If f(x) = 3x + 2 and g(x) = x² + 1, we need to find out which of the expressions is equal to (f.g)(x). Solution: To solve the given problem, we need to use the formula of composition of two functions:f.g(x) = f[g(x)] = 3[x² + 1] + 2f.g(x) = 3x² + 3 + 2f.g(x) = 3x² + 5
Therefore, the expression 3x² + 5 is equivalent to (f.g)(x).That is, (f.g)(x) = 3x² + 5In the above solution, we have used the formula of composition of two functions, which is given below:If f(x) and g(x) are two functions, then the composition of two functions f(x) and g(x) is defined as
f[g(x)].If f(x) = 3x + 2 and g(x) = x² + 1, then (f.g)(x) = f[g(x)] = 3[x² + 1] + 2 = 3x² + 3 + 2 = 3x² + 5, which means the expression 3x² + 5 is equivalent to (f.g)(x).The explanation of the solution is written in more than 100 words.
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Part B: The weatherman claimed that the temperature on Friday was the opposite of Thursday’s temperature. Which of the following statements support this claim? Select all that apply.
A.
The temperatures on Thursday and Friday are opposites because they are on different sides of 0 on the number line.
B.
The temperatures on Thursday and Friday are opposites because they have a sum of 0.
C.
The temperatures on Thursday and Friday are opposites because they both contain a 3.
D.
The temperatures on Thursday and Friday are opposites because they are the same distance from 0 on the number line.
Answer:
it will be d
Step-by-step explanation:
because I had a assignment over this and I put d and got it correct
The points represented by the table lie on a line. Find the slope of the line.
Step-by-step explanation:
11. step 1. m = (4 - 7)/(-3 - (-5))
step 2. m = -3/2.
Two friends have recently graduated from college and are now looking for jobs. They are debating which type of job is better: hourly or salary. One hourly position that pays $18 an hour, with time-and-a-half pay for overtime. One salary position for the same type of job pays $38,000, does not pay for overtime. If employees work exactly 40 hours per week, which job has a higher hourly rate? How can we calculate this? Describe (compare) how these two different hourly rates would look when graphed as a line. When interviewing for the salaried job, the friends learn that they may have to work about 10 hours of overtime each week. Explain why this math is crucial to determining which job pays more.
Answer: This is a CRQ so you will want to answer using R.A.C.E
Step-by-step explanation:
First, restate the question: "If employees work exactly 40 hours the job with the higher pay rate is..."
Now let's figure it out who gets paid more. The hourly employee gets $18 per hour, for 40 hours each week... 18 times 40. That's $720 for each week.
But they don't work for just one week, they have to work the whole year! So that's 52 weeks. Take the $720 and multiply by 52 weeks.
Now you have the total for how much hourly guy will make in a whole year.
Compare this number with the salary guy who is making $38,000 per year. Which person get's paid more? Hourly or Salary? Don't forget to include your calculations!
.............................................................................
Next part of the question: "When graphed as a line..." This part of the question you do not have to do because we did not cover slope of a line yet. (Hi, I'm your math teacher by the way lol)
.............................................................................
Next part of the question adds 10 hours of overtime to their work week. This changes everything! Remember, the salary guy gets $38,000 every year, no matter how many hours of overtime he works.
However, the hourly guy gets extra money for these extra hours! For overtime, the hourly employee gets "time and a half" pay whenever he has to work extra time. This means he gets his original $18 per hour, AND now also gets half of that ($9 per hour) ... which adds up to a whopping $27 per hour for overtime (nice!)
Hourly guy works 10 extra hours per week, at $27 per hour. Multiply that and you get $270 per week. Remember, 52 weeks per year, so now take the $270 and multiply by 52 weeks. This gives you the total amount of overtime money hourly guy makes.
Combine his overtime money with his regular money (the first thing we did at the start of this problem) to get his new grand total for the year.
Salary guy still makes $38,000 per year. So now that they work overtime... who gets paid more?
Remember to answer in R.A.C.E format. Restate your question, Answer all parts of the question, Cite a math term/definition/concept that supports your answer (maybe use "hourly rate" or "salary"), and Explain your steps and thinking.
Good luck! send me an email for more help.
Mrs. B
Isabel put $4,000 into a saving account that pays interest monthly at a simple-interest rate of 2.5% per year. If she takes the interest interest out of the account each month, how much money should she expect to earn after 6 months?
9514 1404 393
Answer:
$49.98
Step-by-step explanation:
The interest credited to Isabel's account each month is ...
I = Prt
I = $4000·(0.025)(1/12) = $8.33
If she withdraws that amount each month, the original balance is restored, and she will earn the same amount the next month.
Isabel's total earnings in 6 months will be ...
$8.33 · 6 = $49.98
Things that are equivalent to 5 : 2
Answer:
2/5
Step-by-step explanation:
Answer:
10 : 4, 15 : 6, 20 : 8,
Step-by-step explanation:
increase the first number by 5 then add two to the second number
help. mee
Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.
Answer:
distributive property
9x+15
Step-by-step explanation:
The distributive property is whenever you have () and distribute until you have zero of these ()
The equivalent expression simply means write this equation differently.
In 1995, there were 85 rabbits in Central Park. The population increased by 8.5% each year. How much rabbits were in Central Park in 2005
==============================================
Work Shown:
A = P*(1+r)^t
A = 85*(1+0.085)^10
A = 192.183592562981
A = 192
-----------
Notes:
P = 85 is the starting population.r = 0.085 is the decimal form of 8.5%, so we can say 8.5% = (8.5)/100 = 0.085t = 10 years have elapsed from 1995 to 2005.The formula shown above helps with exponential growth and decay problems.The rabbit population in Central Park in 2005 is 192 rabbits.
To find the rabbit population in Central Park in 2005, we need to calculate the growth from 1995 to 2005.
From 1995 to 2005, there is a total of 10 years.
Using the growth rate of 8.5% per year, we can calculate the population in 2005:
Population in 2005 = 85 rabbits(1 + 0.085)¹⁰
Calculating this expression:
Population in 2005 = 85 rabbits(1.085)¹⁰
= 85 rabbits × 2.2609
= 192 rabbits
Therefore, the estimated rabbit population in Central Park in 2005 is 192 rabbits.
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que es una organizacion
por favor es urgente
Step-by-step explanation:
Las organizaciones son estructuras administrativas y sistemas administrativos creadas para lograr metas u objetivos con el apoyo de las propias personas, o con apoyo del talento humano o de otras características similares.
Which multiplication expression does the model represent?
Answer: I think the answer is A. because it's 1/2 of 4 and it takes only one "quarter of the 4" all though it is split in half it still decared as a whole
Step-by-step explanation:
The multiplication expression represent the model is 1/2×4.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
In the given figure, there are 4 equal parts.
One part is divided into two equal parts.
1/2×4
Therefore, the multiplication expression represent the model is 1/2×4.
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An airplane can ascend at a rate of 54 1/2 meters in 2/3 of a second. How many meters can the airplane ascend in one second?
Answer:
The airplane ascends [tex]81\,\frac{3}{4}[/tex] meters in one second.
Step-by-step explanation:
Given that the airplane ascends [tex]54\,\frac{1}{2}[/tex] ([tex]\frac{109}{2}[/tex]) meters in [tex]\frac{2}{3}[/tex] seconds, we calculate the ascent rate of the airplane by simple rule of three:
[tex]x = \frac{\frac{109}{2}\,m }{\frac{2}{3}\,s } \times 1\,s[/tex]
[tex]x = \frac{327}{4}\,m[/tex]
[tex]x = 81\,\frac{3}{4}\,m[/tex]
The airplane ascends [tex]81\,\frac{3}{4}[/tex] meters in one second.
Plsss help me ASAP plss
Answer: x gte -6 if not try -6 lte x
Step-by-step explanation:
Use the slope formula to find the slope between the given two points.
(-4, -1) and (-2, -5)
Answer:
y2 -y1 over x2 - x1
Step-by-step explanation: plz mark brainliest
Find the midpoint of the interval [-3, 6] along the number line.
Answer:
1.5 or 3/2
Step-by-step explanation:
The midpoint of the interval [-3, 6] along the number line is 1.5.
The midpoint of an interval is the point that lies exactly in the middle of the two endpoints.
To find the midpoint of the interval [-3, 6], we use the midpoint formula:
Midpoint = (Endpoint1 + Endpoint2) / 2
In this case, Endpoint1 is -3, and Endpoint2 is 6:
Midpoint = (-3 + 6) / 2
Midpoint = 3 / 2
Midpoint = 1.5
The midpoint of the interval [-3, 6] is 3/2. This means that the point exactly halfway between -3 and 6 on the number line is 1.5 units to the right of -3 and 1.5 units to the left of 6.
Visually, if you plot -3 and 6 on a number line, the midpoint 3/2 (or 1.5) would be located at the center, equidistant from both endpoints.
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What is the unit ratio for 360 oranges growing to 9 trees
Answer:
360/9=40
Step-by-step explanation:
Answer:
40
all you have to do is divide the first term by the second term
example: 360 divided by 9 = 40
Please guys I need help
[tex]8000 \: pounds \times \frac{1 \: ton}{2000 \: pounds} = 4 \: tons[/tex]
[tex]7 + 4 = 11 \: tons[/tex]
Evaluate each expression when y=5.
