!! 100 PTS+BRAINLIEST 4 CORRECT ANSWER+EXPLANATION!!
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[tex]\text{Given that,}\\\\f(x)= \dfrac{x+1}{x-1}\\\\\\f'(x)=\lim\limits_{h \to 0} \dfrac{f(x+h) - f(x) }{h}\\\\\\ ~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\left( \tfrac{x+h+1}{x+h-1}\right) - \tfrac{x+1}{x-1}}{h}\\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{(x+h+1)(x-1) - (x+1)(x+h-1)}{(x+h-1)(x-1)}}{h} \\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{x^2-x+hx-h+x-1 - x^2-xh+x-x-h+1}{(x+h-1)(x-1)}}{h}\\\\\\~~~~~~~~[/tex]

       [tex]~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{-2h}{(x+h-1)(x-1)}}{h}\\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{-2}{(x+h-1)(x-1)}\\\\\\~~~~~~~~=\dfrac{-2}{(x+0-1)(x-1)}\\[/tex]

       [tex]\\\\~~~~~~~~=\dfrac{-2}{(x-1)(x-1)}\\\\\\~~~~~~~~=\dfrac{-2}{(x-1)^2}[/tex]

You have something resembling a Riemann sum. Multiply through the summand by 1/n², then you can write

[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{r=0}^{2n-1} \frac{1}{1+4\left(\frac rn\right)^2} = \int_0^2 \frac{dx}{1+4x^2} = \boxed{\frac12 \tan^{-1}(4)}[/tex]

Answer:

x=1/4 Y=-1/2 z=1/3

Step-by-step explanation:

due to large fractions the answer is explained in the image above

the piece-wise function is, -x - 5 when x ≠ -2

and when x = -2, the function's value is -2

what that means is when x = -4, the subfunction of -x - 5 is the one to use, because x = -4 is in that range

so f(-4) = -(-4) - 5 => f(-4) = -1.

so the function's graph look more or less like the one below, with a solid line going but with a gap at x = -2.

Answer:

49/3 or 16.33...

Step-by-step explanation:

15 + 4/3.

15/1 + 4/3

45/3 + 4/3.

ANSWER: 49/3

Two hemispheres will be equal to a spheres, hence the volume of 10 hemispheres is 266.581 cubic inches

Given Data

Let us find the volume of sphere

Volume = 4/3 *πr^3

Volume = 4/3*3.124* 4^3

Volume = 4/3*3.124*64

Volume =266.581 cubic inches

Learn more about hemispheres here:

https://brainly.com/question/25641436

Answer:

7

Step-by-step explanation:

Equation: (3*8-3)/3

Step 1: (24-3)/3

Step 2: 21/3

Step 3: 7

Order of operations is used in this equation. You simplify the terms in the parentheses before the other terms in the equation. According to the order of operations (parentheses, exponents, multiplication, division, addition, and subtraction, you do the multiplication before the subtraction in the parentheses. Then you subtract your three from your multiplication result (twenty-four). This leaves you with 21. Finally, you divide twenty-one by three. This gets you seven.

Answer:

80 cm²

Step-by-step explanation:

Let's break down the composite shape into two parts. (Image attached)

⇒ The side length of "a" is 4 cm.

⇒ The side length of "b" is 8 cm.

First, let's find the area of square "a". Keep in mind that the area of a square is the side multiplied by itself.

⇒ (Side)² = A

⇒ (4)² = Area of "a"

⇒ (4)(4) = Area of "a"

⇒ 16 cm² = Area of "a"

Next, find the area of square "b". Keep in mind that the area of a square is the side multiplied by itself.

⇒ (Side)² = A

⇒ (8)² = Area of "b"

⇒ (8)(8) = Area of "b"

⇒ 64 cm² = Area of "b"

Finally, let's sum up the area of square "a" and "b" to find the area of the composite shape.

⇒ Area of composite shape = Area of "a" + Area of "b"

⇒ Area of composite shape = 16 + 64

⇒ Area of composite shape = 80 cm²

Answer:

[tex]y=\frac{1}{4}x-5[/tex]

Step-by-step explanation:

Write an equation of the line in slope-intercept form where slope equals 1/4 and y-intercept equals 0, - 5 ​

Slope-intercept form: y = mx + b

m = slope

b = y-intercept (when x = 0)

Ex:

y = 5x + 2

For our problem:

[tex]y=\frac{1}{4}x-5[/tex]

Hope this helps!

Answer:

-41 degrees

Step-by-step explanation:

Since we're getting colder you would subtract 24 from the current -17 degrees.
-17-24 = -41

Answer: 12 1/28

Step-by-step explanation:

Add whole numbers. Solve fractions by finding the LCD.

Step-by-step explanation:

x > 5, both terms are positive

x < - 5, both terms are negative

This is not clear

If x>5

Hence..

If x<-5 terms are negative

If x=-5

Answer:

The second expression

Step-by-step explanation:

[tex]\sum_{n=3}^{20}{n(n+1)}=\sum_{n=3}^{20}{(n^2+n)}=\sum_{n=3}^{20}n^2+\sum_{n=3}^{20}n[/tex]

You can split up sums.

Answer:   5 personal training sessions

Step-by-step explanation:

Given only 1 month, then set the 2 equations equal to each other, given that x=# of personal training sessions:

    25+45x = 75 + 35x

    -25-35x    -25-35x

    So, 10x=50; divide both sides by 10, to get:

           5, so, 5 personal training sessions per month to make the 2 costs equal to one another.

Answer:

Camille can make 6 cards and will have 2 ribbons left

Step-by-step explanation:

Answer:

THE ANSWER IS 7/4

Step-by-step explanation:

Step-by-step explanation:

[tex]5 \times \frac{7}{20} \\ = \frac{35}{20} \\ = \frac{7}{4} [/tex]

answerr......

Answer:

Option D

Step-by-step explanation:

[tex]6\dfrac{3}{5}*\dfrac{5}{8}=\dfrac{5}{8}*6\dfrac{3}{5}[/tex]

Poperty : Commutative property of multiplication.

When two numberes are multiplied, changing the order of numbers  will not change the result.

Answer:

x=6

Step-by-step explanation:

The first thing you should start with is distributing the 6 inside the parentheses, which would give us (12x - 66) + 15 = 21. Now we can add like terms on this side of the equation to get: 12x -51 = 21. Add the 51 to the right side to get 12x = 72, then divide both sides by 12 to get x = 72/12 or 6.

x=6

Hope this helps!

Marking this brainliest also helps me out too :)

Answer:

True

Step-by-step explanation:

A ratio is normally written using whole numbers only, with no units, in its simplest form. The numbers in a ratio must be written using the same units.

e.g. ratio of 1:2

False, ratio's do no have units.

Answer:

50% or 1/2

Step-by-step explanation:

The probability of grabbing either colored block from the bag is 50% or 1/2.

Answer: I dont know if im right for sure but the answer should be 4

Step-by-step explanation

8 goes into 2 4 times (8 divided by 2 = 4)

Each child ate 2 pieces (4-2=2)

so therefore for it to be 2 pieces left over there were 4 kids I think.

Answer:

11

Step-by-step explanation:

So each pizza has 8 equal slices but we don't know the amount pizzas but we can find it by doing this ⬇️

1 pizza= 8 slices

3 pizzas = x

you cross multiply it and it will end up as 3×8= 24 slices.

now each kid ate 2 pieces and there was a leftover of 2

therefore, 24-2= 22 pieces divided 2 is 11

or; 3×8=24-2=22÷2=11

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Answer:

......................

Step-by-step explanation:

Answer:

20times bc u times 5 by 10 then divide 8 u get 6.2

Answer:

1. 3 hours   2. 150 ft

Step-by-step explanation:

1. a) 50 + 60 + 60 + 60 = $230 = 3 hours

  b) 80 + 50 + 50 + 50 = $230 = 3 hours  

  Answer: 3 hours

2. 10 * 5 * 3 = 150 ft

Answer:1 3 hours 2 150

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

1) Calculating the numerator value

2) Calculating the denominator value

The solution will be in the form :

Answer:

about 49.3 inches

Step-by-step explanation:

[tex]42 \times {1.055}^{3} = 49.318[/tex]