For questions 3 - 6, find F'(x), the inverse of F(x).
3. F(x) = x-10
4. F (x) = x/6 + 3
5. F(x) = 3x + 7
6. F(x) = 8x
Answer:
3) f'(x) = x + 10
4) f'(x) = 6x - 18
5) [tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex]
6) f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex]
Step-by-step explanation:
3. f(x) = x - 10Step 1: In order to find the inverse function of f(x) = x - 10, start by replacing f(x) with y.
y = x - 10
Step 2: Switch x and y:
x = y - 10
Step 3: Add 10 to both sides to isolate y:
x + 10 = y - 10 + 10
x + 10 = y
Step 4: Replace y with f'(x):
f'(x) = x + 10 ⇒ This is the inverse function of f(x).
4. [tex]\displaystyle\mathsf{f(x)=\:\frac{x}{6}\:+\:3}[/tex]Replace f(x) with y:
[tex]\displaystyle\mathsf{y=\:\frac{x}{6}\:+\:3}[/tex]Switch x and y:
[tex]\displaystyle\mathsf{x=\:\frac{y}{6}\:+\:3}[/tex]Subtract 3 from both sides:
[tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}\:+\:3-3}[/tex][tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}}[/tex]Multiply both sides by 6 to isolate y:
[tex]\displaystyle\mathsf{6(x-3)=\:\frac{y}{6}(6)}[/tex]6x - 18 = y
Replace y with f'(x):
f'(x) = 6x - 18 ⇒ This is the inverse function of f(x).
5. f(x) = 3x + 7Replace f(x) with y:
y = 3x + 7
Switch x and y:
x = 3y + 7
Subtract 7 from both sides:
x - 7 = 3y + 7 - 7
x - 7 = 3y
Multiply both sides by ⅓:
⅓(x - 7) = 3y (⅓)
[tex]\displaystyle\mathsf{\frac{1}{3}x-\frac{7}{3}=y}[/tex]
Replace y with f'(x):
[tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex] ⇒ This is the inverse function of f(x).
6. f(x) = 8x
Replace f(x) with y:
y = 8x
Switch x and y:
x = 8y
Multiply both sides by ⅛:
⅛(x) = ⅛(8y)
⅛x = y or [tex]\displaystyle\mathsf{\frac{x}{8}=y}[/tex]
Replace y with f'(x):
f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex] ⇒ This is the inverse function of f(x).
You accelerate from 5m/s to 60m/s in 11 seconds what is the average acceleration.
Change in acceleration: 60 - 5 = 55 m/s
Average acceleration = 55 m/s / 11 second = 5 meters per second squared ( m/s^2)
Answer: 5 m/s^2
Can anybody answer this for me?
[tex]\\\text{Given that,}\\\\(x_1 , y_1) = (5,6) ,~~ (x_2, y_2) = (-5,-4)\\\\\text{Slope},~m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-4-6}{-5-5} = \dfrac{-10}{-10} = 1[/tex]
Convert to an exponential equation.
In 17 = 2.8332
Answer:
17 = e^2.8332
Step-by-step explanation:
you’ll live 100 more years if you help me answer 1 through 5 :D!!!
Answer:
You need to give me a thanks and brainliest: 1. = 16 ; 2. = 100 ; 3. = 64; 4. = 604; 5. Cant see the problem in the screen shot.
Step-by-step explanation:
Sara has only nickels in her hand, and David has exactly the same
number of dimes and no other coins. Together, they have a total of $1.05. How many nickels does Sara have? How many dimes does David have? Show your work
using numbers, labeled sketches, or words.
Will give brainliest
Answer:
down - up +
Step-by-step explanation:
Evaluate - (3 ^ - 5) * (3 ^ 3)
Answer:
1 / 3^2 = 1/9
Step-by-step explanation:
3^-5 = 1/3^5
(1/3^5) * (3^3) = 3^3 / 1/3^5 = 3^3 / 3^5 = 1/3^2
The value of the given expression is 1/9 .
Given,
[tex](3^{-5}) (3^{3} )[/tex]
According to the power rule,
[tex](a^{m}) (a^{n} ) = a^{m + n}[/tex]
Now,
[tex](3^{-5}) (3^{2}) = 3^{-5 + 3}\\ \\ (3^{-5}) (3^{2}) = 3^{-2}[/tex]
[tex](3^{-5}) (3^{2}) = 1/3^{2}[/tex]
[tex](3^{-5}) (3^{2} ) = 1/9[/tex]
Thus with the power rule answer will be 1/9.
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A small town has two local high schools. High School A currently has 250 students and is projected to grow by 50 students each year. High School B currently has 450 students and is projected to grow by 25 students each year. Let A represent the number of students in High School A in t years, and let B represent the number of students in High School B after t years. Graph each function and determine after how many years, t, the number of students in both high schools would be the same.
give me the corrdent plan point i need 2 for example
(5,2) and (4,1) like that on the graph
Answer: ________
students
students per year
years
years of student
Answer:
in 8 years both school will have 650 students
Step-by-step explanation:
HS A (t) = 250+50t
HSB (t) = 450+25t
250 + 50t = 450 + 25t
25t=200
t=8
in 8 years
to graph this:
HSA points (0,250) (2, 350) (4, 450) (8, 650)(10, 750)
HSB points (0, 450) ( 2, 500) (4, 550) (8, 650) (10, 700)
when you graph then you will notice they intercept at 8, which gives you 650 students
The equilateral triangle with side 12 has altitude
Answer:
C
Step-by-step explanation:
100 POINTS! show work or i report!
Michael purchases a refrigerator for $4,000. On average, it costs $120 per year in electricity to leave it running 24/7. What is the average yearly cost to own and operate this refrigerator at the end of 6 years?
Answer:
$4,720
Step-by-step explanation:
$4,000 fridge
$120/1 year
[tex]\frac{120}{1} = \frac{x}{6}[/tex]
120 * 6 = 720
720 / 1 = 720
$720 for 6 years
720 + 4,000 = 4,720
$4,720
Answer:
$4,720
Step-by-step explanation:
the length of the house is 1,200 feet and 1,100 feet wide. what is the perimiter
Answer:
4,600
Step-by-step explanation:
1,200+1,200+1,100+1,100
Which of the following statements is most correct? Select one:
a. Other things equal, the higher the dividends, the lower the stock price.
b. Other things equal, the investment holding period does not affect the stock price.
c. Other things equal, the higher the required rate of return, the higher the stock price. d. Other things equal, the higher the dividend growth rate, the lower the stock price.
e. Other things equal, the lower the market value of debt, the lower the value of equity.
Answer:a
Step-by-step explanation:
the answer is a because it is
Addison plays 6 songs in of an hr. How many
songs can she play for 4 hours?
Answer:
24
Step-by-step explanation:
4x6=12or 2x6=12so then 12+12=24
Answer:
6 songs per hour, so multiply that with the number asked which is four
so four times six is24
so she can play 24 songs in four hours!
~ ...
~ !
~ !
When you have > or <, the solutions are only in the shaded area.
True
or
False
Answer: True
Step-by-step explanation: Because the solutions can not land on the dotted lines.
A water tank has volume of 300 m3. If the length and width of the tank is 5 m and 300 cm, find the height of the tank.
Answer:
volume=300m3
length=5m
width=300cm=300/100=3m
To find: height of tank .
so,
volume=l×b×h
300=5×3×h
300/15=h
finally,h=20m
PLEASE HELP WITH THE FOLLOWING
Answer:
2a:
[tex]a^6+\frac{64}{125} =(a^2)^3+(\sqrt[3]{\frac{64}{125} })^3[/tex]
Now, we can apply the sum of cubes formula that goes:
[tex]x^3+y^3=(x+y)(x^2-xy+y^2)[/tex]
Therefore,
[tex](a^2)^3+(\sqrt[3]{\frac{64}{125} })^3=(a^2+\frac{4}{5})(a^4-\frac{4a^2}{5}+(\frac{4}{5} )^2)[/tex]
[tex]=(a^2+\frac{4}{5})(a^4-\frac{4a^2}{5}+\frac{16}{25} )[/tex]
---------------------------------------------
2b:
[tex]16x^8-y^4=(4x^4)^2-(y^2)^2[/tex]
Now, we can apply the difference of two squares formula that goes:
[tex]x^2-y^2=(x+y)(x-y)[/tex]
Therefore,
[tex](4x^4)^2-(y^2)^2=(4x^4+y^2)(4x^4-y^2)[/tex]
You can apply the difference of two squares formula again:
[tex](4x^4+y^2)(4x^4-y^2)=(4x^4+y^2)((2x^2)^2-y^2)[/tex]
[tex](4x^4+y^2)(4x^4-y^2)=(4x^4+y^2)(2x^2+y)(2x^2-y)[/tex]
If Damien works for 10 hours each week and he made $123.60
for the week, how much was he making per hour?
Answer:
12.36
Step-by-step explanation:
Answer:
1 hour = $12.36
Step-by-step explanation:
10 hours = $123.60
=> 10/10 hours = 123.60/10
=> 1 hour = $12.36
Hoped this helped.
There are 14 girls and 15 boys in a sixth grade math class. What is the ratio of girls to total students?
Latonya swims 50 meters in 1/2 minute. What is the slope
Answer: 100
Step-by-step explanation: 50 x 1/2=100
Precalc please help!!
Answer:
Step-by-step explanation:
Kayla is serving vegetables at a soup kitchen. She has 18 carrot sticks and 12 baby potatoes that she wants to divide evenly, with no food left over. What is the greatest number of plates Kayla can prepare?
Group of answer choices
18
12
6
3
Answer: 6
Step-by-step explanation:
18/2=6=12/2
Answer:
6
Step-by-step explanation:
She could put 3 carrots on each plate: 18/3=6. And 2 baby potatoes on each plate: 12/2=6. So, she can make a maximum of 6 plates of veggies. Hope this helps. :D
Highland Park is located between two parallel streets, Walker street and James Avenue. The park faces Walker Street and is bordered by two brick walls that intersect James Avenue at point C, as shown below. Walker St. Highlands Park brick wall brick wall 60 James Ave. What is the measure, in degrees, of ZACB, the angle formed by the park's two bri walls?
Applying the definition of alternate angles and angles on a straight-line: m<ACB = 84°.
Recall:
Alternate angles are congruent and have equal angle measures.Angles on a straight-line = 180 degrees.The diagram showing the information and sketch of the Highland Park is attached below (see attachment).
Thus:
m<BAC = 36° (given)
m<BCE = 60° (given)
<ACD = <BAC (alternate angles)
Therefore,m<ACD = 36°
m<ACB = 180° - (m<ACD + m<BCE) (angles on a straight-line)
Substitutem<ACB = 180° - (36° + 60°)
m<ACB = 84°
Thus, applying the definition of alternate angles and angles on a straight-line: m<ACB = 84°.
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(10 points!!!) AND I’LL MAKE YOU BRAINLEST
I ALREADY KNOW THE ANSWER I JUST WANT THE EXPLANATION!!
The answer is ( Jose, $901.31 more)
Janell deposits $2,000 and for 5 years leaves it in an account earning 3% annual interest, compounded quarterly. For 5 years, José saves and deposits $150 per quarter in an account earning 3% interest compounded quarterly. Who will have more money in the account after 5 years? How much more?
Use the table below to answer:
Answer:Jose will make 901.31 more
Step-by-step explana
What is the value of 1027
A. 100
B. 1,000
C. 10,000
D. 100,000
Answer:
huh? this doesn't even make sense or I'm just tripib
Step-by-step explanation:
-xoxo
I need some help math
Answer:
ok I will help you please wait for some time
Answer:
23
Step-by-step explanation:
Add the total number of hours in the given situation
Mariam only saves quarters and dimes. She has already saved 13 quarters and 5 dimes. She wants to purchase a book that costs 7.75. Not including the money she already has, what combinations of quarters and dimes could Mariam save so she has exactly enough money to buy the book?
Answer: 8 Quarters, 20 Dimes
Quarters:
Current/ 13
13x25= 3.25
Dimes:
Current/ 5
5x10= 50 …. 50 cents
Current price: $3.75
Need $4.00
What you need:
Quarters: +8
4 = 100 x2 is 200 …. $2.00
Dimes: + 20
10 = 100 x2 is 200 … $2.00
what is equation of the line shown in this graph
Since this is a horizontal line, the equation for this is simply
[tex]y = -3[/tex]
Vhich number line represents the solution of 4x - 9> -21?
Answer:4x -9 >= -21
4x >= -12
x >= -12/4
x >= -3
so this number line started with -3 and go away till + infinity
hope this will help you
Step-by-step explanation:
5^-x = 6
Help ASAP
STEPS MUST.
We have to Find:
The value of x[tex] \sf \longmapsto5^{ - x }= 6[/tex]
Let's start.
Take Logarithm of both sides[tex] \sf \longmapsto log(5^{-x}) = log(6) [/tex]
Solving Further[tex] \sf \longmapsto - x \: log(5) = log(6)[/tex]
[tex] \sf \longmapsto - x = \dfrac{ log(6) }{ log(5) } [/tex]
Take the minus from (-x) and put in on log(6)[tex] \sf \longmapsto \: x = \dfrac{ -log(6) }{ + log(5)} [/tex]
Done