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Explanation:
If g(x) is the inverse of f(x), and vice versa, then we have these two properties:
f(g(x)) = xg(f(x)) = xSince we want to find a function that is its own inverse, we want f(x) and g(x) to be the same function.
Through trial and error, you should find that f(x) = g(x) = x fit the description.
f(x) = x
f( g(x) ) = g(x) ... replace every x with g(x)
f( g(x) ) = x
You should find that g(f(x)) = x as well.
One possible answer is f(x) = x
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Through more trial and error, you should find that f(x) = g(x) = 1/x works as well. In fact, anything of the form f(x) = g(x) = k/x will work.
The proof can be written as follows
f(x) = k/x
f( g(x) ) = k/( g(x) )
f( g(x) ) = k/( k/x )
f( g(x) ) = (k/1) divide (k/x)
f( g(x) ) = (k/1) * (x/k)
f( g(x) ) = x
Through similar steps, you should find that g(f(x)) = x is the case also.
This proves that f(x) = k/x is its own inverse, where k is a real number constant.
Another possible answer is anything of the form f(x) = k/x
If we pick k = 3, then we get f(x) = 3/x which is the answer I wrote above.
You can pick any k value you want.
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There may be other types of functions that have this property, but I'm blanking on what they might be.
determine if 5yx - 17xy are like terms
Step-by-step explanation:
yes they are because they have the same variables which are X& Y
Answer:
5yx-7xy
they are like terms, it's all multiplication just a different arrangement
5xy-7xy=-2xy
Step-by-step explanation:
hope this is helpful
HELP SOMEONE PLEASE!!!!!!!!!!!!!!!!!!!
Answer:
3/10
Step-by-step explanation:
The question asks for the probability of finding 4 or more, so first, you must add up all of the teenagers that have 4 or more shoes. Both the 4 and 5 categories fit, so add 20 and 10. Then, find the total number of people in the sample size. Overall, 100 teenagers are represented. Finally, put the number of people that have 4 or more shoes, 30, over the sample size, 100. This equals 30/100 which should be simplified to 3/10.
The sum of 9 and a number is less than 12. Which of the following
inequalities expresses the solution?
Answer:
9+x<12
Step-by-step explanation:
add 9 to an unknown number.
9+x
use the < less than symbol (instead of an equal sign) and write 12.
Answer:
x + 9 < 12
Step-by-step explanation:
Let the unknown number = x
Sum of 9 and x : x + 9
x + 9 < 12
factor completely 8y2 + 6y + 1
Answer:
Step-by-step explanation:
8y²+6y+1
=8y²+4y+2y+1
=4y(2y+1)+1(2y+1)
=(2y+1)(8y+1)
The equation d = m/v can be used to calculate the density,d, of an object with mass,m, and volume,V. Which is an equivalent equation solver for V?
Answer:
v = m/d
Step-by-step explanation:
since
[tex]d = \frac{m}{v} \: \\ \\ v = \frac{m}{d} [/tex]
If
5
3 cosα = in the first quadrant, what does cot α
equal?
Answer:
5/4
Step-by-step explanation:
To Find :-
cot a .Solution :-
By question ,
=> cos a = 5/3 = b/h
=> p = √ 5² - 3² = √ 25 -9 = 4
Therefore ,
=> cot a = b/p = 5/4
The sum of three consecutive odd numbers is 63. What are the numbers?
Answer:
19, 21 and 23
Step-by-step explanation:
→ Make an algebraic expression for the 3 consecutive numbers
2x + 1, 2x + 3 and 2x + 5
→ Add the expressions together and make it equal to 63
2x + 1 + 2x + 3 + 2x + 5 = 63
→ Simplify
6x + 9 = 63
→ Minus 9 from both sides
6x = 54
→ Divide both sides by 6
x = 9
→ Resubstitute x = 9 into the 3 expressions
x = 9 into 2x + 1 is 19
x = 9 into 2x + 3 is 21
x = 9 into 2x + 5 is 23
what is the value of b in this equation?
A. -20
B. -6
C. 6
D. 20
Answer:
Step-by-step explanation:
a- 12
b- 2
c- 11
and the next part is
x- 6
y- 18
Answer:
B
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex]a^{-m}[/tex] = [tex]\frac{1}{m}[/tex]
Then
[tex](y^b)^{4}[/tex] = [tex]\frac{1}{y^{24} }[/tex]
[tex]y^{4b}[/tex] = [tex]y^{-24}[/tex]
Equate the exponents
4b = - 24 ( divide both sides by 4 )
b = - 6 → C
a^2×c^2/c^2×d^2+bc/ad reduce the algebraic
Answer:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Required
Simplify
We have:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Cancel out [tex]c^2[/tex]
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^2}{d^2}+\frac{bc}{ad}[/tex]
Take LCM
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Need help ASAP !!!when creating a question for a survey , the way a question is written:
Answer:
The third one i think
Step-by-step explanation:
Since a survey shouldn't be biased or anything.
plz help me with this math and also explain
Step-by-step explanation:
[1]SI = $250Rate (R) = 12[tex] \sf \dfrac{1}{2}[/tex] %Time (t) = 4 years[tex]\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 \times 100 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { 25000 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { \dfrac{25000}{50} = P } \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ [/tex]
Therefore principal is $500.
__________________[2]2/7 of the balls are red.3/5 of the balls are blue.Rest are yellow.Number of yellow balls = 36Let the total number of balls be x.
→ Red balls + Blue balls + Yellow balls = Total number of balls
[tex]\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ 31x + 1260= 35x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 35x-31x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 4x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ [/tex]
Total number of balls is 315.
A/Q,
3/5 of the balls are blue.
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ [/tex]
Find the value of y
Help please
Answer:
6
Step-by-step explanation:
Set your formula up as
15 = 2y+3
15 - 3 = 2y
12 = 2y
12 / 2 = y
6 = y
The measure of an angle is eight times the measure of its supplementary angle. What is the measure of each angle?
Answer:
160°
Step-by-step explanation:
Let one angle be x
Let second angle be 8x
Sum of supplementary angles = 180°
x+ 8x = 180°
9x = 180
x = 180/9 = 20
First angle= x= 20°
Second angle = 8x = 8*20 = 160°
The polygons are similar, but not necessarily drawn to scale. Find the value of x. PLEASE HELPPPP
Answer:
x = 27.5.
Step-by-step explanation:
There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.
So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.
With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.
Therefore, x = 27.5.
If f(x) = 2x2 + 1, what is f(x) when x = 3?
Answer:
18
Step-by-step explanation:
f(x)=2x(2+1)
f(3)=2(3)(2+1)
=6(2+1)
=12+6
=18
Students were asked to choose their favorite season. If 2/9 of the students
chose spring and 5/9 chose summer, what fraction chose either spring or
summer?
Answer:
7/9
Step-by-step explanation:
2/9+5/9=7/9
Find (a) the mean, (b) the median, and
(c) the mode of the number of verses in
the first eight chapters of Proverbs.
Proverbs 1 23 4 5 6 7 8
Verses 33 22352723352736
(a)
(b)
(c)
Answer:
Mean = 33+ 22+35+27+23+35+27+36 = 238/8 = 29.75
Median = 27+23 = 50/2 = 25
Mode = 35
Range = 36 - 22 = 14
Step-by-step explanation:
Stay Blessed
solve the simultaneous equation: x-y=2
xy=36
Answer:
Y= –7.08, 5.08
Step-by-step explanation:
hope ya ready bro.
X=36/Y
replace 36/y instead of X
36/Y–Y=2===> 36–Y²=2Y===> Y²+2Y–36=0
Y1= –1+√37≈ –7.08
Y2= –1–√37≈ 5.08
Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3.4%/year. At the end of the year, he earned simpler interest of $413. How much did he invest at 5%/year?
Answer:
$4,562.5
Step-by-step explanation:
The amount Arvin has to invest, P = $10,000
The interest paid on the investment in the term deposit = 5%/year
The interest paid om the investment in Canada savings bonds = 3.4%/year
The amount Arvin earned at the of the year as simple interest, A = $413
Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations
x + y = 10,000...(1)
0.05·x + 0.034·y = 413...(2)
Making y the subject of equation (1) and substituting the value in equation (2), we get;
From equation (1), we get, y = 10,000 - x
Plugging the above value of y in equation (2) gives;
0.05·x + 0.034 × (10,000 - x) = 413
∴ 0.05·x - 0.034·x + 340 = 413
x = (413 - 340)/(0.05 - 0.034) = 4,562.5
Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5
(y = 10,000 - x
∴ y = 10,000 - 4,562.5 = 5,437.5
The amount Arvin invested in Canada savings bonds, y = $5,437.5.)
I would raise it to 1grand but I’m very broke
Answer:
ITS A LOL
Step-by-step explanation:
[tex]solve : - \\ \\ (4 {}^{2} + 5 {}^{2} ) = {?}[/tex]
Step-by-step explanation:
4² = 16
5² = 25
16+25 = 41
41 is the answer.
Hope it helps! :)
Answer:
[tex]( {4}^{2} + {5}^{2} ) \\ (16 + 25) \\ = 41[/tex]
Does anyone know the answer to this question?
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer:
Ji Gud afternoon.
I'm fine
what about you madam.
Hope u r fine and stay safe and healthy
Solve for x. Round to the nearest tenth, if necessary.
Answer:
25.5402665394
Step-by-step explanation:
x=24/cos(20) = 25.54026653942
How do I solve for X HELP
Answer:
x = 4 degrees
Step-by-step explanation:
The two angles have the same measurement. They are opposite angles.
26x + 7 = 31x - 13
Group like terms:
26x - 31x = -13 - 7
-5x = -20
x = 4
Check if you want to make sure.
Step-by-step explanation:
[tex]here \: is \: your \: solution : - \\ \\ both \: angles \: are \: equal \: (vertical \: anges) \\ \\ 26x + 7 = 31x - 13 \\ \\ solving \: the \: equation \: \\ \\ 26x - 31x = - 13 - 7 \\ \\ - 5x = 20 \\ \\ x = -20 \div 5 \\ \\ x = \: 4 \: degrees \: \: \: \:(Answer ✓✓✓( \\ \\ \huge\mathcal\blue{happy \: life (. ❛ ᴗ ❛.) }[/tex]
if u help me i will give you brainliest <3
Answer:
a) 6
b) 12:35 ( not so sure about this one)
Step-by-step explanation:
a)
distance = speed * time
ruths distance = 4* 1.5 (because it takes her 1h 30 mins)
distance = 6miles
b) 1/4 here is quarter so, 15mins
10:30 and then add 50 mins to that.
she leaves at 11:20 and takes 1h and 15 mins ( 75mins) to walk home
so 11:20 + 1h 15min
= 12:35
hope this helps :)
Answer:
a) 6 miles
b) 12:35 pm
Step-by-step explanation:
a) 9 am to 10:30 am = 1 hour and 30 mins = 1.5 hours
4mph x 1.5 = 6miles
b) 10:30 am + 50 mins = 11:20 am
1 hour = 60 mins
60/4 = 15 mins
1 1/4 = 1 hour 15 mins
11:20 am + 1 hour 15 mins = 12:35 pm
Draw graph for equation 0.25x+0.50y<3
i13(12)-2give answer
a 10 foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle betwween the top of the ladder and the wall changing when that angle is
Answer:
d∅/dt = √2/5 Rad/sec
Step-by-step explanation:
According to the Question,
Given That, a 10-foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle between the top of the ladder and the wall changing when that angle is π/4.Solution,
Let x be the Distance between the base of the wall and the bottom of the ladder.
and let ∅ be the angle between the top of the ladder and the wall.
Then, Sin∅ =x/10 so, x=sin∅ *10
Differentiating with respect to time t we get,
dx/dt = 10 * cos∅ * d∅ /dt
We have given that dx/dt = 2 ft/s and ∅ =π/4Now, Put these value we get
2 = 10 *(cos(π/4))* d∅/dt
2 = 10/√2 * d∅/dt
d∅/dt = √2/5 Rad/sec
A ABC has vertices A (-7, -13), B (12, -8), and C(-17, 19). Which of the following represents the
reflection of AABC across the line y = x and its rotation of 90° about the origin?
Answer:
brainliest and 20 points! Which best explains whether or not ΔABC ≅ ΔLMN? The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN. The figures are congruent because a 90 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN. The figures are not congruent because point B corresponds with point N and point C corresponds with point M. The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.
Step-by-step explanation:
it's is the answr