Henry can run 2.5 miles in 1/4 of an hour if he maintains the same pace how many miles can Henry run in 1 1/2 hours

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:

Step 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).

Replace f(x) with y:

Switch x and y:

Subtract 3 from both sides:

Multiply both sides by 6 to isolate y:

6x - 18 = y

Replace y with f'(x):

f'(x) = 6x - 18  ⇒ This is the inverse function of f(x).

Replace 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).

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).

Answer: ???

Step-by-step explanation:

Answer:

The quotient is 10x+16

The remainder is 28x^2+10x+22

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:

Answer:

down - up +

Step-by-step explanation:

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!

~ ...

~ !

~ !

Answer:

A

Step-by-step explanation:

Because the x doesn't repeating

Hope it can help you lovelots

#LEARN WITH BRAINLY

Answer:

17 = e^2.8332

Step-by-step explanation:

Answer:

Step-by-step explanation:

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.

Learn more about power rule,

https://brainly.com/question/23418174

#SPJ6

Answer:

huh? this doesn't even make sense or I'm just tripib

Step-by-step explanation:

-xoxo

Answer:

The amount of discount is $120

The sale price is $480

Step-by-step explanation:

The amount of discount = Original price × the Percentage off

The amount of discount = $600 × 20 %

The amount of discount = $600 × .20

The amount of discount = $120

The sale price = Original price - Discount

The sale price = $600 - $120

The sale price = $480

Answer:

f^-1(x) = [ln (x + 4)]/2

Step-by-step explanation:

f(x) = e^(2x) - 4

y = e^(2x) - 4

x = e^(2y) - 4

x + 4 = e^(2y)

ln (x + 4) = ln (e^(2y))

ln (x + 4) = 2y

y = [ln (x + 4)]/2

f^-1(x) = [ln (x + 4)]/2

Answer: Thus, after the transformation, the graph consists of points (x,y) satisfying y=2(x−3)2. This is the equation of the transformed graph.

Step-by-step explanation:

Consider the graph y=x2. Suppose the graph is dilated from the x-axis by a factor of 2, and then translated 3 units to the right. What is the equation of the resulting graph?

Solution

The transformation given is Trans(3,0)∘Dilx-axis,2. Denote by (x′,y′) the image of a point (x,y) under this transformation. A point (x,y) is sent to (x,2y) by the dilation, and then to (x+3,2y) by the translation, so (x′,y′)=(x+3,2y).

The original graph consists of points (x,y) such that y=x2. Then it is transformed so that (x,y)↦(x′,y′)=(x+3,2y). We must find what equation is satisfied by x′ and y′.

Since x′=x+3 and y′=2y, we have x=x′−3 and y=y′/2. Thus y=x2 implies

y′2=(x′−3)2or equivalentlyy′=2(x′−3)2.

[tex](a)\\\\m=6.1\times 10^{-5},~~ t=1.7 \times 10^{-6} \\G = \sqrt{\dfrac{m}{t^2}} = \sqrt{\dfrac{6.1\times 10^{-5}}{\left(1.7 \times 10^{-6}\right)^2} } ~=4590\\\\\\(b)\\\\m=6.1\times 10^{-5}(1+ 8\%) = 6.1\times 10^{-5}(1+0.08) = 0.0000648\\\\t=1.7\times 10^{-6}(1+ 5\%)= 1.7\times 10^{-6}(1+0.05) =0.000001785\\\\\\G=\sqrt{\dfrac{m}{t^2}} = \sqrt{\dfrac{0.0000648}{(0.000001785)^2}}=4510[/tex]

If f(x) = g(x)

Then :

(x-4)/(x²+1) = (x² - 4) / (x²+ 1)

We can simplify on both sides by x² + 1 :

x - 4 = x² - 4

x = x²

x - x² = 0

x(1-x) = 0

So either x = 0, or x = 1

S = {0,1}

Good Luck

Answer:

Step-by-step explanation:

( x , y )

( 0 , - 4 )

( 1 , - 1.5 )

[tex]y_{1}[/tex] = - 4

[tex]y_{2}[/tex] = - 1.5

Answer:

m = -6 (slope)

b = (1/2)

The Y posistion is (0, 0.5) and the slope of the graph is -6/1 (down 6, right 1).

Some examples of where the line is could be:

(1, -5.5)

(-1, 6.5)

Anwser: 12 feet long

Answer:

pulmonary function is the blood or gas flow from or to the lungs

Step-by-step explanation:

the lungs take in oxygen and take out c02

The lungs' main role is to bring in air from the atmosphere and pass oxygen into the bloodstream. From there, it circulates to the rest of the body. Help is required from structures outside of the lungs in order to breathe properly.

Answer:

i think it would round to 4031.08

Step-by-step explanation:

3200.00 * 1.08^3

=4032.0784

Answer:

0.014

Step-by-step explanation:

Minused old price from New then divided the answer by the old price then divided that by 6 to get yearly inflation

Answer:

Knewton as of May 15, 2022 8.70%

Step-by-step explanation:

Answer: True

Step-by-step explanation: Because the solutions can not land on the dotted lines.

Answer:

I think 25.5678

it's the correct answer

Step-by-step explanation:

gamsahamnida

Answer: 100

Step-by-step explanation: 50 x 1/2=100

Answer:

Step-by-step explanation:

The volume of the tank= (50x30X20) cm^3

                                       = 30000cm^3

                                       = 30 l

1 l costs 300 tk

therefore 30 l costs= 30X300 taka

                                = 90000 taka

Using the given confidence interval, it is found that the correct option is:

The 95% confidence interval is (0.289, 0.416).

Using the above justification, the correct option is:

A similar problem is given at https://brainly.com/question/17097944