hello please help will give brainliest!

Answer:A

Step-by-step explanation:

yes

Answer:

Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

\(\rm \: f(x) = log(1 + x) - \dfrac{2x}{x + 2}\)

~Let first define the domain of f(x).

\({ \underline { \underline{ {\rule{200cm}{0.4cm}}}}}\)

\(\sf \: f(x) = log(1 + x) - \dfrac{2x}{x + 2}\)

w. r. t. x, we get

\(\rm {\: \longmapsto\dfrac{d}{dx}f(x) =\dfrac{d}{dx}\bigg[ log(1 + x) - \dfrac{2x}{x + 2}}\)

\(\boxed{\sf{ \longmapsto\dfrac{d}{dx}logx \: = \: \dfrac{1}{x}}}\)

\(\boxed{\sf{\longmapsto \dfrac{d}{dx} \dfrac{u}{v} = \dfrac{v\dfrac{d}{dx}u \: - \: u\dfrac{d}{dx}v}{ {v}^{2} } \: }}\)

~So, using these results, we get

\(\sf {\:\longmapsto f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)\dfrac{d}{dx}2x - 2x\dfrac{d}{dx}(x + 2)}{ {(x + 2)}^{2} }}\)

\(\boxed{\rm{\longmapsto \dfrac{d}{dx}x = \sf \pink{ 1 \:} }} \)

And-

\(\begin{gathered}\boxed{\sf{\longmapsto\dfrac{d}{dx}k = 0 \: }} \\ \end{gathered}\)

☼︎~So, using this result, we get

\(\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)2 - 2x(1 + 0)}{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)2(x+2)2−2x(1+0)

\(\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)2 - 2x(1 + 0)}{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)2(x+2)2−2x(1+0)\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{2x + 4 - 2x}{ {(x + 2)}^{2} }\)

\(\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{4 }{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)24\)

\(\rm \: f'(x) = \dfrac{ {(x + 2)}^{2} - 4(x + 1)}{(x + 1) {(x + 2)}^{2} }\)

\(\rm \: f'(x) = \dfrac{ {x}^{2} + 4 + 4x - 4x - 4}{(x + 1) {(x + 2)}^{2} }\)

\(\rm \: f'(x) = \dfrac{ {x}^{2} }{(x + 1) {(x + 2)}^{2} }\)

\(\longmapsto\rm {\: {x}^{2} \geqslant 0x2⩾0}\)

\(\longmapsto\sf\:{(x+2)}^{2} > 0\)

\(\longmapsto\sf\: x + 1 > 0x+1>0\)

\(\sf\longmapsto \:\rm \: f'(x) = \dfrac{ {x}^{2} }{(x + 1) {(x + 2)}^{2} } \geqslant 0\)

\({ \underline { \underline{ \bold {\rule{200cm}{0.4cm}}}}}\)

\(\boxed{\begin{array}{c|c} \bf f(x) & \tt \dfrac{d}{dx}f(x) \\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf 0 \\ \\ \sf sinx & \sf cosx \\ \\ \sf cosx & \sf - \: sinx \\ \\ \sf tanx & \sf {sec}^{2}x \\ \\ \sf cotx & \sf - {cosec}^{2}x \\ \\ \sf secx & \sf secx \: tanx\\ \\ \sf cosecx & \sf - \: cosecx \: cotx\\ \\ \sf \sqrt{x} & \sf \dfrac{1}{2 \sqrt{x} } \\ \\ \sf logx & \sf \dfrac{1}{x}\\ \\ \sf {e}^{x} & \sf {e}^{x} \end{array}}\)

\({ \underline { \underline{ \bold {\rule{200cm}{0.3cm}}}}}\)

Answer:

Find f(g(x)):

f (-2x) = 2

Find g(f(x)):

g (2) = -4

Step-by-step explanation:

Set up the composite function and evaluate.

Answer:

B

Step-by-step explanation:

The only decreasing function if we don't take -/+ into account which indicates it's absolute value is less than 1

Answer:

60

Step-by-step explanation:

12x5 is equal to 60

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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Answer:

She did not add 5 to 30. ... Mona subtracted 5 where she should have divided 5.

Step-by-step explanation:

Answer:

B. She did not divide 30 by 5

Step-by-step explanation:

This is the only way to cancel out the 5 and get the variable alone

Answer:

0.75 inches is the correct answer

Answer:

0.75 inches

The coin is 0.75 inches (19.05 mm) in diameter and 0.0598 inches (1.52 mm) in thickness.

Answer:

The ratio is 6

Step-by-step explanation:

10×10+24×24= third side ×third side

third side ×third side =100+576

third side × third side=676

third side=√676

third side=26

Answer:

29 miles were used per gallon

Step-by-step explanation:

257 / 9 = 28.555..

We can round 28.555 to about 29.

So John got 29 miles per gallon.

Answer:

-3, -4, -5

Step-by-step explanation:

x = 1st integer

x+1 = 2nd integer

x+2 = 3rd integer

x+x+1 = 3(x+2)

2x + 1 = 3x + 6

1 = x + 6

-5 = x

-4 = x+1

-3 = x+2

Answer:

Try contacting the Help center located at the bottom part of the home page of this site. It is recoverable as long as no violation committed

answer: 8.75ft

Step:

7/12*15

=8.75

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

There are 16 buses

Step-by-step explanation:

HOPE THIS IS HELPFUL!!!

Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have

f^(-1)(f(x)) = x

Differentiating with the chain rule gives

(f^(-1))'(f(x)) f'(x) = 1

so that

(f^(-1))'(f(x)) = 1/f'(x)

Let x = a; then

(f^(-1))'(f(a)) = 1/f'(a)

(f^(-1))'(b) = 1/f'(a)

In particular, we take a = 2 and b = 7; then

(f^(-1))'(7) = 1/f'(2) = 1/5

The function f(x) is an increasing function about which little else is known about other than f(2)=7 and f'(2)=5. Then the value of (f⁻¹)'(7) is 1/5

To find (f⁻¹)'(7), we can use the inverse function theorem. The formula for the derivative of the inverse function is given by:

\((f^{-1})'(y) = \frac{1}{f'(x)},\)

where y = f(x). Since we know that f(2) = 7 and f'(2) = 5, we have x = 2 and y = 7. Substituting these values into the formula:

\((f^{-1})'(7) = \frac{1}{f'(2)} = \frac{1}{5}.\)

Therefore,

\((f^{-1})'(7) = \frac{1}{5}.\)

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Answer:

Yes

Step-by-step explanation:

They are on the same shape, the triangle at the bottom. Coplanar means that they are on the same shape/plane.

Answer:

x=12

Step-by-step explanation:

As a straight line is equal to 180. Here, we have one angle given, which is 134. So,

w+134=180

w=46

And the sum of all the angles of a triangle is equal to 180.

By adding all the angles,

8x-10+5x-12+46=180

13x-22+46=180

13x+24=180

13x=180-24

13x=156

x=156/13

x=12

Step-by-step explanation:

➝8x-10+5x-12=134

➝8x+5x-10-12=134

➝13x-22=134

➝13x=134+22

➝13x=156

➝x=156/13

➝x=12

The lower absolute value in negative will be greater than the higher negative so -4 > -5 is correct thus option (E) will be correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

In a negative value, a number will be very less if the magnitude is high.

For example, -100 is very less than -20.

Therefore, the lower absolute value in the negative will be greater than the higher negative.

-4 is a lower absolute value so it will be greater than -5

Therefore, -4 > -5 will be correct.

Hence "Since the higher negative will always be smaller than the lower negative, -4 > -"5

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Answer:

h(6) = 8

Step-by-step explanation:

h(6) is find the value of the function when x=6

What is the y value  ( the value of the blue line) when x=6

Go to x=6 and go up to the blue line

y =8

h(6) = 8

Answer:

At X = 6 , h(X) = 8

plug the value of x

h (6) = 8

please see the attached picture..

Hope this helps...

Good luck on your assignment...

The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10

Answer:270

Step-by-step explanation:3/5 * 450  reduce the lowest term 3 * 90  calculate first two terms : 270

A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.

library(UsingR)

attach(normtemp)

print(normtemp)

hist(normtemp$temperature)

shapiro.test(normtemp$temperature)

qqnorm(normtemp$temperature)

qqline(normtemp$temperature)

We can observe that the data follows a normal distribution from the histogram and q plot.

The points in the q plot fall on a straight line and correspond to a normal distribution.

P-value = 0.2332, P>0.05, from the Shapiro test

hence, we fail to reject null htpothesis.

On accepting the null hypothesis we get to know that the data follows normal distribution.

The output for the given code will be ,

data: normtemp$temperature

t = 1527.9, df = 129, p-value < 2.2e-16

alternative hypothesis: true mean ≠0

90 percent confidence interval:

98.14269 98.35577

sample estimates:

mean of x

98.24923

Therefore , we can conclude that ,

The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.

98.6 is not included in the 90% confidence interval.

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Answer:

\(\frac{1}{10}\)

Step-by-step explanation:

Answer:

The Answer is gonna C.Computing and reporting net cash provided or used by investing activities.

Step-by-step explanation:

I hope I helped

The distance after 45 minutes is 35 miles and the distance after 75 minutes is 55 miles

The table of values is given as:

t (minutes) 15,30,45,60,75

f(t) (miles) 5,20,35,50,55

The above means that the variable f is a function of t

i.e f(t) and the inverse function is f-1(t)

From the table of values, we have:

f(45) = 35

This means that the distance after 45 minutes is 35 miles

Also,

From the table of values, we have:

f-1(55) = 75

This means that the distance after 75 minutes is 55 miles

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a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have

\(\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}\)

so both conditions are met and f(y) is indeed a PDF.

b) The probability P(Y > 4) is given by the integral,

\(\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}\)

c) The mean is given by the integral,

\(\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy\)

Integrate by parts, with

\(u = y \implies du = dy\)

\(dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}\)

Then

\(\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)\)

\(\displaystyle \cdots = \int_0^\infty e^{-\frac y4} \, dy\)

\(\displaystyle \cdots = -4 \left(\lim_{y\to\infty} e^{-\frac y4} - e^0\right) = \boxed{4}\)