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 P(x)= x2 + x + 3 and Q(x) = 9x2 - 3, find P(8).
P(8)=D
(Type an integer or a fraction.)
Answers
Clare has 150$ in her bank account. She buys a bike for 200$. What is Clares account balance now?
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount left in the bank account is -$50.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the bank account = $150
Cost of the bike = $200
The amount left in the bank account.
= 150 - 200
= -$50
Thus,
The amount left in the bank account is -$50.
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Please help! Simplify: 3(2x-4y) - 2(4y-x) Thank you!
Answers
Answer:
8x-20y
Step-by-step explanation:
Use the distributive property then add or subtract the terms(like terms)
3(2x-4y)-2(4y-x)
6x-12y-8y+2x
6x+2x-12y-8y
8x-20y
Hope this helps ;) ❤❤❤
Answer:
8x-20y
Step-by-step explanation:
3(2x-4y)-2(4y-x)
6x-12y-8y+2x
6x+2x-12y-8y
8x-12y-8y
8x-20y
Please show ALL work!!!!
Answers
Answer:
[tex]$\boxed{\log _2\left(\frac{zx^2}{y^2} \right) +\log _9(y^4 x^{12})} $[/tex]
Step-by-step explanation:
[tex]\log _2z+2\log _2x+4\log _9y+12\log _9x-2\log _2y[/tex]
We have logarithms in base 2 and 9. Let's rewrite it:
[tex]\log _2z+2\log _2x-2\log _2y+4\log _9y+12\log _9x[/tex]
Remember that:
[tex]\boxed{p\log _bc=\log _b c^p}[/tex]
[tex]\log _2z+\log _2 x^2 -\log _2y^2 +\log _9y^4+\log _9x^{12}[/tex]
Remember the Product Rule:
[tex]\boxed{\log_b(xy)=\log_bx + \log_by}[/tex]
[tex]\log _2(zx^2) -\log _2y^2 +\log _9(y^4 x^{12})[/tex]
Finally, remember the Quotient Rule:
[tex]$\boxed{\log_b\left(\frac{x}{y} \right)=\log_bx - \log_by}$[/tex]
[tex]$\log _2\left(\frac{zx^2}{y^2} \right) +\log _9(y^4 x^{12})$[/tex]
I only know how to get the answer but not explain
Alexander bought a box of crackers at the store. He ate half of the crackers in the box on Monday, and he ate 1/2 of what was left on Tuesday. On Wednesday, he ate 1/3 of what was left after he was finished eating the crackers on Tuesday.
1) What fractional part of the total crackers originally in the box did Alexander
eat on Wednesday?
2) what fractional part of the total crackers originally in the box are left. 3) if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened. (Please help!)
Answers
Answer:
Given the equivocal nature of this question, I will need to draw an assumption: I will assume that Ali ate from the cake and so did Jason — not Ali ate from the cake and Jason ate from Ali’s slice.
With that being said, the first approach is make both of these fractions have a common denominator, so that we can find how much each respective person ate from the total amount of slices. Intuitively, the common denominator is 12
12
, so this must be true:
Ali ate 4/12
4
/
12
of the cake;
Jason ate 3/12
3
/
12
of the cake
Adding these two fractions will give us 7/12
7
/
12
— the total amount eaten. Now, to find the amount left, we need only subtract 7/12
7
/
12
from 12/12
12
/
12
(the total amount of the cake). Doing so will give us
Step-by-step explanation:
1/3 = 4.
1/3 < 1/2
3/3 = 2/2
4 x 3 = 12.
if there were still 4 crackers AFTER eating 1/3 on wednesday, you add 12 + 4 = 16
Simplify.
sin x cot x
Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function.
(please help, no idea how to solve this problem)
Answers
Answer:
cos x
Step-by-step explanation:
sin x = (sin x) / (1) and cot x = (cos x) / (sin x)
Put those fractions next to each other and multiply them out (numerator times numerator, denominator times denominator).
Cancel out the (sin x) in the numerator and denominator
You should be left with just (cos x) / (1), whoch equals just (cos x).
Hope this helps!
My brother said that’s it
What is the product of the complex numbers 8i and 5i? (1 point)
040
402
40
40i
JUST NEED SOME HELP :(
Answers
Answer:
-40
Step-by-step explanation:
8i* 5i
40 i^2
We know that i^2 = -1
40 *-1
-40
Answer:
-40
I hope this helps. i had the same question and it was right
Savannah is currently one more than twice the age of her cat, Selena Gomez. In thirteen years, Savannah will be 1.5 times as old as Selena. What is Savannah's current age?
Answers
Answer:
23 years old
Step-by-step explanation:
Savannah's age = x
Selena's age = y
Right now, x = 2y + 1
In 13 years, x = 1.5y
Here, we must use simultaneous equations to work it out.
x = 2y + 1
x + 13 = 1.5 x (y + 13) --> x + 13 = 1.5y + 1.5 x 13 --> x + 13 = 1.5y + 19.5
x + 13 = 1.5y + 19.5
- 13
x = 1.5y + 6.5
x = 1.5y + 6.5 = 2y + 1
1.5y + 6.5 = 2y + 1
- 1
1.5y + 5.5 = 2y
- 1.5y
5.5 = 0.5y
x 2
11 = y
We know that y = 11
Savannah is currently twice her cat's age plus 1, so...
11 x 2 + 1 = 22 + 1 = 23 years old
Hope this helps!
P.S. If the cat lives 13 more years after this, it will be a very old cat lol :)
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answers
Answer: 24
Step-by-step explanation:
Colleen painted 7 windows, some of which were her mother's.
Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.
If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.
8+7+3+3+3=24
The total windows in the house are 21.
What is an algebraic expression?It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.
In our given problem, the algebraic relation between different members work output and total windows can be expressed as:
Windows painted by colleen and her mother = 7
Windows painted by father = (Windows painted by colleen and her mother + 1)
= (7 + 1) = 8
∴ Windows painted by father = 8
Now, as given,
2 Windows painted by mother = Windows painted by father
∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4
and Windows painted by colleen = 7 - 4 = 3
Colleen and her 2 brothers paint equal windows;
∴ They painted 3 windows each.
The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:
⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21
Hence the total windows in the house are 21.
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Which property is shown by -6 + 0 = -6? A. Commutative Property of Addition B. Identity Property of Addition C. Distributive Property D. Associative Property of Addition
Answers
Answer:
C
Step-by-step explanation:
It is c because you are adding. the 6 and o.
Answer:
Would be C.
Step-by-step explanation:
Just adding the 6 and the 0 basically.
COME ON!! What’s the answer 53 points!
Answers
Answer:
X : -6, 3, 15, -12
Y : 11, 5, -3, 15
Step-by-step explanation:
Hey there!
To find the y values we need to plug the x values into th given equation,
y = -2/3x + 7
-6 ⇒ 11
15 ⇒ -3
Now we have a x value missing to that that we work backwards,
we plug in 15 for y in the given equation,
15 ⇒-12
Hope this helps :)
Step-by-step explanation:
[tex]y = - \frac{2}{3} x + 7[/tex]
Substituting the values of x into the expression we have
For x = - 6[tex]y = - \frac{2 }{3} ( - 6) + 7[/tex]
y = 11 For y = 5Make x the subject
[tex]5 = - \frac{2}{3} x + 7[/tex]
Multiply through by 3
15 = - 2x + 21
-2x = 15 - 21
- 2x = - 6
Divide both sides by - 2
x = 3For x = 15[tex]y = - \frac{2}{3} (15) + 7[/tex]
y = - 10 + 7
y = - 3For y = 15[tex]15 = - \frac{2}{3} x + 7[/tex]
Multiply through by 3
45 = - 2x + 21
- 2x = 45 - 21
- 2x = 24
Divide both sides by - 2
x = - 12Hope this helps you
-15 POINTS PLS HURRY- Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 4.5 cm to 4 cm
Answers
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{9cm}{8cm}}[/tex]
We can disregard the units temporarily to create a ratio for 4.5 to 4:
4.5 is not a whole number- we can convert this number in the ratio to a whole number by multiplying both numbers by 2:
2 · (4.5 : 4) = 9 : 8
Express as a fraction:
[tex]9cm : 8cm = \frac{9cm}{8cm}[/tex]
what is the right answerrrr??
Answers
Answer:
C. Two lines are perpendicular if they have opposite slopes
Step-by-step explanation:
Hey there!
Well 2 lines that are perpendicylar have reciprocal slopes for example,
2 and 1/2 are 2 slopes that are perpendicular.
Hope this helps :)
Figure B is a scaled copy of Figure A.
9
3.6
3.6
9
Figure A
1.2
3
1.2
3
Figure B
What is the scale factor from Figure A to Figure B?
Answers
Answer:
1/3
Step-by-step explanation:
We are going to a small shape from a big shape, so the scale factor must be less than 1.
3 (which is a side on the blue figure) and 9 (a side on the green figure)
3 and 9 are easy numbers (for me...) so 3:9 is smaller than 1.
3:9 simplified is 1:3 = 1/3
so 1/3 is the scale factor.
Let's make sure it's right....
9 * 1/3 (green figure to blue figure) is = 3.
3.6 * 1/3 = 1.2
you can check it yourself on a calculator if you don't believe me
I hope this helps have a great day!!!!
Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews an SRS of 50 of the
175 students living in the dormitory. She finds that 14 think the dorm food is good.
What is the numerical value of the sample proportion p from Tonya's sample? Round to two decimal places if necessary.
p = ?
Answers
Answer: [tex]\hat{p}=0.28[/tex]
Step-by-step explanation:
Given : Tonya interviews an SRS of 50 of the 175 students living in the dormitory.
i.e. Sample size : n= 50
Number of students think the dorm food is good: x = 14
Now , the numerical value of the sample proportion p from Tonya's sample:
[tex]\hat{p}=\dfrac{x}{n}[/tex]
[tex]=\dfrac{14}{50}=0.28[/tex]
Hence, the numerical value of the sample proportion p from Tonya's sample is 0.28.
Clara has a lawn in front of her house as mapped on the coordinate plane. She wants to plant a bed of flowers between the points P and Q. Find the length of the bed of flowers. Question 2 options: A) 2 units B) 7 units C) 13 units D) 8 units
Answers
Answer:
Look Below In the Explanation
Step-by-step explanation:
Point P has coordinates of (4,4) and point Q has coordinates of (4,-4).
Since both points have the same x-coordinates we can subtract point Q's y-coordinate from point P's y-coordinate.
I will set the equation up and try and figure this part by yourself. I hope you learned what to do from previous questions that are very similar to this that I answered.
4 - ( -4) = length of the bed of flowers
Hope that helps and maybe earns a brainliest!
Have a splendid day! :^)
The length of the bed of flowers will be 8 units.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
Clara wants to plant a bed of flowers between the points P and Q.
And, The value of P = (4, 4)
And, The value of Q = (4, - 4)
Now,
Since, Clara wants to plant a bed of flowers between the points P and Q.
And, The value of P = (4, 4)
And, The value of Q = (4, - 4)
Hence, The length of the bed of flowers will be;
PQ = √ (- 4 - 4)² + (4 - 4)²
PQ = √64
PQ = 8 units
Thus, The length of the bed of flowers will be 8 units.
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Look at the graph in the image. 1. What are the coordinates of point P? A. (4,3) B. (4,30) C. (4,90) D. (40,90) 2. What is the independent variable? A. Bike A B. Bike B C. Time D. Distance Please include work!
Answers
Answer:
1.C (4,90) 2.C.Time
Step-by-step explanation:
the answer to number 1 is C because the x coordinate is 4 and the y coordinate is 90. The answer to 2 is c because the independent variable represents x, which is time in this case because it is labeled on the coordinate plane.
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
hello can plzz help me with this question wil mark u brainlest and its for 18 points the file is down below thank u :)
Answers
Answer:
a rectangular prism
Step-by-step explanation:
consists of 6 faces which are rectangles
the graph of y=f(x) is shown below. find all the values of x where f(x)=8
Answers
Answer:
x = 4
Step-by-step explanation:
Find 8 on the y-axis. Draw a horizontal line through y =8. Determine the x value for which the graph intersects this horizontal line y = 8. It is x = 4
The value of x when f(x) = 8 according to the graph is; 4.
According to the graph;
To determine the value of x when f(x) = 8.We must plot a line of the equation; y = 8.
This line of y = 8 results in an horizontal line.The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.Ultimately, the x coordinates of this point is 4 and hence, the value of x when f(x) = 8 is 4.
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Jill has two dimes she is going to use to perform a probability experiment. What is the theoretical probability that at least one of the two coins will turn up
heads?
75%
50%
Answers
Answer:
50%
Step-by-step explanation:
its a 50/50 chance on it landing either heads or tails
A dime has two sides with a 50% chance of landing on either one.
A teacher has 1,425 marbles to divide equally among 9 groups of students to use in an experiment. What is the least number of marbles he could have left after the marbles are distributed?
Answers
Answer:
3
Step-by-step explanation:
Basically we need to find out whats the remainder of 1425 when you divide by 9.
1425/9 = 158 R3
R3 is 3 marbles left, so the answer is 3.
If -1< y< 0, which of the following has the greatest value?
Answers
Answer:
[tex]\boxed{\sf B}[/tex]
Step-by-step explanation:
-1 < y < 0
The value of y is negative.
Let’s take the number -0.5.
(-0.5)² = 0.25
1 - (-0.5) = 1.5
1 + (-0.5) = 0.5
2(-0.5) = -1
The greatest value is 1.5.
The answer is 1 - y.
write the percent as a fraction or mixed number in simpelst form 35% A) 3 1/2 B) 13/20 C) 6 1/2 D) 7/20
Answers
Answer:
7/20
Step-by-step explanation:It is the same thing as .35. So just turn it into fraction and simplify.
Answer:
D) 7/20
Step-by-step explanation:
Divide 35 by 100:
35 / 100 = .35
Convert into a fraction and simplify:
[tex].35=\frac{35}{100}=\frac{35/5}{100/5}=\boxed{\frac{7}{20}}[/tex]
Option D should be the correct answer.
What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.
Answers
Answer:
[tex]x=\pm 7\text{ or } x=\pm i\sqrt{2}[/tex]
Step-by-step explanation:
We have the equation:
[tex]x^4-5x^2-14=0[/tex]
Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:
[tex]u=x^2[/tex]
Then by substitution:
[tex]u^2-5x-14=0[/tex]
Now we can solve normally. Factor:
[tex](u-7)(u+2)=0[/tex]
Zero Product Property:
[tex]u=7\text{ or } u=-2[/tex]
Back-substitute:
[tex]x^2=7\text{ and } x^2=-2[/tex]
Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:
[tex]x=\pm 7\text{ and }x=\sqrt{-2}[/tex]
Therefore, our solutions are:
[tex]x=\pm7\text{ and } x=\pm i\sqrt{2}[/tex]
What is D+26/-17 = - 25
Answers
Answer:
-399/17
Step-by-step explanation:
D+26/-17=-25
D=-25-(-26/17)
D=-25+26/17
D=-425/17+26/17
D=-399/17
The answer is D= -399/17
Veronica wants to buy a house that costs $249,900. She is going to make a 20% down payment. How
much is her down payment in dollars?
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
$49,980
▹ Step-by-Step Explanation
[tex]\frac{20}{100} * $249,900 \\\\= $49,980[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
49,900
Step-by-step-explanation
go two across and place the decimal there, so 20% will be turned into 0.20 and multiply 0.20 by the 249,900. When you are done you will get the amount.
Hope this helped!
A circle has a radius of 26.85 inches. What is the circumference of this circle? Use 3.14 for pi. Round your final answer to the nearest tenth. Enter your answer as a decimal in the box. the first choose dropdown has :0.25 and 4 then is the scale factor an enlargement or not THE TRIANGLE ON THE LEFT IS 1.5 AND THERE IS AN ARROW GOING INTO A BIGGER TRIANGLE THAT IS 6
Answers
Answer:
Step-by-step explanation:
Circumference of the circle = 2 x pi x r
= 2 x 3.14 x 26.85
= 168.618 Inches
after rounding to nearest tenth, 168.6 inches
Answer:
168.6 inches
Step-by-step explanation:
The formula for finding the circumference of a circle is:
[tex]\pi r2[/tex] (Basically multiplying [tex]\pi[/tex] by the diameter since the radius is half the diameter)
Let's substitute and solve!
3.14(26.85 × 2) =
3.14 × 53.7 =
168.61800............but if we round to the nearest tenth, it will be 168.6 inches!
Hope that helps and maybe earns a brainliest!
Have a great day! > <
U
If the probability that a person will die in the next year is 771/100,000
what is the probability that the person will not die in the next year?
A. 0.771%
B. 99.229%
C. 0.229%
D. 99.771%
Answers
Answer:
(B) 99.229%
Step-by-step explanation:
If the probability of someone dying next year is [tex]\frac{771}{100000}[/tex], that means the probability of someone NOT dying next year is [tex]\frac{100000-771}{100000} = \frac{99229}{100000}[/tex].
To find the percent value of this fraction, we divide 99229 by 100000 and multiply by 100.
[tex]\frac{99229}{100000} = 0.99229\cdot100=99.229[/tex]
So, the answer is B, 99.229%.
Hope this helped!
Use the clues in the sentences to determine the best meaning for each bolded word
"He was a tenacious worker, and by sticking firmly to his plan, he succeeded."
"Students planning to become scientists must select a science major, such as biology, chemistry, or physics."
"I want to take a class in calligraphy, or artistic writing, at the community center."
Done
Answers
Answer:
1. Determined
2. area of study
3. artistic writing
Step-by-step explanation:
Hope this helps! <3
Answer:
✔ determined
✔ area of study
✔ artistic writing
Explanation:
