Given:
[tex](g\circ f)(a)=|a|-2[/tex]
To find:
The functions f(x) and g(x).
Solution:
We know that,
[tex](g\circ f)(a)=g[f(a)][/tex]
If [tex]f(a)=a^2-4[/tex] and [tex]g(a)=\sqrt{a}[/tex], then
[tex](g\circ f)(a)=g[a^2-4][/tex]
[tex](g\circ f)(a)=\sqrt{a^2-4}\neq |a|-2[/tex]
Option A is incorrect.
If [tex]f(a)=\dfrac{1}{2}a-1[/tex] and [tex]g(a)=2a-2[/tex], then
[tex](g\circ f)(a)=g[\dfrac{1}{2}a-1][/tex]
[tex](g\circ f)(a)=2(\dfrac{1}{2}a-1)-2[/tex]
[tex](g\circ f)(a)=a-2-2[/tex]
[tex](g\circ f)(a)=a-4\neq |a|-2[/tex]
Option B is incorrect.
If [tex]f(a)=5+a^2[/tex] and [tex]g(a)=\sqrt{a-5}-2[/tex], then
[tex](g\circ f)(a)=g[5+a^2][/tex]
[tex](g\circ f)(a)=\sqrt{5+a^2-5}-2[/tex]
[tex](g\circ f)(a)=\sqrt{a^2}-2[/tex]
[tex](g\circ f)(a)=|a|-2[/tex]
Option C is correct.
If [tex]f(a)=3-3a[/tex] and [tex]g(a)=4a-5[/tex], then
[tex](g\circ f)(a)=g[3-3a][/tex]
[tex](g\circ f)(a)=4(3-3a)-5[/tex]
[tex](g\circ f)(a)=12-12a-5[/tex]
[tex](g\circ f)(a)=7-12x\neq |a|-2[/tex]
Option D is incorrect.
Therefore, the correct option is C.
Solve the real-world situation by using the substitution method.
One smartphone plan costs $30 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone plan costs $60 per month for talk and messaging and $3 per gigabyte of data used each month. Let c represent the total cost in dollars and d represent the amount of data used in gigabytes. The system of equations lbrace c = 30 + 8d c = 60 + 3d can be used to represent this situation.
How many gigabytes would have to be used for the plans to cost the same? What would that cost be?
Both plans would cost $_____
if _____ gigabytes of data are used.
The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls. Jalen's Mobile Phone Cost Number of minutes, X 150 220 250 275 x Cost, y $7.50 $11.00 $12.50 $13.75 If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation? O y = 0.05% O y = 20x O y = 157.58 O y = 1125x Save and Exit Net Submit Mark this and return
Answer: y=0.5x
Step-by-step explanation: hope this would be helpful ∵∵∵∵∵∵∵∵∴∴∴∴∴∴∴∴∴
An above-ground garden is in the shape of a rectangular prism measuring 5 feet by 8 feet by 1.5 feet. The organic soil costs $1.20 per cubic foot. How much will it cost to fill the above-ground garden fully?
Answer:$72.00
Step-by-step explanation: To find the volume you do 5×8×1.5 which equals 60. Then you multiply 60 by 1.20 to find your total cost. Answer is 72
Order the following from Least to Greatest: 0, -4 1/4, -1/2, 1, -3 3/5, 2, -4.1, -0.6, 23/5, 6, -1, 4.5, -5, 2.1
Answer:
-5, -4 1/4, -4.1, -3 3/5, -1, -0.6, 0, 1, 2, 2.1, 4.5
Step-by-step explanation:
1. Find the value of n
(show your work)
n + 7.5 = 48
MUST SHOW WORK!!!
Answer:
40.5
Step-by-step explanation:
48 - 4.5 = 40.5
40.5 + 7.5 = 48
BRAINLIEST PLEASE
Answer:
40.5
Step-by-step explanation:
48-7.5 (48-7=41-0.5=40.5 so there for that would be your answer :D)
Answer- 40.5
yes the person was correct but here is a understanding ! :D
Find the simple interest on a loan of 23,000 at 5.4% interest for 11 months
Answer:
Simple interest=1138.5
Step-by-step explanation:
Simple interest=23000×(5.4/100)×(11/12)
S.I=23000×0.054×(11/12)
S.I=1138.5
this is due in a few hours can yall help me
Answer:
18%, 34%, 9/25, 0.25
Step-by-step explanation:
36% = 18%
17/50 = 34%
0.18 = 9/25
1/4 = 0.25
xander takes a quiz worth 50 points. each question is worth 10 points. sketch a graph to show his score if he missed 1,2,3,4 or 5 questions
Only need a answer for problem a
The answer is 120. Find the supplementary angles by subtracting 60 from 180.
180-60=120
pleaseee help
A job placement agency helps match job seekers with potential employers. The agency would like to design a simulation in order to help predict the likely job placement outcomes for job seekers based on historical trends and patterns. Which of the following is most likely to be a benefit of the simulation?
A. The computer simulation will be able to include more details and complexity than the real-world job placement process.
B. The computer simulation could be used to test hypotheses about patterns in the job placement process that are costly or time consuming to observe in reality.
C. The computer simulation will be able to precisely predict the real-world outcomes for each job seeker.
D. The computer simulation will remove the bias that may arise in the real-world job placement process.
Answer:
B.
Step-by-step explanation:
All computer simulations are designed to test a large number of different scenarios with various sets of data in order to understand each output that certain data generates and ultimately find the best solution. This is the overall main reason why simulations are created. The same applies in this scenario, this simulation will be used to test hypotheses about patterns in the job placement process that are costly or time-consuming to observe in reality. If such tests had to be conducted by actual people it would take months, years, or even decades to generate and analyze all the data.
Answer:
Its D
Step-by-step explanation:
You gotta believe me
LOOK AT THE PICTURE TO ANSWER
Answer:
I think it would be 41
Step-by-step explanation:
First you fill in the letters with the numbers
Then you have the exponent and you do that and get +49
then you have 2 × b and so that would be 8
49-8=41
Step-by-step explanation:
.............................It's 41
Lisa is a hairdresser. A cut and color is $85. If her customer gives her a 15% tip on the total cost, how much of a tip would Lisa get?
Answer:
$12.75 I think
Step-by-step explanation:
Answer:
Lisa got a total tip of $12.75.
Step-by-step explanation:
To answer this question, we just need to find 15% if $85.
85 x 0.15 = 12.75
This means, Lisa got a total tip of $12.75.
Hope this helps! :D
I'm not understanding
Answer:
D. x = 3
Step-by-step explanation:
We would like to find out for what value of x does f(x) = g(x). This is essentially the same as asking us to find the x-value for which f(x) = k, where k is some number, and g(x) = k, as well.
Looking at the two tables provided, we notice that when x = 3, both f(x) and g(x) equal -2. So, the answer is D.
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION I NEED TO TURN IT IN TODAY
Answer:
The answer is 833.65384615385
Step-by-step explanation:
Click the photo to find the measures of the interior angles (3 answers required)
Answer:
the correct answer is:
68 + x + ( x-24) =180
x + (x-24) = 112
2x - 24 = 112
2x = 112 + 24
2x = 136
x = 68
so ...for another : 68 - 24 = 44
18:
A line has a slope of -4 and includes the points (-10,10) and (-7,k). What is the
value for k?
k=
19:
the point (3,4) lies on the graph of the equation 3y=ax+7, then the value of a is
Note: Use slash (/) to separate the numerator and denominator.
200:
Consider a sequence whose first five terms are: -1.75,-0.5,0.75,2,3.25
Which function (with domain all integers n21) could be used to define and continue this
sequence?
A f(n)=7/4(n-1)-5/4
B f(n)=5/4(n-1)-7/4
C f(n)=(7/4)n-5/4
D f(n)=(5/4)n-7/4
Need help with 18-20 plz help I put a picture there to I really need these ASAP
Which inequality has the solution shown in the graph?
a – 3 ≤ –5
a – 3 –2
Answer:
-2
Step-by-step explanation:
Trust me
does anyone know the answer, answer ASAP please!!
Answer:
A = 39 m²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Identify Variables
Shorter Diagonal d2 = 3m + 3m = 6m
Longer Diagonal d1 = 9m + 4m = 13m
Step 2: Find Area
Substitute into formula: A = 1/2(13m)(6m)Multiplication: A = 1/2(78m²)Multiplication: A = 39 m²Game Pitches Seen
1 25
2 20
3 20
4 17
5 15
6 14
The table lists the number of pitches seen by a player in 6 games. What is the mean of the data set?
A.
11
B.
14.5
C.
18.5
D.
20
Answer:
C. 18.5
Step-by-step explanation:
all you have to do is add all the numbers together. Your equation should be 25+20+20+17+15+14 to get the answer of 111. After this all you have to do is divide 111 by how many games were played which is 6. 111÷6 is 18.5
Answer:
a
Step-by-step explanation:
Calc I Question help
The way the question is phrased, it sounds like the height stays fixed at 18 in. If L and W denote the raft's length and width, respectively, then its volume V is given by
V = 18 L W
Differentiating both sides with respect to time t gives
dV/dt = (18 in) W dL/dt + (18 in) L dW/dt
We're told that dL/dt = -1 in/s and dW/dt = -2 in/s, so that at the moment L = 11 in and W = 4 in, the volume is changing at a rate of
dV/dt = (18 in) (4 in) (-1 in/s) + (18 in) (11 in) (-2 in/s)
dV/dt = -468 in³/s
so the raft is losing air at a rate of 468 in³/s. (Note that "losing" captures the negative sign from before.)
which equation is equivalent to y= Ax + By = C
Answer:
slope intercept form
Step-by-step explanation:
that's what ax + by = c is
xoxo, your highness...Write the explicit rule for the arithmetic sequence
-10, -3, 4, 11,...
a
0
=
4
a
i
=
a
i
−
1
+
7
XXXX
possibly with the restriction 1<=i<=4 if this is not intended to be a continuous sequence
Explanation:
This is a simple arithmetic sequence with a difference of
7
between ascending sequence terms.
You earn 30% commissions on the sales of your new app. If you earn $600 in commissions, what were your total sales?
Answer:
600.3
Step-by-step explanation:
600.3
The total sale was $2000.
What is percentage?Percentages are fractions that are counted out of 100. The number is followed by this symbol: %. A percentage of an object is how many parts of it there are out of 100 equal parts
Given that, You earn 30% commissions on the sales of your new app, you earn $600 in commissions,
Let the total sales be x,
Therefore, according to the question,
30% of x = 600
x × 30/100 = 600
x = 600 × 100/30
x = 2000
Hence, the total sale was $2000.
Learn more about percentage, click;
https://brainly.com/question/29306119
#SPJ5
HELP!!!!!A school is having a competition to see who can read the most books in one month (30 days). In the first 5 days, Jake reads 4 books. Meanwhile, Amy reads 5 books over 6 days. If they continue at these rates, who will win? By how many books?
is there a rate because im not understanding
Which of these is the simplest form of x2-2x/x2-4?
Answer:
The first one
Step-by-step explanation: hope this helps!
Please help!!!!
Are the two triangles similar?
Answer:
No because they are not proportanial
have a great day you are loved and you matter
Step-by-step explanation:
$545 at 4% for 2 1/2 years. Answer
Answer:
Total amount of money (including interest) = $ 1417
Step-by-step explanation:
Total amount = 545 × [tex]\frac{100+4}{100}[/tex] × 2.5
= 1417
To find interest only, minus 545 from 1417 :)
6plus 6 times 1 divide 9
Answer:
6+6x1/9= 6.66666666667
Thats the long way and i used mental math and quick math to get the answer :)
HAVE A WONDERFUL DAY
-ary
Answer:
6.666...
Step-by-step explanation:
6 + 6 * 1 / 9
6 + 6 / 9
6 + 2/3
6.666....
Write an equation for the graph, where y depends on x.
Answer:
y = -3x + 6
Step-by-step explanation:
Equation of straight line is given by,
y = mx + b
m = slope of the line
b = y-intercept
From the graph attached,
m = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{-6}{2}[/tex]
= -3
y intercept 'b' = 6
Therefore, equation of the line will be,
y = -3x + 6
Two printers working together can complete a job in 6 hours. Working alone, one
printer takes three times as long as the other printer. How many hours would each
printer need to complete the job alone?
Answer:
Press A takes 10 hours to do a certain job. So Press A does (1/10)th of the job in an hour.
Press A and Press B, together do (1/2.5) or (4/10)th of the job in an hour.
So Press B does (4/10)-(1/10) = (3/10)th of the job in an hour. So Press B can do the job in (10/3) hours or 3 hour and 20 mins.
Check: A does (1/10)th and B does (3/10)th part of the job in an hour. A and B together will take (1/10)+(3/10) = 4/10th of the job in an hour. So they will complete the job in 10/4 = 2.5 hours. Correct.
Answer: Press B can do the job in 3 hour and 20 mins.
Step-by-step explanation: