Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1). an algebra tile configuration. 4 tiles are in the factor 1 spot: 2 are labeled negative x and 2 are labeled negative. 3 tiles are in the factor 2 spot: 2 are labeled x and 1 is labeled negative. 12 tiles are in the product spot: 4 are labeled negative x squared, 4 are labeled negative x, 2 are labeled x, and 2 are labeled . which is true regarding adi’s use of algebra tiles?

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Descriptive statistics summarize numbers and inferential statistics determine whether the results are significant.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

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Answer:

[tex]\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]

Step-by-step explanation:

Setting the expression equal to zero to find the roots,

[tex]3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}[/tex]

This means that

[tex]3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]

For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.

A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.

The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.

A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.

Given 300 2   and p 0.45

p = 0.45 Up

and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287

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The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.

Herein we have two circular sections of equal area, whose expressions are described by the following geometric equations:

Semicircle

A = 0.5π · x²     (1)

Half Semicircle

A = 0.25π · (x + 2)²      (2)

By equalizing (1) and (2):

0.5π · x² = 0.25π · (x + 2)²  

2 · x² = (x + 2)²  

2 · x² = x² + 4 · x + 4

x² - 4 · x - 4 = 0

x² - 4 · x + 4 = 8

(x - 2)² = 8

x - 2 = ±√8

x = 2 ± √8

x = 2 ± 2√2

x = 2 · (1 ± √2)

x = 2 · (1 ± 1.41)

x₁ = 2 · 2.41   ∨   x₂ = 2 · (- 0.41)

x₁ = 4.82   ∨   x₂ = - 0.82

The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.

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The standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.

A standard form polynomial is a polynomial expression written whereby the term with the highest degree or power on a variable is written first in the expression, followed by the least, then the constant of the polynomial comes last.

What is the Volume of a Rectangular Prism?

The Volume of a rectangular prism = (length)(width)(height).

The shipping container is a rectangular prism with the following dimensions:

Length of container = 4x² + 3x

Width of container = x² - 8

Height = 6x + 15

Plug in the values

Volume of container = (4x² + 3x)(x² - 8 )(6x + 15)

Expand

Volume of container = 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x

Thus, using the formula for the volume of a rectangular prism, the standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.

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Answer:

y-9=-4(x+2)

Step-by-step explanation:

The point-slope formula is:

y-y1=m(x-x1)

m=-4 and use the point (-2, 9)

                                       x1    y1

Plug in the information.

y-9=-4(x+2)

This is the equation written in point-slope form using the point (-2, 9).

Hope this helps!

Answer:

20 cm

Step-by-step explanation:

The volume, V, of a cone with radius r and height h is given by the formula

V = [tex](1/3) \pi r^2 h[/tex]

Since it is given that the ratio of h to r is 3/4 we have the relationship

h/r = 3/4 ==> h = (3/4)r

Substituting for h in the volume equation gives us an expression in terms of r

[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]

So the expression simplifies to[tex](1/4)\pi r^3[/tex]

We are given that this volume is 2000π cm³

So

(1/4)πr³ = 2000π

Eliminating π on both sides and multiplying by 4 on both sides gives

r³ = 8000

r = ∛8000 = 20 cm   Answer

Answer:

-93312a²

Step-by-step explanation:

1) Simplify 36³ to 46656.

-2a² × 46656

2) Simplify 2a² × 46656 to 93312a².

-93312a²

Answer:

-1/2

Step-by-step explanation:

The cosine is equal to the x coordinate of the point where the terminal side of the angle intersects the unit circle.

The greatest common factor−5k2 20k − 30 is  [tex]-5(k^{2} -4k-6).[/tex]

To find the greatest common factor:

−5k2 20k − 30.

Factor the expression:   [tex]5(-k^{2} +4k-6)[/tex]

Factor the expression:   [tex]5(-k^{2} -4k+6)[/tex]

Multiply the monomials: [tex]5(k^{2} +4k+6)[/tex]

The greatest common factor: [tex]-5(k^{2} -4k-6).[/tex]

The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]

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The complete question is:

Factor the greatest common factor: [tex]-5k^2+ 20k - 30.[/tex]

a) [tex]-1(5k^2- 20k+ 30)[/tex]

b) [tex]-5(k^2 -4k+ 6)[/tex]

c)[tex]-5k(k^2 - 4k +6)[/tex]

d) [tex]-5(k^2 +4k - 6)[/tex]

The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).

Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).

The greatest common factor (GCF) of a set of numbers exists the biggest factor that all the numbers share.

Given :  −5k² + 20k − 30.

Taking common -5 from each term, we get

−5k² + 20k − 30  = -5 ( k² - 4k + 6 ).

The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).

Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).

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Answer:

Step-by-step explanation:

The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

In this question,

The curves are x = 7 cos(t), y = 4 sin(t) cos(t)

Two tangents at (0, 0)

In this case, the parametric derivative of x and y are expressed in terms of t.

The first derivative dy/dx can be expressed as

[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

Now, dy/dt is obtained by differentiate y with respect to t,

[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]

⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]

Now, dx/dt is obtained by differentiate x with respect to t,

[tex]\frac{dx}{dt} =7(-sin(t))[/tex]

⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]

Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]

At (0,0) x = 0 and y = 0, Then

0 = 7 cos(t)

0 = 4 sin(t) cos(t)

and

cos(t) = 0

sin(t) cos(t) = 0

There are two values between -π and π which satisfy these equations simultaneously are

t = π/2

t = -π/2

The equation of a straight line given a point and its slope is

y-y₀ = m(x-x₀)

The two tangents lies at (0,0), so the equation becomes

y = mx

Then the two straight lines will be

y = m₁x  and

y = m₂x

For t = π/2,

[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]

⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]

⇒ [tex]m_1=\frac{4}{7}[/tex]

For t = -π/2,

[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]

⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]

⇒ [tex]m_2=-\frac{4}{7}[/tex]

Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

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Answer:

Step-by-step explanation:

6 > x² - 5x.

The answer for the inequality is -1 the greater than sign x greater than 6

The interval notation is ( -1,6)

Answer:

[tex]-1 < x < 6[/tex]

Step-by-step explanation:

Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.

Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we consider:

Hence the costs for x hours of moving from each company are given as follows:

For 7 hours, the costs are given as follows:

Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.

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The next step in the process of constructing parallel line CD is C. Set the compass width to the distance between point E and where the arc crosses line AB.

It's important to draw a line parellel to line AB. Then, on should set compasses' width to the distance where the lower arc crosses the two lines.

After that, it's vital to move the compasses to where the upper arc crosses the transverse.

In conclusion, the correct option is C.

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Answer:

The answer is A

Step-by-step explanation:

The areas of the parallelograms can be compared as: A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

A parallelogram refers to a geometrical shape and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Mathematically, the area of a triangle can be calculated by using this formula:

Area = ½ × b × h

Where:

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

Next, we would determine the area of the two parallelograms as follows:

Area of parallelogram 1 = Area of red-rectangular figure - Area of triangle A - Area of triangle B - Area of triangle C - Area of triangle D.

Substituting the given parameters into the formula, we have;

Area of parallelogram 1 = (6 × 6) - (½ × 4 × 2) - (½ × 2 × 4)- (½ × 4 × 2) - (½ × 2 × 4)

Area of parallelogram 1 = 36 - 4 - 4 - 4 - 4

Area of parallelogram 1 = 36 - 16

Area of parallelogram 1 = 20 units².

For parallelogram 2, we have:

Area of parallelogram 2 = Area of blue-rectangular figure - Area of triangle P - Area of triangle Q - Area of triangle R - Area of triangle S.

Substituting the given parameters into the formula, we have;

Area of parallelogram 2 = (8 × 4) - (½ × 2 × 2) - (½ × 6 × 2)- (½ × 2 × 2) - (½ × 2 × 6)

Area of parallelogram 2 = 32 - 2 - 6 - 2 - 6

Area of parallelogram 2 = 32 - 16

Area of parallelogram 2 = 16 units².

Difference = Area of parallelogram 1 - Area of parallelogram 2

Difference = 20 - 16

Difference = 4 units².

In conclusion, we can infer and logically deduce that the area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

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Answer: I believe it is 4m

Step-by-step explanation:

m+m+m+m would be equivalent to 4m which is 4 times m

Step-by-step explanation:

It's like you're adding 1+1+1+1 which equals 4 so that's what I think

Answer:

x=2 and y=-2

Step-by-step explanation:

Solution Given:

6x+2y=8....................................................[1]

12x+y=22....................................................[2]

Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get

equation 1 becomes 12x+4y=16

and subtracting by equation 2 we get

12x+4y=16

-12x-y=-22[Note: while subtracting we must change sigh)

__________________

0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]

3y=-6

dividing both side by 3, we get

3y/3=-6/3

we get y=-2

Again similarly

Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get

equation 2 becomes 24x+2y=44

and subtracting by equation 1 we get

24x+2y=44

-6x-2y=-8

_____________________

18x-0y=36

18x=36

dividing both side by 18, we get

18x/18=36/18

x=2

1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.

2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.

Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.

From the given table it is clear that the total number of the person who is older than 35 years exists 162.

75+x+40 = 162

x+116 = 162

x = 162-116

x = 46

The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.

1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists

P = Probability who is older than 35 years has a hemoglobin level                                                              

     between 9 and 11 / Person who exists older than 35

P = 46/162 = 0.284

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.

