PLEASE HELP A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.
Answers
Answer:
Part A : see composition process below
Part B : [tex]Domain=\{x\,|\,x\neq 0\}[/tex]
Step-by-step explanation:
Part A
Let's use the composition of functions to find if they give the identity : [tex]f(g(x))=x[/tex] thus proving they are the inverses of each other:
[tex]f(g(x))=f(\frac{5x+1}{x} )=\frac{1}{\frac{5x+1}{x}-5} =\frac{1}{\frac{5x+1-5x}{x}} =\frac{1}{\frac{1}{x} } =x[/tex]
So we have proved they are the inverses of each other.
Part B
Given that the composition is:
[tex]f(g(x))=\frac{1}{\frac{1}{x} }[/tex]
the Domain must exclude x=0, for which this quotient is undefined.
The Domain is then:
[tex]Domain=\{x\,|\,x\neq 0\}[/tex]
Related Questions
If you have a problem that has multiple variables, you can solve it using a
system of equations. Think of a real-world example where you would need
to solve using a system of equations. Write two or three sentences
describing your example. Include the equations in your description, but do
not solve the system. That will be left to your classmates. helppppp
Answers
Step-by-step explanation:
two times of a number added to 18 gives 70
what is value of X.
2x + 18 = 70
2x = 52
X = 26 is answer
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The system of equations representing the described condition will be [tex]x+y=15\;and \;2x+4y=40[/tex].
A variety of problems can be solved using the system of equations.
Consider a simple problem of purchasing notebooks and pens from the market.
You bought some pens at $2 per pen and some notebooks at $4 per notebook from the market. At the end of shopping, you have spent $40 and you got 15 objects in your bag.
Write the given situation in the form of equations.
Let x be the number of pens bought and y be the number of notebooks bought.
So, the equations can be made as,
[tex]x+y=15\\2x+4y=40[/tex]
Therefore, the system of equations representing the described condition will be [tex]x+y=15\;and \;2x+4y=40[/tex].
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Find the measure of a A. 44 B. 88 C. 46 D. 90
Answers
====================================================
Explanation:
Since we have a circle, the segments extending from the center outward to the edge of the circle are radius segments. Any two radii of the same circle are the same length. The triangle on the left with the 92 degree angle is isosceles. Any isosceles triangle has exactly two side lengths that are the same, which leads to the base angles being the same as well.
For the triangle on the left with angles a,b,92, the base angles are 'a' and 'b'. So a = b.
For any triangle, the angles add to 180
a+b+92 = 180
a+a+92 = 180 ... Replace b with 'a'
2a+92 = 180
2a = 180-92
2a = 88
a = 88/2
a = 44
angle b is also 44 as well
a+b+92 = 44+44+92 = 180
A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches. What is the length of the base of the triangle? A. 17.5 in. B. 35 in. C. 42.7 in. D. 56 in. Please include all work.
Answers
Answer:
A. 17.5 in.
Step-by-step explanation:
The formula for the area of a triangle is 1/2 * (b * h), where h represents the height and b represents the base. We can solve from reverse using area/height = base*2
369.25/42.2 = 8.75
1/2base = 8.75
base = 8.75 * 2
base = 17.5
Answer:
369.25/42.2 = 8.75
1/2base = 8.75
base = 8.75 * 2
base = 17.5
hope I helped you
A is plotted on a coordinate grid at start bracket 3 and 1 over 2, negative 1 end bracket.. Choose the correct grid that best shows the location of the point. A coordinate grid that shows a point located 4 units to the left and 1 unit down from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the right and 1 unit down from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the left and 1 unit up from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the right and 1 unit up from the origin.
Answers
Answer:
im so sorry for the other answer i reported it and im gonna help with this question because i have the same question on my test.
ok so i got C it makes the most sense to me but if im wrong then ill delete this.
If im correct please mark me as brainliest
Step-by-step explanation:
yes this is wrong but i cant delete it so just ignore it
Answer:
B 3 1/2 to the right and one unit down
Step-by-step explanation:
Easy question
I need the answers only for (d) and (e) parts.
plz help
will give the brainliest
Need explanation.
Please answer correctly.
Answers
Answer:
d)33
e)80
Step-by-step explanation:
I'm sorry I don't really know how to explain this.
If for [tex] x[/tex] cumulative frequency the marks are $y$ (as given on the graph), we have $x$ students with marks equal to or less than $y$
d)
Total students are $140$. Hence three-fifths of that is $140\times \frac{3}{5}=84$. Find the marks at $84$ in the graph for the passing marks.
e)
From the graph we have $60$ students having less than or equal to $30$ marks. Total students are $140$.
Subtracting, $140-60=80$ we get the numbee of students achieving more than 30 marks.
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
Answers
Answer:
x=127°
Step-by-step explanation:First you have to solve for n and to do so you have to add the interior angles together and equal them to the remote exterior angle.
n+7+6n+22=197-5n
12n+29=197
12n=168
n-14
once you get n you have to plug it into 197-5n
197-5(14)
197-70
127
The required value of exterior angle m∠x is 127.
From figure x is remote exterior angle m∠x=(197−5n)°. and y and z are interior angles m∠y=(6n+22)° and m∠z=(n+7)° respectively. value of x to be determine.
Angle made at outer side of the corner is called exterior angles.
Here, by properties, sum of the interior angle = remoter exterior angle
So,
m∠x = m∠y + m∠z
197−5n = 6n+22+n+7
168 = 12n
n = 14
put n in m∠x
m∠x=(197−5n)°
m∠x=(197−5*14)°
m∠x=(197−70)°
m∠x=127°
Thus, the required value of exterior angle m∠x is 127.
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What is 3 divided by 2,127
Answers
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[tex]3\ \div \ 2127[/tex]
[tex]= \frac{1}{709}[/tex] (Decimal: 0.00141)
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If this helped you, could you maybe give brainliest..?
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Which of the following are exterior angles? Check all that apply.
6
52
3
O A. 21
O B. 25
O c. 24
O D. 23
E. 22
O F. 26
Answers
Using it's concept, it is found that the exterior angles of the triangle are given as follows:
B. <5
C. <4
What are the exterior angles of a triangle?The exterior angles of a triangle are the angles that are outside the triangle.
In this problem, the angles are 4 and 5, which means that options B and C are correct.
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How is 30% equivalent to 1.3?
Answers
Answer:
30% = 30/100 = 0.3
1.3 would be 130%
I hope this helps you!
30% is equivalent to 0.30 or 3/10, but not 1.3.
There seems to be an error in the statement that 30% is equivalent to 1.3. That is not correct.
To clarify, 30% is equivalent to the decimal value 0.30 or the fraction 3/10.
To convert a percentage to a decimal, we divide the percentage value by 100. In this case, 30 divided by 100 equals 0.30.
If you were looking for a value that represents a 30% increase or an amount including a 30% addition, you would multiply the original value by 1.3, not 30%. For example, if you have a value of $100 and want to increase it by 30%, you would multiply $100 by 1.3, resulting in $130.
So, 30% is equivalent to 0.30 or 3/10, but not 1.3.
Learn more about percentage here
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Find the distance between the points P and Q shown. Question 6 options: A. 73−−√ B. 13−−√ C. 5–√ D. 65−−√
Answers
Answer:
[tex]d=\sqrt{73}[/tex]
Step-by-step explanation:
[tex]Q(5, -1)[/tex]
[tex]P(-3, 2)[/tex]
Using the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_2+y_1)^2}[/tex]
[tex]d=\sqrt{(-3-5)^2+(2-(-1))^2}[/tex]
[tex]d=\sqrt{(-8)^2+(3)^2}[/tex]
[tex]d=\sqrt{64+9}[/tex]
[tex]d=\sqrt{64+9}[/tex]
[tex]d=\sqrt{73}[/tex]
[tex]d\approx 8.5[/tex]
22% of $900 = twenty two percent of $900 =
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
$198
▹ Step-by-Step Explanation
[tex]\frac{22}{100} * 900\\\\\frac{22}{1} * 9 = \frac{198}{1} \\\\= 198[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
198
Step-by-step explanation:
22% of 900
22% * 900
Change to decimal form
.22 * 900
198
Plzz help I’ll mark brainliest
Answers
Answer:
c
Step-by-step explanation:
the correct answer is c
plz mark me brainliest
WILL GIVE BRAINLY PLEASE HELP!!!!A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
x2 – 99 = 0
x2 – 99x = 0
x2 + 5x + 104 = 0
x2 + 5x – 104 = 0
Answers
Answer: x2 + 5x – 104 = 0
Step-by-step explanation:
Distribute the x into the x + 5 to make it x2 + 5xSubtract 104 from the other side to set the equation equal to zeroFinal answer is x2 + 5x – 104 = 0if alan had bought a figure at a discount of 5%, he would pay $20 less. How much would he pay if he had bought it at a discount of 20%
Answers
Answer:
80
Step-by-step explanation:
5%-->20% is increased by x4, therefore you multiply 20 by 4 which is 80 or you can set an proportion
5/20=20/x5x=400x=80The first step in solving this is hidden in the sentence “discount of 5%, he would pay $20 less”. This informs us that 5% of the price and $20 are the same
Our next step is to find how much 100% of the price is
Multiplying 5 and 20 gets us 100, so multiplying 5% by 20 will get us 100%
We already know that 5% is $20, so we can multiply $20 by 20 to get to 100% percent of the price
(20*20=400)
Now that we know the total price, we can find a discount of any percent. Since we know that a five percent discount will give you $20 dollars off, we can deduce that a 20% discount will give us $80 off.
(20/5=4)
(4*20=80)
(400-80=320!)
Hopefully this helps, if you need me to explain anything again I’ll try my best!
The parallelogram shown below has an area of 120 units^2 . Find the missing height.
Answers
Answer:
Step-by-step explanation:
133
Math Question (10 Points):
Answers
Answer:
A
Step-by-step explanation:
Becuase It expands the (2+4)8=2*8+8*4=6*8=48
Hope this helps! <3
TELL ME THE FORMULA FOR VOLUME AND SURFACE AREA OF PRISMS
Answers
Answer:
surfacevolume = 1/2 (bh) l
surfacearea = bh + pl
The graph of f(x) = xx is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
Answers
Answer:C and F are correct
Step-by-step explanation:
got it right on edge
Find RS. A. 5 B. 10 C. 9 D. 12
Answers
Answer:
x=9
Step-by-step explanation:
PQ + QR + RS = PS
2x-6 + 1 + x-4 = 18
Combine like terms
3x -9 = 18
Add 9 to each side
3x-9+9= 18-9
3x = 27
Divide by 3
3x/3 = 27/3
x = 9
Answer:
RS=5
Step-by-step explanation:
solve for x:
2x-6+1+x-4 = 18
combine like terms
3x-9=18
subtract both sides to make x isolated
3x=27
divide by 3 to get x
x=9
RS=x-4
RS=9-4
RS=5
simplify (45) - (+14)
Answers
Answer:
31
Step-by-step explanation:
(45) - (+14)
45 - 14 (Negative sign is distributed)
=31
Cause 45 -14 =31
Which is a Qualitative graph?
Answers
Answer:
No qualitative graph shown here.
Step-by-step explanation:
No qualititative graph is shown here. The given graph is quantitative, as it involves numerical measures.
Answer:
qualitative graph are graph that are used to represent situation that do not necessarily have numerial value it repressent the essential elements of a situation in a graphical form
What is the value of the expression in the image? A. 216 B. 224 C. 666 D. 678
Answers
Answer:
C. 666
Step-by-step explanation:
USING PEMDAS we can solve this problem.
[tex]675-(15-12)^3 / 3\\15-12=3\\675-(3)^3/3\\675-27/3\\675-9=666[/tex]
Answer:
666
Step-by-step explanation:
Following Order of Operations rules (PEMDAS), we must do first any operations that appear inside parentheses. Here (15 - 12) = (3).
Next we must perform any exponentiation. Here we have 3^3 = 27.
Then we have 675 - 27 / 3, or 666 (Answer C)
PLS HELP ME I NEED THIS FOR HOMEWORK!!!!
Answers
Answer:
36 degrees
Step-by-step explanation:
Because it's a right angle, AOB and BOC are complementary, meaning they add up to 90 degrees.
(3x+30)+(6x-12)=90
9x+18=90
9x=72
x=8
AOB = 6x-12, so substituting
8 in for x gives us 48-12=36
Simplify
-
12 – 81 – 9
5.12
- 451
Answers
Answer:
-615.12
Step-by-step explanation:
hope this helps
plz mark as brainliest!!
Can check using a calculator
PLEASE HELP ME!!!!!!!!!!!!
Answers
Answer:
1. 4, 4, 6, 8
2. 5, 11, 3, 1
3. 11, 27, 111
4. [tex]16\sqrt{14}-31[/tex]
5. [tex]20\sqrt{2}-56[/tex]
Step-by-step explanation:
For the tables remember that after you solve any negative number will turn positive
For 4-5 just plug in what is in the parenthesis into x and solve
2. 5,11,3,1
3. 11, 27, 111
__
4. 16\|14 -31
___
5. 20\|2 - 56
A power line stretches down a 400-foot country road. A pole is to be put at each end of the road, and 1 in the midpoint of the wire. How far apart is the center pole from the left-most pole?
Answers
Answer:
200 ft
Step-by-step explanation:
Since the road is 400 ft, the midpoint of the road is 200 ft from each end of the road.
Jason’s budget is shown in the circle graph below. His total monthly budget is $3,000. How much does Jason spend on groceries? A. $25 B. $150 C.$450 D.$750
Answers
Answer:
D.$750
Step-by-step explanation:
3000 x 0.25 = 750
Answer:
$750
Step-by-step explanation:
First you have to find 2% of the total of $300. To do this you multiply 3000 by .25 to get 750, this is your answer.
I don't understand this question, somebody help
Answers
Answer:
H. 50 sq cm
Step-by-step explanation:
Triangle PSU is an equilateral triangle because each side of it is a radius of semicircle TRP. Also, the radius of semicircle TRP is the short side of the rectangle. So, if the total perimeter of the triangle is 15, each side is 5 cm. So, the short side of the rectangle is 5cm and the long side is 5*2 = 10 cm.
5 * 10 = 50 sq cm
Please help me with this geometry question:((
Answers
Answer:
x = 13
Arc RQ = 180°
Step-by-step explanation:
PEQ is an inscribed angle and the measure of an inscribed angle in a circle is equal to half of the arc it sees.
The perimeter of a circle is always 360° therefore
2 × (5x + 15) + 9x + 17 + 6x - 12 = 25x + 35 = 360°
25x = 360 - 35
25x = 325
x = 13
Since arc RQ is equal to 10x + 30 we replace x with the value we just got
10×13 + 30 = 160°
PLS PLEASE HELP!!!!!!
Evaluate 18 + 4 ÷ 2 − 8. (5 points) 2 8 12 3
Answers
18 + 4 ÷ 2 − 8
Following PEDMAS, divide first:
18 + 2 -8
Now add and subtract to get the final answer:
18+2 = 20
20-8 = 12
The answer is 12
Answer:
12
Step-by-step explanation:
