Answer:
f−1(f(x)) = f(f−1(x)) = x
Step-by-step explanation:
Follow this simple example using the function f(x) = x + 2
f(x) = x + 2
NOw we find the inverse function f^(1)(x).
y = x + 2
x = y + 2
y = x - 2
f^(-1)(x) = x - 2
The inverse function is f^(-1)(x) = x - 2
Now we do the two compositions of functions:
f^(-1)(f(x)) = x + 2 - 2 = x
f(f^(-1)(x)) = x - 2 + 2 = x
Both are equal to x.
Answer: f−1(f(x)) = f(f−1(x)) = x
The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]
We are to prove the relationship;
[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]
To get the unknown, let f(x) = x - 2
Find its inverse:
Let y = x - 2
Replace y with x;
x = y - 2
y = x+2
Hence [tex]f^{-1}x = x+2[/tex]
Next is to get [tex]f(f^{-1}(x))[/tex]
[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]
We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]
Learn more here: https://brainly.com/question/12220962
The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.
Answer:
The two numbers are 15 and 6.
Step-by-step explanation:
Given:
The difference between two numbers is 9.
The first number plus twice the other number is 27.
Now, to find the two numbers.
Let the first number be [tex]x.[/tex]
And the other number be [tex]y.[/tex]
So, the difference between two numbers is 9.
[tex]x-y=9[/tex]
[tex]x=9+y[/tex] ............(1)
As, given the first number plus twice the other number is 27.
According to question:
[tex]x+2y=27[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex](9+y)+2y=27\\9+y+2y=27\\9+3y=27[/tex]
Subtracting both sides by 9 we get:
[tex]3y=18[/tex]
Dividing both sides by 3 we get:
[tex]y=6.[/tex]
The other number = 6.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=9+y\\x=9+6\\x=15.[/tex]
The first number = 15.
Therefore, the two numbers are 15 and 6.
If a function uses variables other than xand y for its input and output
variables, you take the original equation and solve for the input variable to
find the inverse.
A. True
B. False
Answer:
True
Step-by-step explanation:
Sorry if it's wrong lol
what is 0.793 rounded to the nearest hundredths
Answer:
0.800
Step-by-step explanation:
its almost 0.800
Answer:
.800
If the second digit after the decimal is 50 or is over 50 you change the first digit after the decimal point to the next digit up, and make the rest of the digits after the decimal point zero. If it is lower than 50 then you do the same but keep the same first number after the decimal point.
The variable is directly proportional to the variable . If y = 10 when x = 6, what is the value of y when x = 15?
Answer:
y = 25
Step-by-step explanation:
Given that the quantities are proportional then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 10 when x = 6
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] x ← equation of proportion
When x = 15, then
y = [tex]\frac{5}{3}[/tex] × 15 = 5 × 5 = 25
What is 2/20 + 10/75
[tex]\text{Hey there!}[/tex]
[tex]\text{What is }\dfrac{2}{20}+\dfrac{10}{75}[/tex]
[tex]\text{For the LCD (Lowest Common Denominator) it should be equal to 300}[/tex]
[tex]\dfrac{2\times15}{20\times15}+\dfrac{10\times4}{75\times4}[/tex]
[tex]\bf{2\times15=30}\\\bf{20\times15=300}\\\\\bf{10\times4=40}\\\bf{75\times4=300}[/tex]
[tex]\text{Your new equation}\rightarrow\dfrac{30}{300}+\dfrac{40}{300}[/tex]
[tex]\text{With the denominators being alike we can leave the same}[/tex]
[tex]\text{New equation}\rightarrow\dfrac{30+40}{300}[/tex]
[tex]\text{30 + 40 = 70}[/tex]
[tex]\text{New equation}\rightarrow\dfrac{70}{100}[/tex]
[tex]\text{Since both of the terms have 10 in their like terms, let's divide both sides by it}[/tex]
[tex]\dfrac{70\div10}{300\div10}[/tex]
[tex]\bf{70\div10=7}[/tex] [tex]\leftarrow\text{Your numerator}[/tex]
[tex]\bf{300\div10=30}[/tex] [tex]\leftarrow\text{Your denominator}[/tex]
[tex]\boxed{\bf{Thus,\ your\ answer\ should\ be:\dfrac{7}{30}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
[tex]\frak{LoveYourselfFirst:)}[/tex]
What is the simplest form of RootIndex 3 StartRoot 27 a cubed b Superscript 7 Baseline EndRoot?
