Answers
Answer:
see explanation
Step-by-step explanation:
(a)
Substitute x = - 1 into f(x)
f(- 1) = 6 - 2(- 1) = 6 + 2 = 8
(b)
Substitute x = [tex]\frac{1}{3}[/tex] into g(x)
g([tex]\frac{1}{3}[/tex] ) = [tex]\frac{9}{\frac{1}{3} }[/tex] = 9 × 3 = 27
(c)
Substitute x = f(x) into h(x)
h(6 - 2x)
= 6 + (6 - 2x)² ← expand using FOIL
= 6 + 36 - 24x + 4x² ← collect like terms
= 4x² - 24x + 42
(d)
Substitute x = f(x) into g(x)
g(6 - 2x)
= [tex]\frac{9}{6-2x}[/tex]
(e)
Evaluate g(12) then substitute value obtained into f(x)
g(12) = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] , then
f([tex]\frac{3}{4}[/tex] ) = 6 - (2 × [tex]\frac{3}{4}[/tex] ) = 6 - [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]
(f)
Evaluate f(- 9) then substitute the value obtained into h(x)
f(- 9) = 6 - 2(- 9) = 6 + 18 = 24 , then
h(24) = 6 + 24² = 6 + 576 = 582
Related Questions
The temperature is -8 degrees Fahrenheit. The height pressure front increases the temperature to 7 degrees Fahrenheit. By how many degrees did the temperature increase.
(Please show work and explanation)
Answers
Answer:
3 dregreess 5 degrees temperature
Given f(x) = x + 2, describe how setting k = 4 affects the slope and y-intercept of the graph of g compared to the graph of f.
g(x) = (4x) + 2
g(x)=4(x+2)
Answers
Answer:
g(2)=(4x) +2=7y
g(3)=4(x+2)
Don Swifter earns $9.75 per hour as a clerk. He starts work Monday through Friday morning at 8:00 AM. He takes a one-half hour lunch break every day. If he finishes work at 3:30 PM Monday through Thursday, how late must he work on Friday to have total pay of $360.75 for the week?
Answers
Answer:
He works until 5:30.
Step-by-step explanation:
ok so first, every day don would take a total of 7 hours and 30 minutes on mon-Thurs. If we subtract his lunch from that total it would be 7 hours so next we do 7 hours times 9.75 which is 68.25$. Now that we know how much he makes per day, we times that by 4 since mon-thurs is 4 days. This would be 273$. Now we need to get to 360.75 so we subtract that. This would be 87.75$. Now if a normal day is 68.25$ and friday is 87.75, we find the diffrence which is 19.50. which is also 9.75(an hour) x 2 resulting in 2 hours extra. Therefore, he works 9 hours and 30 minutes on fridays (until 5:30). Thanks for putting in the work to understand and have a nice day!
Don must work approximately 9 additional hours on Friday to have a total pay of $360.75 for the week.
How to determine how late he must workDon works from 8:00 AM to 3:30 PM Monday through Thursday. Let's calculate his total work hours for these four days:
Total work hours from Monday to Thursday:
(3:30 PM - 8:00 AM) - 0.5 hours (lunch break)
= 7.5 hours - 0.5 hours
= 7 hours (per day)
Total work hours for the week (Monday to Thursday):
4 days x 7 hours/day = 28 hours
Total pay for the week = Hourly rate x Total work hours + Additional hours on Friday
$360.75 = $9.75 x 28 hours + Additional hours on Friday
Additional hours on Friday = ($360.75 - $9.75 x 28) / $9.75
Additional hours on Friday = ($360.75 - $273) / $9.75
Additional hours on Friday = $87.75 / $9.75
Additional hours on Friday ≈ 9 hours (rounded to the nearest hour)
Learn more about work hours
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2(3x-12)=6(x-2)
PLEASE HELP!!!
Answers
WORTH 50 POINTS. The graph represents the journey of a bus from the bus stop to different locations:
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)
Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)
Part C: Is the graph linear or non-linear? Explain your answer. (2 points)
Answers
Answer:
3
Step-by-step explanation:
How do I fully simplify this?