2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.

The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists

P = Probability who is older than 35 years has a hemoglobin level  

       between 9 and above / Person who is older than 35

P = 86/162 = 0.531.

The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.

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Answer:

T tof = 2 ( v 0 sin θ 0 ) g . T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.

x=-2

Step-by-step explanation:

Solution Given:

3(x-3) = 5(2x + 1)

Opening bracket we get

3x-9=10x+5

keeping common value in same side

-9-5=10x-3x

-14=7x

x=-14/7

x= -2

Answer:

-2 =x

Step-by-step explanation:

3(x-3) = 5(2x + 1)

To solve for x

Distribute

3x -9 = 10x +5

Subtract 3x from each side

3x-9-3x = 10x -3x+5

-9 = 7x+5

Subtract 5 from each side

-9-5 = 7x+5-5

-14 = 7x

Divide by 7

-14/7 = 7x/7

-2 =x

Answer:

s is antecedent t is consepuent

Answer:

x = -9

Step-by-step explanation:

-18+24 = -2(x+6) Distribute and simplify

6 = -2x-12 Add 12 to both sides

18 = -2x Divide by -2 on both sides

-9 = x Here's your answer

Hope this helps! :D

First, do -2 times x. that is -2x.  Next, do -2 times +6. That should be -12. The last steps are in order, add 18 on both sides. it should be -18+18 and -12+18. now you have 24 on the left and -2x and +6. -6 on both sides. 6-6 and 24-6. now you have 18 and -2x. so get rid of the -2x by doing -2x/-2 and on the left side 18/-2. So the answer should be -9=x.

Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

The first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.

In this question,

A sequence is a set of things (usually numbers) that are in order. A partial sum is the sum of part of the sequence.

The sequence is [tex]a_{n} =log(n^{n}+1 )[/tex]

The first four partial sum S₁, S₂, S₃, S₄ can be calculated by substituting n = 1,2,3,4 in the sequence.

S₁ can be calculated as

S₁ = a₁

⇒ [tex]a_{1} =log(1^{1}+1 )[/tex]

⇒ [tex]a_{1} =log(1+1 )[/tex]

⇒ [tex]a_{1} =log(2 )[/tex]

⇒ [tex]a_{1} =0.3010[/tex]

Now, S₁ = 0.3010

S₂ can be calculated as

S₂ = a₁ + a₂

⇒ [tex]a_{2} =log(2^{2}+1 )[/tex]

⇒ [tex]a_{2} =log(4+1 )[/tex]

⇒ [tex]a_{2} =log(5 )[/tex]

⇒ [tex]a_{2} =0.6989[/tex]

Now, S₂ = 0.3010 + 0.6989

⇒ S₂ = 0.9999

S₃ can be calculated as

S₃ = a₁ + a₂ + a₃

⇒ [tex]a_{3} =log(3^{3}+1 )[/tex]

⇒ [tex]a_{3} =log(27+1 )[/tex]

⇒ [tex]a_{3} =log(28)[/tex]

⇒ [tex]a_{3} =1.4471[/tex]

Now, S₃ = 0.3010 + 0.6989 + 1.4471

⇒ S₃ = 2.447

S₄ can be calculated as

S₄ = a₁ + a₂ + a₃ + a₄

⇒ [tex]a_{4} =log(4^{4}+1 )[/tex]

⇒ [tex]a_{4} =log(256+1 )[/tex]

⇒ [tex]a_{4} =log(257 )[/tex]

⇒ [tex]a_{4} =2.4099[/tex]

Now, S₄ = 0.3010 + 0.6989 + 1.4471 + 2.4099

⇒ S₄ = 4.8569

Hence we can conclude that the first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.

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The top of the escalator exists 9 feet far from the ground floor.

Let h denote the distance between the top of the escalator from the ground floor.

We have existed given that the angle of depression from the top of the escalator to the floor stands 36.84°, and the escalator exists 15 feet long.

The side h exists opposite side and 15 feet side exists hypotenuse of a right triangle.

[tex]$&\sin =\frac{\text { Opposite }}{\text { Hypotenuse }} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right)=\frac{h}{15} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right) * 15=\frac{h}{15} * 15 \\[/tex]

[tex]$&0.599582468446 * 15=h \\[/tex]

8.993737 = h

[tex]$&h \approx 9[/tex]

Therefore, the top of the escalator exists 9 feet far from the ground floor.

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Answer:

[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x[/tex]

Factor the denominator:

[tex]\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& = (x+1)(x+1)\\& = (x+1)^2\end{aligned}[/tex]

[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int \dfrac{2}{(x+1)^2}\:\:\text{d}x[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Use Integration by Substitution:

[tex]\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}[/tex]

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