Answer: [tex]3a\sqrt[3]{b^{7}}[/tex]
Step-by-step explanation:
We have the following expression:
[tex]\sqrt[3]{27 a^{3} b^{7}}[/tex]
This can be rearranged as:
[tex]\sqrt[3]{27} \sqrt[3]{a^{3}} \sqrt[3]{b^{7}}[/tex]
Since [tex]\sqrt[3]{27}=3[/tex] and [tex]\sqrt[3]{a^{3}}=a[/tex] we have:
[tex]3a\sqrt[3]{b^{7}}[/tex] This is the simplest form
Answer:
3ab^2 (^3sqrt{ b}) or A on Edg. 2020
Step-by-step explanation:
x/3 = 14 whats the answer
Answer: x = 42
Step-by-step explanation:
Step 1 :
x
Simplify —
3
Equation at the end of step 1 :
x
— - 14 = 0
3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
14 14 • 3
14 = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x - (14 • 3) x - 42
———————————— = ——————
3 3
Equation at the end of step 2 :
x - 42
—————— = 0
3
Step 3 :
When a fraction equals zero :
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
x-42
———— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
x-42 = 0
Solving a Single Variable Equation :
3.2 Solve : x-42 = 0
Add 42 to both sides of the equation :
x = 42
Your answer: x = 42
Answer:
42
Step-by-step explanation:
x / 3 = 14.
The question required you to solve for x.
First, multiply both the LHS and the RHS by 3. The aim is to make x independent.
x/3 * 3 = 14 * 3
Therefore:
x = 42
What value of x is in the solution set of 4x – 12 ≤ 16 + 8x?
Answer:
4x – 12 ≤ 16 + 8x; x>-7
Step-by-step explanation:
i dont remember how i did it
Answer:
x≥-7
Hope this helps
Which absolute value expression represents the distance between 3 and
9
2
on a number line?
A) |3 −
9
2
|
B) |3 − (−
9
2
)|
C) |−3 + (−
9
2
)|
D) |−3 −
9
2
)|
From other source on the internet this question is:
Which absolute value expression represents the distance between 3 and - 2 on a number line?
Answer:
|3 - (-2) |, or|-2 - 3|Both are equivalent.
Explanation:
The distance between two numbers in a number line is the absolute value of the difference between the two numbers.
Thus, the distance between a number x and a number y is |x - y|, which is also equivalent to |y - x|.
In this case the distance between 3 and - 2 can be represented by either of the expressions:
|3 - (-2) |, or|-2 - 3|Note that when you simplify them you get the same value:
|3 - (-2) | = |3 + 2| = |5| = 5|-2 - 3| = | -5| = 5Answer:
The distance between 3 and
9
2
on a number line is |3 −
9
2
|. The distance between two numbers is equal to the absolute value of their difference.
|3 −
9
2
| = |−
3
2
| =
3
2
Step-by-step explanation:
so the answer is A
1) 6x + 5y = -6
y = 2x – 14
log2 (32) =
Answer this
Answer: 5
Step-by-step explanation:
[tex]log_{2}[/tex] 32
32 can be written in index form as 2x2x2x2x2 , which could be written as [tex]2^{5}[/tex].
[tex]log_{2}[/tex] 32 the becomes
[tex]log_{2}[/tex] [tex]2^{5}[/tex]
Which could be written as
5 [tex]log_{2}[/tex] 2
From law of logarithms; [tex]log_{2}[/tex] 2 = 1
Therefore : 5 [tex]log_{2}[/tex] 2 = 5 x 1 = 5
17•blank=1. As a fraction ASAP pls
the answer for this question is:
1/17
please help me with #4
The chances of it being less than 5 is 4/6
So if he spins it 150 times the chances of it landing on 5 or less than it will be: 4/6 * 150 = 100 (c)
Answer:
i think its c 100
Step-by-step explanation:
sorry if it makes no sense
Need help with question number 13. Can’t figure it out.
Answer:
least common multiple
Step-by-step explanation:
Find the lcm of the given numbers, do you know how to do that?
Alright, so you're looking for the GCF.
Greatest Common Factor
I don't wanna go into detail of what that is (if you don't already know what it is, please watch a video on what it is and how to find it.)
Our numbers are 18, 36, 54
What is the gcf of these numbers? They all are both divisble by 18 and that's the largest 18 can go, so 18 is the GCF.
18 is the answer.
Are 8÷2 and 2÷8 equivalent
No they are not.
8÷2=4
2÷8=0.25
find one terminating decimal and one repeating decimal between -1 1/2 and -1 7/9
Answer:
-1.777...
