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).
help quick due in 10 minutes you will be reported if you spam Ivan is 75 inches tall if his brother Logan was 5 inches shorter, he would be exactly half Evan's height How tall is Logan? Enter your answer as a decimal in the box,
Answer:
42.5 inches
Step-by-step explanation:
Ivan is 75 inches tall, and Logan would be half his size, 37.5 that is, if he were 5 inches shorter. That means logan is 42.5 inches.
Answer:
Logan is 42.5 inches
Step-by-step explanation:
half of Ivan is 37.5
Logan is 5 inches taller than 37.5 so 42.5
Hope this helps!
Let me know if it does and if the answer is right
Determine whether the graphs of given pair of equations are parallel,
perpendicular, or neither. 2x+5y=15
3x+5y=15
Answer:
Neither because x can't equal 3 and equal 2 at the same time and 2x + 5y doesn't equal 3x + 5y. 3x is > 2x by one x
Step-by-step explanation:
Hope this answer works for you!
A rope is 225 centimeters long.
You need the rope to be 1.5 meters long.
How many centimeters should you cut off?
Answer:
1.5 meters = 150 centimeters (multiply by 100)
Therefore, you should cut off [tex]225-150=75[/tex] centimeters.
Use the commutative property to simplify the expression 1/8 x 2/5 x 16?
A. 16 x 1/8 x 2/5 = 2x 2/5 = 4/5
B. 2/5 x 1/8 x 16 = 2/40 x 16 = 3/4
C. (1/8 + 2/5) x 16 + 32/5
D. 1/8 x (2/5 x 16) = 2/5
(1 point) In how many ways can 3 different novels, 2 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can be arranged in any order
Answer:
3 ways
Step-by-step explanation:
three ways it can be arranged on the bookshelf three different novels, two different mathematic, books 1 Biology book are 1 Biology book, two different mathematic books, three different novel books are two different mathematic books three different novel books 1 Biology book arranged on the bookshelf if a the book can be arranged in any order
A recipe for cinnamon rolls calls for 3 cups of flour for every cup of water. Using the same recipe, how much water will you need for 5 cups of flour?
How many cups of water will you need for 5 cups of flour?
Answer:
5/3 cups of flour
Step-by-step explanation:
3/1=5/x x representing the amount of water
cross multiply: 3x=5
divide by 3: x=5/3
please i need help
How many rows of seats are inside the theater? Enter your answer in the box.
Answer:
24 rows
Step-by-step explanation:
384 seats in total, and 16 chairs in a row, so 384/ 16=
24 rows
Hope this helps!
LMK if it does
What does X = please help me Asp now
Answer:
13 degrees
Step-by-step explanation:
Because of the alternate interior angles, I know that angle EB is also 77. Now, knowing that it's a right angle, I can subtract 77 from 90 to get 13.
If 7 cats take 7 minutes to catch 7 mice how long will it take for 21 cats to catch 21 mice
Answer:
21 min
Step-by-step explanation:
What is an equation of the line that passes through the points (-2,1) and (6,-7)
The largest frog in the world is the goliath, It can grow to be 12 inches long. The smallest frog in the world is about 2.5% as log as the goliath. About how long is the smallest frog in the world
Answer:
0.3 inches
Step-by-step explanation:
2.5% = 0.025
The smallest frog is 12 * 0.025 inches, which is 0.3 inches.
Below are the graphs of the functions y=2x and y3x What is the same about both lines?
Celia's scores in the 5 quizzes Math are 18,12,15,19. What is her average score in Math?
d. 18
a. 15
c. 17
b. 16
Step-by-step explanation:
(18+12+15+19)÷5
64÷5
15
1. What percent of 120 is 18?
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
120 · 15% = 18
I hope this helps!!
A square is 3 inches by 3 inches. What is its area
Answer:
9
Step-by-step explanation:
Because area is multipication, you need to multiply legth and width. So 3x3=6. Hope it helps! :)
write an equation to represent CJ’s total pay
Answer:
P = 15h
I hope it helps.
which of the following explains why 2/3(x+3)=2/3(x-6)has no solution
Answer:
D. The coefficients are the same, and the constants are different
Step-by-step explanation:
This means that because we have the same coefficient (2/3), if we wanted the same equation, the constants (x +/- #) would have to be the same, and since they are not in this instance, that makes the equation false, and therefore has no solution
write the percent as a decimal .84
Answer: 84%
Step-by-step explanation:
Someone help me pls
Answer:
-1 = 2(-1 -1) = -4
0 = 2(0-1) = -2
1 = 2(1-1) = 0
2 = 2(2-1) = 2
Step-by-step explanation:
x = the number on the left column
for the middle colum, you need to do 2(x -1)
for the right column, you do : (x - 1) x 2)
A Subchapter S corporation:
is similar to a partnership in that it carries unlimited liability.
is a separate legal entity which is treated like a normal corporation.
has all the organizational benefits of a corporation and its income is only taxed once.
all of the above.
Evaluate the expression -2
Answer: 2x for x=3: 2(3) = 6.
Step-by-step explanation:
What is the equation of the line in slope-intercept form?
Answer:
y=3/5x+3
Step-by-step explanation:
3 is the y-intercept so that is the "b". To find the slope simply use rise/run.
how many times can 2 go into 67
fourth grade help
Answer:
Step-by-step explanation:
To answer this, divide 67 by 2, writing the answer as a mixed number:
67
---- = 33 1/2
2
thus, 2 can go into 67 33 times, keeping in mind that there's a remainder (1/2).
Please help and give real answers it would be much appreciated
Answer:
x = 8, x = 10
Step-by-step explanation:
[tex]\sqrt{4x - 31}[/tex] = x - 7 ( square both sides )
4x - 31 = (x - 7)² ← expand using FOIL
4x - 31 = x² - 14x + 49 ( sub 4x - 31 from both sides )
0 = x² - 18x + 80 ← in standard form
0 = (x - 8)(x - 10) ← in factored form
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x - 10 = 0 ⇒ x = 10
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 8
left side = [tex]\sqrt{4(8)-31 }[/tex] = [tex]\sqrt{32-31}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 8 - 7 = 1
Then x = 8 is a solution
x = 10
left side = [tex]\sqrt{4(10)-31}[/tex] = [tex]\sqrt{40-31}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = 10 - 7 = 3
Then x = 10 is a solution
50 Points! Please only answer if you know! Thank you.
Graph the system of linear inequalities. Your graph should demonstrate that you're following the instructions below.
Use x- and y- intercepts to graph inequality A.
Use point-slope form to graph inequality B.
A) 3x - 9y > 27
B) (y-3) ≤ -4/3 (x+7)
Show ALL work and EXPLAIN all your steps.
Thank you for helping me understand this.
Answer:
See belowStep-by-step explanation:
A) 3x - 9y > 27
x- intercept at y = 0 is:
3x = 27x = 9y-intercept at x = 0 is:
- 9y = 27y = -3Connect the two points (9, 0) and (0, -3) with dotted line (because of <) and shade below line (because y < ).
B) (y-3) ≤ -4/3 (x+7)
Use one point from the equation:
(-7, 3)Find the second point using the slope - 4/3, add 3 to x and - 4 to y:
x = -7 + 3 = - 4y = 3 - 4 = - 1Connect these two points (-7, 3) and (-4, -1) with solid line (because of ≤ ).
Shade the area below the line (because y ≤ ).
A rectangular plot of land is 100 feet long and 50 feet wide. How long is the walkway along the diagonal? Round to the nearest foot.
A.
75 feet
B.
87 feet
C.
112 feet
D.
150 feet
Answer:
C
Step-by-step explanation:
Pythagorean theorem
A^2 + B^2 = C^2
4) 4+ 1 =
a) 5
b) 572
12
c) 51
d) 572
6
12
Answer:
4+1=5
Step-by-step explanation:
Note down the below rules
(+)(+)=(+)(-)(+)=(-)(+)(-)=(-)(-)(-)=(+)what is the probability of a 200 year flood this year
Answer:
0.5 chance
Step-by-step explanation:
Likewise, the term "100-year storm" is used to define a rainfall event that statistically has this same 1-percent chance of occurring.
Answer:
0.5
Step-by-step explanation:
The possibility are very very very low, but never a no
PLEASE HELP ME IN THIS, THIS ASSIGNMENT IS DUE IN 4 MINUTES, ITS A 6TH GRADER QUESTION
Answer:
3
Step-by-step explanation:
jesushhhh
A right triangle is shown in the graph. Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points) Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points) Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)
Answer:
Part A, write out the equation by subtracting the vertex from x and y, then set it equal to the radius square. All of this information is given in the picture. Then the domain is all the x's and the range is all the y's starting at the center and going out 10 in each direction since 10 is the radius.
Step-by-step explanation:
Use the circle formula that you learned in lesson 3.02 using the given points. Remember this quiz was open note and your formula should be in your notes. Also, it should be familiar to you from Geometry and middle school math where you first learned about circles:)