Answers
Explanation
3xy + 4xy + 3xy = 10xy
The others cant be simplified so
10xy + 2y + 8x + 7
The vertices of quadrilateral PQRS are listed.
P(3,7), Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS
A.
Quadrilateral PQRS is a square.
B.
Quadrilateral PQRS is a trapezoid.
C.
Quadrilateral PQRS is a rectangle.
D.
Quadrilateral PQRS is a parallelogram.
Answers
Answer:
It's C. for plato. It's a rectangle
Step-by-step explanation:
FILE BELOWAnswer:
its a rectangle .
Step-by-step explanation:
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )
Answers
Answer:
A = (0,1)
B = (1,-1)
C = (-1,-1)
Step-by-step explanation:
If this helped leave a brainliest
Last year, 50 students attended the movie night. This year, 65 students attended the movie night. fine the percent of increase in the number of students who attended the movie night.
Answers
Answer: 30%
Step-by-step explanation:
It increased by 15 so it increased by 15/50=30/100=30%
I hope this helped!
The amount of money in a savings account is an example of which of the following?
a. investment asset
b. liquid asset
C. long term asset
d. use asset
Answers
Answer: b. liquid asset.
The money in your checking account, savings account, or money market account is considered liquid because it can be withdrawn easily to settle liabilities.
A savings account is a liquid asset that can be easily converted into cash. Hence, option b is correct.
A savings account is considered a liquid asset because it can be easily converted into cash without any significant loss in value.
Unlike long-term assets that may require a lengthy process to convert into cash, such as real estate or investments, savings accounts offer quick access to funds.
This makes them highly liquid and suitable for short-term financial needs. Liquid assets provide individuals with a sense of financial security and flexibility, as they can be readily used to cover emergencies, expenses, or investments.
Overall, a savings account serves as a convenient and safe option for individuals to save and access their money when needed.
Hence, It is an example of a liquid asset which is option b.
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Add 8.563 and 4.8292. then times the answer by 9.183 divide it 2 times by 1.192. Add to the answer with this number after your finished: "19.323
Answers
Answer:
105.876373581
Step-by-step explanation:
8.563 + 4.8292 = 13.3922
13.3922 × 9.183 = 122.9805726
122.9805726 ÷ 1.192 = 103.171621309
103.171621309 ÷ 1.192 = 86.5533735811
86.5533735811 + 19.323 = 105.876373581
Step-by-step explanation:
8.563+4.8292=A
( A*9.183)÷1.192÷1.192=B
B+19.323=C
Given the following polynomials
x = (a + b + c)^2
y= a^2 + b^ 2 + C^2
z = ab + bc + ac
Which identity is true?
A. x=y-z
B. x=y+z
C. x=y-2z
D. x=y+2z
Answers
Answer:
D. x=y+2z
Step-by-step explanation:
if you expand out the first equation (x) you will get: a^2+b^2+c^2+2ab+2bc+2ac
then looking at all of the choices, it can be seen that the third equation (z) needs to be multiplied by to get 2ab+2bc+2ac and then added to the second equation (y) which would result in D being the correct answer.
D. x=y+2z
find the value of 7u+7 given that -3u-5=4
Answers
What is 7C3? Thanks.
Answers
Answer:
C7,3=7!( 3!)( 7−3)!= 7! I think tell me if I'm wrong?
Answer:
7C3 = 7! / (7 - 3)! 3! = 7 x 6 x 5 x 4! / 4!
A parabola can be drawn given a focus of (4,6) and a directrix of y = 2. What can be
said about the parabola?
Answers
Answer:
A.
Step-by-step explanation:
11
For your job, you often fly between Seattle and Miami. The distance between these cities is 2,724 miles. You earn a free flight after you accumulate 25,000 miles of travel. How many round trips (back and forth) mus!
you make between Seattle and Miami in order to earn a free flight?
b. 5
c. 8
d. 9
e. 10
Answer 5
Answers
Answer:
b
Step-by-step explanation:
one trip = 2724 miles
one round trip = 2 trips = 2724 * 2 = 5448 miles
We want to see how many round trips go into the miles needed for a free flight. We want to see how many times 5448 goes into 25000. To do this, we can use division.
25000/5448 ≈ 4.6
If we only have 4 round trips, it will not be enough for 4.6, so we will not be able to obtain a free flight. If we have 5, we will be able to, as 5 > 4.6
Create a storyline (word problem) for the real-world graph below.
(I can do the story part I just need the numbers)
Answers
Answer:
Y would equal X on Day 65
Step-by-step explanation:
Im guessing by looking at the chart
Answer:
One line represents something getting heavier over time, while the line pointing down represents something getting lighter over time at a slightly slower rate.
HELP QUICK!
Read the description of f below, and then use the drop-down menus to complete an explanation of why f is or is not a function.
f relates each student in South High School to their grade point average (GPA) and number of credits earned.
Answers
Using the function concept, it is found that f is a function, as each student is related to only one GPA and only one number of credits.
In a function, one value of the input can be related to only one value of the output.
In this problem:
The input is the student.The output is the student GPA, and the number of credits earned.Each student is related to only one GPA and only one number of credits, hence one value of the input is related to only one value of the output, and f is a function.
To learn more about the function concept, you can take a look at https://brainly.com/question/12463448
Find the expected value of the winnings from a game that has the following payout probability distribution: Payout ($) 1 2 5 8 10 Probability 0.35 0.2 0.1 0.2 0.15 = Expected Value = [?] Round to the nearest hundredth. Enter
Answers
Multiply each payout by the corresponding probability, and add these up:
1•0.35 + 2•0.2 + 5•0.1 + 8•0.2 + 10•0.15 = 4.35
So one can expect to win $4.35 from playing the game.
If f(x) = 2x2 + 3x and g(x) = x 2- 7, find (f +g)(x)
Answers
Answer:
3x²+3x-7
Step-by-step explanation:
(f+g)(x)=2x²+x²+3x-7
=3x²+3x-7
4. The population of a town is modeled by the equation P = 3485e
0.125
, where "P"
represents the population as of the year 2000.
• According to the model, what will the population of the town be in 2010?
In approximately what year will the population reach 50,000 people?
Must answer and show appropriate work for both questions here.
Student's Work
Student's Answer
A. Part A: 11,571 people in 2010
Part B: approx. 22 years
B. Part A: 38,416 people in 2010
Part B: approx. 13 years
C. Part A: 11,571 people in 2010;
Answers
The population of the town be in 2010 will be 121634, and it will take 21 years for the population to get to 50000
The population model is given as:
[tex]P(x) = 3485e^{0.125x}[/tex]
(a) The population in 2010
In 2010, the value of x is 10.
So, we have:
[tex]P(10) = 3485 * e^{(0.125 \times 10)}[/tex]
Evaluate the exponent
[tex]P(10) = 3485 * e^{(1.25)}[/tex]
This gives
[tex]P(10) = 121634[/tex]
(b) Year to reach 50000
This means that P = 50000.
So, we have:
[tex]50000 = 3485e^{0.125x}[/tex]
Divide both sides of the equation by 3485
[tex]14.35 = e^{0.125x}[/tex]
Take natural logarithm of both sides
[tex]\ln(14.35) =0.125x[/tex]
[tex]2.66 =0.125x[/tex]
Divide both sides by 0.125
[tex]21.28 = x[/tex]
Rewrite as:
[tex]x =21.28[/tex]
Approximate
[tex]x =21[/tex]
Hence, the population of the town be in 2010 will be 121634, and it will take 21 years for the population to get to 50000
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A proportional relationship is formed when y = 24 and x = 32. What is the value of y when x = -2? Explain how you solved the problem.
Answers
Answer:
-1.5
Step-by-step explanation:
24 : 32 is the ratio between y and x respectively. To change a number but keep the ratio equal, we must divide/multiply both sides by the same amount.