Step-by-step explanation:
Using the LCM of 18 for the denominator, these values are:
-1 7/9 -1 1/2
-32/18 -27/18 0
--------------|-------------------|-------------------------------------|-----------
So, the easy values to identify are: -31/18, -30/18, -29/18, and -28/18
All of these numbers have repeating decimals (because 9 is a factor of the denominator).
Now, you may realize that -1 3/4 is within the range specified.
-1 7/9 -1 1/2
-32/18 -27/18 0
--------------|-------------------|-------------------------------------|-----------
|
-1 3/4
-1.75
This is because -1.75 is between -1.5 and -1.7777.... Note that it is not repeating.
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Jackie says that the fraction 7/8 is equivalent to 3/4. Is she right? Explain
Answer:
Jackie is incorrect.
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] [tex]\left {x2} \atop {x2}} \right.[/tex] = [tex]\frac{6}{8}[/tex]
[tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex] not [tex]\frac{7}{8}[/tex]
Jackie is mistaken when she claims that the fraction 7/8 is equal to 3/4. We compare the numerator (the top number) and denominator (the bottom number) of two fractions to see if they are equal.
In this instance, 3/4 has a denominator of 3 and a numerator of 4, whereas 7/8 has a numerator of 7 and a denominator of 8, respectively. The fractions cannot be equal since the numerators and denominators vary.
Two fractions must have the same numerator to denominator ratio in order for them to be equal. In this situation, 7/8 is a bigger fraction than 3/4. Jackie's assertion that 7/8 is comparable to 3/4 is therefore false.
To know more about Fraction :
https://brainly.com/question/10354322
#SPJ1.
i go backwards 8m in 4s what is my velocity
Answer:2m/s
Step-by-step explanation:
Velocity=distance÷time
Velocity=8÷4
Velocity=2m/s
One of two or more Expressions that are multiplied together to get a product
Answer:
factor
Step-by-step explanation:
We assume this is a vocabulary question and you want the word that has the definition you have supplied.
Such an expression is called a factor.
Eduardo has 45 yards of rupe light.
Exactly how many more yards does he need to finish the car's ceiling?
Item
Length of Rope Light (yds)
Front spoiler
Rear spoiler
Ceiling
DONE
Naimmis
Dashboard
What is the fraction
Answer: 2 1/6
Step-by-step explanation:
Because the denominators are different, and there are whole numbers involved, then first make the fractions improper.
4 1/2 -> 9/2
6 2/3 -> 20/3
Next, make the denominators the same by multiplying each fraction by the denominator of the other.
9/2 * 3 = 27/6
20/3 * 2 = 40/6
Then you can subtract the numerators because the denominators are the same:
40/6-27/6= 13/6
Then you can convert to a mixed fraction if need be.
|6 3/8-2|+|-8 5/8+(-1)|
To answer the question, we evaluated two absolute value expressions individually by converting mixed numbers to improper fractions, performing the operations, and taking absolute values. The sum of these evaluations is 14.
The question involves evaluating two absolute value expressions and adding the results. We will work through each expression step by step.
First Expression
|6 3/8 - 2|
To solve this, convert the mixed number to an improper fraction, subtract 2, and then find the absolute value.
Convert 6 3/8 to an improper fraction: (6 × 8) + 3 = 51/8.
Subtract 2 (written as 16/8) from 51/8: 51/8 - 16/8 = 35/8.
The absolute value of 35/8 is 35/8, as it is already positive.
Second Expression
|-8 5/8 + (-1)|
Similar approach: convert to an improper fraction, add -1, and find the absolute value.
Convert -8 5/8 to an improper fraction: (-8 × 8) - 5 = -69/8.
Add -1 (written as -8/8) to -69/8: -69/8 - 8/8 = -77/8.
The absolute value of -77/8 is 77/8, as we discard the negative sign in absolute value operations.
Add the results of both expressions: 35/8 + 77/8 = 112/8 = 14.
24 cupcakes for 168$ what is unit rate
Answer:
$7 per cupcake
Step-by-step explanation:
A unit rate is the cost of one item. So we would do $168 divided by twenty-four. That would be equivalent to seven.
write and solve the differential equation that models the following statment. "the rate if change of W with respect to x is proportional to x+18."
Answer:
[tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.
Step-by-step explanation:
i)it is given that the rate of change of W with respect to x is proportional to
x + 18. Therefore [tex]\frac{dW}{dx}[/tex] = k(x + 18) where k is a constant.
ii) Therefore [tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.
iii) the complete solution can only be found if we know the constant of proportion and also the constant of integration.
What is the solution to this system of linear equations? Y-x=6 y+x=-10 (-2,-8) (-8,-2) (6,-10) (-10,6)
Answer:
x=-8, y=-2. (-8, -2).
Step-by-step explanation:
y-x=6
y+x=-10
--------------
2y=-4
y=-4/2=-2
-2-x=6
x=-2-6=-8
Answer:
x=-8, y=-2. (-8, -2).
Step-by-step explanation:
What is 3(n+1)= 3+1=4
Answer:
n = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
3(n+1) = 4
distributive property means multiply every term in the parentheses by the number on the left and add the new terms.
(3*n) + (3*1) = 4
3n + 3 = 4
-3 -3 subtract 3 from both sides.
3n = 1
/3 /3 divide by 3 on both sides.
n = [tex]\frac{1}{3}[/tex]
Pacho starts saving for college by opening a savings account and depositing $50. He plans to make a deposit every month to continue saving. The amount of money in Pacho's savings account can be modeled by the sequence A0=50, An=An−1 + 25, where n is the number of months since his initial deposit. Is the sequence An a function? Why or why not?
The sequence is a function
Step-by-step explanation:
The sequence is given as;
[tex]A_n=A_n-1 +25[/tex]
where n is the number of months since his initial deposits, and A₀=50
The sequence is a function because its domain is a set of natural numbers.
For example,
A₁=A₀+25 =75
A₂=A₁+25=100
A₃=A₂+25=125
A₄=A₃+25=150
Learn More
Sequence:https://brainly.com/question/14005212
Keywords : saving, college, depositing, amount, money, modeled, sequence
#LearnwithBrainly
Answer:
Yes, because for each input value, , there is only one possible output value.
Step-by-step explanation:
i just did it on IM
which of the following are solutions to this equation 3n+4=24-n a) n=1 b) n=3 c) n=5 d) n=7
Answer:
The correct option is c) n=5.
Therefore the solution to
[tex]3n+4=24-n[/tex]
is
[tex]n=5[/tex]
Step-by-step explanation:
Given:
[tex]3n+4=24-n[/tex]
To Find;
n = ?
Solution:
[tex]3n+4=24-n[/tex] ........Given
Add + n to both the side
[tex]3n+4+ n=24-n+n\\4n+4=24[/tex]
Now Subtract 4 on both the side
[tex]4n+4-4=24-4\\4n=20[/tex]
Dividing by 4 on both side
[tex]\dfrac{4n}{4}=\dfrac{20}{4}\\\\n=5[/tex]
Therefore the solution to
[tex]3n+4=24-n[/tex]
is
[tex]n=5[/tex]
On average, seawater in the world oceans has a salinity of about 3.5%.
How much seawater need to have evaporated to leave 100g salt?
Find it in Grams
i suppose that 3.5% means every 100g of water there is 3.5g if salt...so...
3.5g ->100g
1g ->100/3.5
100g->(100/3.5)*100
=10000/3.5
2857.1428g
=2.857kg
Answer:
3.5 grams
Step-by-step explanation:
100g x 3.5% = 3.5 grams
I need help on this problem( picture included)
hmmm first off, let's convert the decimal to a fraction, and then the mixed fraction to an improper fraction and proceed from there.
[tex]\bf 6.\underline{2}\implies \cfrac{62}{1\underline{0}}\implies \cfrac{31}{5}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ 6.2\div (2x+1)=2\frac{1}{3}\div 4\implies \cfrac{31}{5}\div (2x+1) = \cfrac{7}{3}\div 4[/tex]
[tex]\bf \cfrac{31}{5}\div \cfrac{(2x+1)}{1} = \cfrac{7}{3}\div \cfrac{4}{1}\implies \cfrac{31}{5}\cdot \cfrac{1}{(2x+1)} = \cfrac{7}{3}\cdot \cfrac{1}{4}\implies \cfrac{31}{5(2x+1)}=\cfrac{7}{12} \\\\\\ \cfrac{31}{10x+5}=\cfrac{7}{12}\implies \stackrel{\textit{cross multipling}}{372 = 7(10x+5)}\implies 372=70x+35\implies 337=70x \\\\\\ \cfrac{337}{70}=x\implies 4\frac{57}{70}=x\implies 4.81\approx x[/tex]
Create a proportional ratio
to the given ratio
1/8 = ?
Answer:
Step-by-step explanation: 2:16 because Proportion is a mathematical concept, which states the equality of two ratios or fractions. meaning it's kind of like equivalent fractions and if you times 1/8 times 2 you get 2/16 and all you do is turn it into a ratio