Answer:
The domain of [tex]f(x)[/tex] is restricted to [tex]x\leq 0[/tex], and the domain of [tex]f^{-1}(x)[/tex] is restricted to [tex]x\geq 4[/tex].
Step-by-step explanation:
From Function Theory we know that domain of a function is the set of values such that an image exist. Let [tex]f(x) = x^{2}+4[/tex] and [tex]f^{-1}(x) = \sqrt{x-4}[/tex] the function and its inverse, respectively.
At first glance we notice that function is a second order polynomial and every polinomial is a continuous function and therefore, there exists an image for every element of domain.
But domain of its inverse is restricted to every value of x so that [tex]x-4 \geq 0[/tex], which means that [tex]x\geq 4[/tex].
Finally, we concluded that following answer offers the best approximation to our result:
The domain of [tex]f(x)[/tex] is restricted to [tex]x\leq 0[/tex], and the domain of [tex]f^{-1}(x)[/tex] is restricted to [tex]x\geq 4[/tex].
Answer:
C. The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≥ 4.
Step-by-step explanation:
What is the following fraction in simplest form 4/16
Answer:
1/4
Step-by-step explanation:
it is 1/4 because 4 dived by 16 is 4 so it is 1/4
f(x)=x^2 to f(x)= -4(x+6)^2-3
Gwendolyn was physically present in the United States for 96 days in 2019, 198 days in 2018, and 66 days in 2017. Under the substantial presence test formula, how many days is Gwendolyn deemed physically present in the United States in 2019 g
Answer:
173 days
Step-by-step explanation:
The formula for substantial presence test is;
SBT = (Total of number of days present in the current tax year) + (1/3)(number of days in the year that was before the tax year) + (1/6)(number of days in the year that was two years before the tax year)
From the question, present tax year is 2019 and number of days is 96 days.
Year before tax year is 2018 and number of days is 198 days
2 years before tax year is 2017 and number of days is 66 days.
Thus;
SBT = 96 + ((1/3)198) + ((1/6)66)
SBT = 173 days
plss helpp !! *worth 25 points*
Answer:
Purple Circle : 28.27
Yellow Circle : 43.98
Step-by-step explanation:
Radius of Purple Circle : 4.5
2 * π * 4.5 = 28.27
Radius of Yellow Circle : 7
2 * π * 7 = 43.98
I need help with mixed numbers when subtracting plz
Answer:
turn it into an improper fraction then subtract
Step-by-step explanation:
5×6=30
30+1=31
31/6
3×6=18
18+5=21
21/6
31/6 - 21/6 = 10/6
simplify: 5/3 ♡
I'm not sure tho lol
List and give the meaning of the y-intercept in this problem
Answer:
The y-intercept is 360 and it means that the hiking elevation will be 360 feet after 18 minutes
Pls help me plssss. Bella measured the heights of her corn stalks in centimeters. The heights are 81, 88, 69,65, 87.
What is the mean height of Bella's corn stalks? ——————————
O A 69 cm
O B. 75 cm
O C. 78 cm
OD 80 cm
O E 81 cm
Answer:
the answer is C. 78
Step-by-step explanation:
First, you have to add together 81, 88, 69, 65, and 87; its total is 390. The next step is to see how many numbers there are. In total there are 5 numbers. Lastly, you have to divide 390 by 5 which is 78.
Micah found the least common multiple of 8 and 12. His work is shown below.
Multiples of 8: 8, 12, 16, 20, 24, 28, . . .
Multiples of 12: 12, 24, 36, 48, 60, . . .
The least common multiple is 12.
What is Micah’s error?
Answer:when he was doing the multipleis of 8 he put 20 when there is no 20
Step-by-step explanation:
at a Halloween fair, you see a huge Ferris wheel. There are ten seats on the wheel, with two people placed on each seat. Every minute, a seat passes by the exit platform. The Ferris wheel opened for 30 minutes at 11 a.m. and doubled its speed after fifteen minutes. How many people rode the wheel during this time?
This is just a fun question I need answered!
90 people
We are told that;
Total number of seats = 10
Number of people in each seat = 2 Total duration of the Ferris wheel = 30 minutes
For the fist 15 minutes of normal speed, since 2 people were placed on each seat, it means that;Number of people to ride for the first 15 minutes = 15 × 2 = 30 people
Now, the speed has been doubled for the remaining 15 minutes.This means that 2 seats will pass per minute and thus;
Number of people to ride for 15 minutes at this double speed = 15 × 2(2) = 60
2(2) was used because a seat can take 2 people.
Thus, total number to ride the wheel overall = 30 + 60 = 90 peopleRead more at; brainly.in/question/1728461
PLEASE HELP I AM STUCK
12,049=-58,642+y
Answer:
70,691
Step-by-step explanation:
One month, two search engines were used to conduct a total of 3.52 billion online searches. Search engine A was used to conduct 0.66 billion more searches than search engine B. How many searches were conducted on each search engine?
FAST PLS
Answer:
Search Engine A = 2.09 billion searches.
Search Engine B = 1.43 billion searches.
