we find that 4x + 12 = 360. Subtract 12 from both sides to get 4x = 348, and then divide by 4 to find that x = 87 feet. Thus, the width of the field is 87 feet. Since the length is 6 feet more than the width, we add 6 to 87 to get a length of 93 feet.
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Find the mean and the median of this data set: 9, 6, 5, 3, 28, 6, 4, 7
Answer:
The means is 8.5 The Median is 6
Step-by-step explanation:
1) to find the mean just Simply add all the numbers together and divided by how many numbers that is giving. (Because you are simply finding the average)
9+6+5+3+28+6+4+7=68
68 divided by 8 = 8.5
2) to find the median simply organize the numbers from least to greatest Like this: (3,4,5,6,6,7,9,28) Then keep crossing out from both sides teal you find the middle Number.
If there a odd amount of number the median will be one Number, if even 2 numbers ( if 2 numbers just add them both and divide by 2)
In This Case the Median is 6,6 but Its actually 6 Why (6+6=12) and (12/2=6) so your median is 6.
Hopes This helps!
The mean of the given data 9, 6, 5, 3, 28, 6, 4, 7 is 8.5 and the median is 6.
The mean is defined as the average of all the values or the mean can be defined as the sum of all observations by the total number of observations.
[tex]Mean =\dfrac {\ Sum \ of \ all \ observation}{Total \ number \ of \ observation}[/tex]
[tex]Mean = \dfrac{9 + 6 + 5 + 3 + 28 + 6 + 4 + 7}{8}[/tex]
Mean = [tex]\dfrac{68}{8}[/tex]
Mean = 8.5
Therefore, the mean of the data set is 8.5.
The median is defined as:
The median is the middle value when the data set is arranged in ascending or descending order.
If there are two middle values, the median is the average of those two values.
Arrange the data set in ascending order: 3, 4, 5, 6, 6, 7, 9, 28.
Here n = 8, since n is even so the median is calculated as:
Median = [tex]\dfrac{(\dfrac{n}{2}) \ th \ observation + (\dfrac{n}{2}+1) \ th \ observation}{2}[/tex]
Median =[tex]\dfrac{( 4 \ th \ observation + 5 \ th \ observation)}{2}[/tex]
The 4th observation is 6 and the 5th observation is 6.
So, this mean will be 6.
Therefore, the median of the data set is 6.
The Mean is 8.5 and the median is 6.
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There are 12 contestants in a coloring contest. Three ribbons will be awarded. How many different ways could the ribbons be awarded?
Answer:
1320 ways
Step-by-step explanation:
Here we have a situation where 3 ribbons will be awarded to 3 of the 12 contestants. We can use the permutation formula, because the order of awarding the ribbons matters.
The permutation formula is:
[tex]_{n}P_{k}=\dfrac{n!}{(n-k)!}[/tex]
n = 12
k = 3
Now that we have our variables, let's plug them into the formula.
[tex]_{12}P_{3}=\dfrac{12!}{(12-3)!}[/tex]
[tex]_{12}P_{3}=\dfrac{12!}{9!}[/tex]
[tex]_{12}P_{3}=1320[/tex]
So there are 1320 different ways that the contestants will be awarded.