B. 4(y+3)
Answer:
B. 4(y+3)=4(5+3)=4×8=32
Answer:
32
Step-by-step explanation:
Step 1: Sub y = 5 into the expression
Find anywhere that has a 'y' and replace it with a 5
4(y+3)
4(5+3)
Step 2: Solve
Use BEDMAS to solve the expression
4(5 + 3)
4(8)
32
Step 3: Therefore Statement
Therefore the expression is equal to 32
pls answer this question
Answer:
id kkk what the quequestion is
Step-by-step explanation:
(-10) + (-10) = 10 –
PLS HELPPPP
Answer:
Step-by-step explanation:
-10 + -10 = -20
so
10 - _ = -20
10 - 30 = -20
please help me solve this problem
Step-by-step explanation:
it seems the answer is four (option a)
If m+6 divided by 2 is 4 less than 4m. What is the value of m?
Answer:
Ok
Step-by-step explanation:
what is the distance between (-1,-2) and (8,10)
Answer:
x1 = 2, x2 =-8
y1=-2, y2 =-2
y2-y1 = |-2+2| =0
x2-x1= |-8-2|= 10
So distance is 10 units
Step-by-step explanation:
What is the distance between the points (2, 3) and (5, -4)?
PLEASE HELP ASAP!!
Answer:
7 point 6
Step-by-step explanation:
What is X - 8 = 15.
Answer:
X = 23
Step-by-step explanation:
X - 8 = 15.
Add 8 to each side
X - 8+8 = 15+8
X = 23
the answer is 23
hope that helped^^
Find the requested information based on the given facts.
Total sales is $55,000.
The commission is 3.5%.
Determine the commission.
Using proportions, it is found that the commission is of $1,925.
What is a proportion?A proportion is a fraction of a total amount, and operations such as multiplication or division are used to find the desired measures in the problem.
One example of application of proportions is for percentage problems, as the percentage is the desired amount divided by the total amount. To find the amount equivalent to a percentage, we multiply the decimal coefficient of the percentage by the total amount.
For this problem, the percentage is of:
3.5%.
Hence the decimal equivalent is:
3.5/100 = 0.035.
The commission is 3.5% of the total sales of $55,000, hence:
C = 0.035 x 55000 = $1,925.
Hence the commission is of $1,925.
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how do you solve 3 divided by x -1 = x + 1
Answer:
multiply (x-1) to both sides and then subtract three from both sides
3 = (x-1)(x+1)
3 = (x^2 -1)
0 = x^2 - 4
(x-2)(x+2) = 0
x = 2
x = -2
Step-by-step explanation:
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing
A. calculator, but he could only see one line. Why is this?
B. because the system of equations actually has only one solution
C. because the system of equations actually has no solution
D. because the graphs of the two equations overlap each other
because the graph of one of the equations does not exist
Three numbers have a ratio of 2: 3: 4. If the largest number if their sum is 24 what is the sum of the three numbers?
Answer:
Step-by-step explanation:
Let r be a multiplier. Then 2r + 3r + 4r = 24, or
9r = 24, or r = 24/9 = 8/3
The three numbers are then (8/3)(2), (8/3)(3), (8/3)(4), and their sum is
(8/3)(2 + 3 + 4) = (8/3)(9) = 24. But the problem tells us that! Please check the wording of your question; something's not quite right there!
Which expression is equal to 4(2+3)
Question 1 options:
A.4+5
B.8+12
C.2+12
D. 8+3
Answer:
B, 8+12
Step-by-step explanation:
2 + 3 is 5, 4 × 5 = 20
Therefore the only option which equals 20 is B.
40. Which two are equivalent to 4?
A A √2
BV8
C V16
D V12
E V64
Answer:
a or b
Step-by-step explanation:
PLS PLS PLS THIS IS VOCAB FOR MATH ONLY HAVE UNTILL 7:30 TO DO SEVERAL ASSIGHNMENTS1. a number belonging to the set made up of the counting numbers: 1, 2, 3, and so on
2. a number that is greater than zero
3. a line that graphically represents all numbers
4. a pair of numbers whose sum is zero
5. any number belonging to the set of counting number, or zero
6. a number that is less than zero
7. a number belonging to the set made up of the whole numbers and their opposites
8. two numbers that are the same distance from zero on the number line but in opposite directions
Answer:
1. natural numbers
2. positive
3. number line
4. zero pair
5. whole number
6. negative
7. integer
8. opposite
Step-by-step explanation:
This is my guess. Take it with a grain of salt. Have a great day!
Answer:
2. positive integers
3. number line
4. I don't know
5. whole number
6. negative integer
7. integers
8. absolute value???