Step-by-step explanation:
Engine A + Engine B = 3.52 billion
Search engine A was used to conduct 0.66 billion more searches than search engine B
A = 0.66 billon + B
Hence:
0.66 billion + B + B = 3.52 billion
2B = 3.52 billion - 0.66 billion
2B = 2.86 billion
B = 2.86 billion/2
B = 1.43 billion searches.
A = 0.66 billion + B
A = 0.66 billion + 1.43 billion
A = 2.09 billion searches.
Therefore:
Search Engine A = 2.09 billion searches.
Search Engine B = 1.43 billion
The probability of getting a white marble from the bag is 1/6. If there are eight white marbles in the bag, what is the total number of marbles in the bag?
A. 36
B. 24
C. 48
D. 14
Answer:
C: 48
Step-by-step explanation:
1/6 chance so multiply by 6, 8 marbles so multiply by 8, 8(6)=48
Answer:
48 marbles, it's C
Step-by-step explanation:
why?
Because 1/6 of the marbles are white. and there are 8 white marbles. so that means, 1/6=8 marbles.
So you just get 1/6 to 6/6
so you do, 8*6 which equals to 48
Express $15 for 6 gallons of gas as a unit rate.
Answer: 0.4 gallons per dollar
Model a desert community where 48% of the area is covered with houses. Place houses on of the 100 squares to represent or 48% houses.
Answer:
100
Step-by-step explanation:
Answer:
Place houses on
48
of the 100 squares to
represent
48/100
or 48% houses.
Which rational number equals 0 point 4 with bar over 4?
==============================================
Work Shown:
[tex]x = 0.\overline{4}\\\\x = 0.4444\ldots\\\\10x = 4.4444\ldots\\\\10x-x = 4.4444\ldots-0.4444\ldots\\\\9x = 4\\\\x = \frac{4}{9}\\\\\frac{4}{9} = 0.\overline{4}= 0.4444\ldots\\\\[/tex]
The idea is that when we subtract 10x and x, the infinite decimal pattern (the 4s that go on forever) will cancel. That leads to 9x = 4 which solves to x = 4/9
Is the equation 6x-15y=-12 in standard form? Why or why not
Answer:
2x-5y=-4
Step-by-step explanation:
No, the GCF is 3 not 1
MATCH THE CORRECT ONE PLEASE HELP
Answer:
same side interior for 2 and 6 i think
he cost of manufacturing a particular videotape is C(x)90009x, where x is the number of tapes produced. The average cost per tape, denoted by , is found by dividing by x. Find .
Answer:
The average cost per tape is 10.
Step-by-step explanation:
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. [tex]\lim_{x \to 9000} \bar C(x)[/tex]
[tex]\bar C(x)=\dfrac{9000+9x}{x}\\\\=\dfrac{9000}{x}+9\\\\ \lim_{n \to 9000} \bar C(x)=\dfrac{9000}{9000}+9\\\\=1+9\\\\=10[/tex]
So, the average cost per tape is 10.
Customers at the Palace Pro Shop receive a 10% discount if they are members. All customers must pay 7% in sales tax. The function f(x)=0.9x is used to determine the price of an item after the 10% member discount, where x is the regular price of the item. The function g(x)=1.07x is used to determine the total amount customers pay for a purchase after all discounts are applied. Which function can be used to determine T(x), the total amount a member pays for an item with a regular price of x dollars?
Answer:
The total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.
Step-by-step explanation:
Key points:
Discount is subtracted from the regular price of an item.Sales tax is added to the regular price of an item.It is provided that the customers receive a 10% discount if they are members and all customers must pay 7% in sales tax.
Two functions are provided are:
f (x) = 0.90x ; the price of an item after the 10% member discount
g (x) = 1.07x ; the total amount customers pay for a purchase after sales tax is applied.
Compute the total amount a member pays for an item with a regular price of x dollars as follows:
T (x) = Discount × Sales Tax
= 0.90 × 1.07 × x
= 0.963x.
Thus, the total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.
You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?
Given:
You are given $893 in one, five, and ten dollar bills.
There are 165 bills.
There are twice as many five dollar bills as there are ones and tens combined.
To find:
How many bills of each type are there?
Solution:
Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.
According to the question,
Number of bills : [tex]x+y+z=165[/tex] ...(1)
Total amount : [tex]1x+5y+10z=893[/tex] ...(2)
Condition : [tex]y=2(x+z)[/tex] ...(3)
Equation (3) can be written as
[tex]\dfrac{y}{2}=x+z[/tex] ...(4)
Substituting [tex]x+z=\dfrac{y}{2}[/tex] in (1), we get
[tex]\dfrac{y}{2}+y=165[/tex]
[tex]\dfrac{3y}{2}=165[/tex]
[tex]3y=330[/tex]
[tex]y=110[/tex]
Substituting y=110 in (4), we get
[tex]x+z=\dfrac{165}{2}[/tex]
[tex]x+z=55[/tex]
[tex]x=55-z[/tex] ...(5)
Substituting y=110 and x=55-z in (2), we get
[tex](55-z)+5(110)+10z=893[/tex]
[tex]55-z+550+10z=893[/tex]
[tex]9z+605=893[/tex]
[tex]9z=893-605[/tex]
[tex]9z=288[/tex]
Dividing both sides by 9, we get
[tex]z=32[/tex]
Substituting z=32 in (5), we get
[tex]x=55-32[/tex]
[tex]x=23[/tex]
Therefore,
One dollar bills = 23
Five dollars bills= 110
Ten dollars bills = 32
Why do we study?give me reason
Answer:
Simple to help us improve our lives
Answer:
To do good in school
Step-by-step explanation:
the thing is teachers want us to study so we remember whatever is on the test for an example and that is good but not alt of people always study.
Taminka received a raise in her hourly pay, from $13.50 to $14.99. Find the percent change. Round to the nearest percent.
Answer:
[tex]\% = 11\%[/tex]
Step-by-step explanation:
Given
[tex]Initial = \$13.50[/tex]
[tex]Final = \$14.99[/tex]
Required
Determine the percentage change
This is calculated as:
[tex]\% = |\frac{Initial - Final}{Initial} * 100\%[/tex]
[tex]\% = |\frac{13.50 - 14.99}{13.50}| * 100\%[/tex]
[tex]\% = |\frac{-1.49}{13.50}| * 100\%[/tex]
[tex]\% = \frac{1.49}{13.50} * 100\%[/tex]
[tex]\% = \frac{1.49* 100\%}{13.50}[/tex]
[tex]\% = \frac{149\%}{13.50}[/tex]
[tex]\% = 11.037037037\%[/tex]
[tex]\% = 11\%[/tex]
Write the equation of the line that is perpendicular to x=7 and passes through point (-3, 5).
If ukuk
Answer: y=5
Step-by-step explanation: I just plotted the given point and graphed the line, then drew a perpendicular line that passed through the point.
Hannah wants to buy a $460 camera. She can save $35 each week from her paycheck. However, before Hannah can buy the camera, she must give her brother $65 that she owes him. For how many weeks will Hannah need to save before she can pay back her and buy the camera?
Answer:
460+65=525/35=15 15 weeks
I need help asap with my math
Answer:
The first and the third one are correct.
Step-by-step explanation:
Answer: 1 & 3 are proportional relationships
Joe is training to run in a half marathon in two months. This week he ran 1, 200,000 millimeters on Monday, 2, 400 meters on
Wednesday, and 4.6 kilometers on Friday. What is the total distance in kilometers that he ran this week?
TI
The total distance he travelled in kilometer is 8.2 km
What is distance?Distance is the total movement of an object without any regard to direction.
Given:
On Monday he walked = 1, 200, 000 mm
On Tuesday he walked= 2,400 m
On Wednesday he walked = 4.6 km
As, 1mm = 1/100,000
1,200,000 mm = 1.2 Km
and, 1 m =1/1000 km
2400m = 2.4 km
Hence, the total distance he travelled = 1.2+ 2.4 + 4. 6 = 8.2 km
Learn more about this concept here:
https://brainly.com/question/3128392
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A single 6-sided die is rolled twice. Find the probability of getting a 3 the first time and a 3 the second time. Express the probability as a simplified fraction.
Answer:
1/36
Step-by-step explanation:
The event is mutually exclusive event. The occurrence of one foew not affect the other.
If a die is rolled once, the total outcome will be 6 since a die has 6 faces.
Probability = expected outcome/total outcome
If 3 is gotten when a die is rolled, the expected outcome will be 1.
Probability of getting a 3 will be 1/6
The probability of getting a3 the second time is also 1/6
The probability of getting a 3 the first time and a 3 the second time = 1/6×1/6 = 1/36
16 less than a number r divided by 8
Answer:r/8>16
Step-by-step explanation:
r/8-16
It says 16 less, so we have to subtract 16 from r divided by 8.
That would be r/8-16.
Mr. Thompson sold 4 vacuum cleaners in the first month. In the second month, he sold 3 times as many vacuum cleaners as the first month. In the third
month, he sold 5 times as many vacuum cleaners as the first month.
a. How many vacuum cleaners did Mr. Thompson sell in the three months?
bers
Mr. Thompson sold ____
vacuum cleaners in the three months.
b. He sold the vacuum cleaners for $435 each. How much money did Mr. Thompson earn? (Be sure to put a comma in your answer.)
bers
Mr. Thompson earned $ ________
In ΔCDE, \text{m}\angle C = (x-4)^{\circ}m∠C=(x−4) ∘ , \text{m}\angle D = (11x-11)^{\circ}m∠D=(11x−11) ∘ , and \text{m}\angle E = (x+13)^{\circ}m∠E=(x+13) ∘ . Find \text{m}\angle C.m∠C.
Answer:
The measure of C is 10°
Step-by-step explanation:
In a triangle CDE, its internal angles are given:
C=x-4
D=11x-11
E=x+13
Since the sum of the internal angles of a triangle is 180°:
x-4+11x-11+x+13=180
Simplifying:
13x-2=180
Adding 2:
13x=182
Solving:
x=182/13
x=14°
The measure of the angles is:
C=x-4 =10°
D=11x-11=143°
E=x+13=27°
The measure of C is 10°