First, we can say that we want to change x to -2. 32/-2 = -16, so we must divide both sides by -16 to keep the ratio but change x to 02
24 : 32 = 24/(-16) : -2 = -1.5 : -2
LAST ATTEMPT !! MARKING AS BRAINIEST!!
Answers
Find the value of x
Answers
Answer:
i think r would be the same as q
Step-by-step explanation:
I believe it's an isosceles triangle, if there were a line going down the center, each half should be symmetrical, so q and r are the same angle.
Answer:
32.5
Step-by-step explanation:
A triangle's angles add up to 180 degrees
(2x+15)+x+(x+35)=180
x=32.5
Identify the digit in the ten thousandths place in every number.
1.) 12.00535
2.)54.01247
3.) 3.98056
4.) 0.00667
5.) 70.70071
6.) 0.07889
7.) 10.00898
Answers
Answer:
Step-by-step explanation:
The decimal point will help you find your way here. Just to the right of the decimal is the tenths place. 0.4 is the number four tenths.
Next, farther to the right is the hundredths place-- 0.04 is the number four hundredths.
Next over is the thousandths place-- 0.004 is the number four thousandths. And finally, the next over is the ten thousandths place...like this, 0.0004 is the number four ten thousandths
So, 1) 12.00535 has a one in the tens place, a two in the ones place, zeros in the tenths and also the hundredths places, fives in the thousandths place and also the hundred thousandths place, AND, what you're looking for-- a 3 in the ten thousandths place.
1) 3
2) 4
3) 5
4) 6
5) 7
6) 8
7) 9
For ten thousandths place, you're looking at the fourth spot on the right side of the decimal.
Which fractions are equivalent to the fraction below? Check all that apply.
5/7
Answers
Answer:
A. 10/14
and
C. 15/21
Step-by-step explanation:
A. 10/14
and
C. 15/21
b) Abus covers 270 km distance in 6 hours. (i) Find the speed of the bus in km per bour. (ii) How many kilometres does it travel in 9 hours at the same speed ?in full languages
Answers
Answer:
(i)= 45 KPH, (ii) = 251 miles
Step-by-step explanation:
'Per' essentially means divide. Thus, to find Kilometres per hour, divide 270 by 6= 45. The bus is travelling at 45 KPH.
Then, to see how far a nine hour trip would cover, distance = speed * time = 251 miles.
Answer:
Below.
Step-by-step explanation:
(i) Speed of the bus = 270/6 = 45 km/hour.
(ii) In 9 hours it travels 45 * 9 = 405 km.
Help help help math math math
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
The curve y= 1/3 x⁴ - 4x² -3x has a gradient of -3 at three points.
Find the coordinates of these points.
Answers
Answer:
[tex]\boxed{(0, 0), (\sqrt{6}, -12-3\sqrt{6}), (-\sqrt{6}, -12+3\sqrt{6})}[/tex]
Step-by-step explanation:
Step 1: Take the derivative of the function with respect to x
[tex]\frac{d}{dx} (\frac{1}{3}x^4-4x^2-3x)\\=\frac{d}{dx} (\frac{1}{3}x^4)-\frac{d}{dx}(4x^2)-\frac{d}{dx}(3x)\\=\frac{4}{3}x^3-8x-3[/tex]
Now, you have the gradient of every point given the x value. We want the gradient to be -3, so,
Step 2: Set the derivative of the function equal to -3 and solve for x
[tex]\frac{4}{3}x^3-8x-3=-3\\\frac{4}{3}x^3-8x=0\\4x(\frac{1}{3}x^2-2)=0\\[/tex]
We can see that one solution is x=0.
The other 2 solutions are:
[tex]\frac{1}{3}x^2-2=0\\\frac{1}{3}x^2=2\\x^2=6\\x=\sqrt{6}, x=-\sqrt{6}[/tex]
Now that we found out the x value, we can plug it in back to the equation to find their respective y value:
x=0: y=0
x=sqrt(6): y=-12-3sqrt(6)
x=-sqrt(6): y=-12+3sqrt(6)
Hence we have our answer.
I need help with this
Answers
240 because i am smart and also nice pencil
Step-by-step explanation: