Expand this equation to write an identity: (a-b)^3

The radial distances from the center (-3, -2), to the points on the circumference (0, -6), and (a, 0), found using the distance formula, indicates that a = -3 ± √21

The distance between points (x₁, y₁), and (x₂, y₂), on the coordinate plane, can be found using the formula; d = √((x₂ - x₁)² + (y₂ - y₁)²).

The coordinates of the center of the circle = (-3, -2)

The coordinates of the locations (on the circumference of the circle), through which the circle passes = (0, -6) and (a, 0)

Therefore the distances between points (0, -6) and (-3, -2) and (a, 0) and (-3, -2) are the same;

The distance from (0, -6) to (-3, -2) = The distance from (a, 0) to (-3, -2)

(-3 - 0)² + (-2 - (-6))² = (-3 - a)² + (-2 - 0)²

25 = a² + 6·a + 9 + 4 = a² + 6·a + 13

a² + 6·a + 13 = 25 (symmetric property)

a² + 6·a + 13 - 25 = 0

a² + 6·a - 12 = 0

a = (-6 ± √(6² - 4×1×(-12)))/(2×1) = (-6 ± √(84))/2

a = (-3 ± √(21))

a ≈ 1.58 and a ≈ -7.58

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The value of w is 5

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors.

Similar shapes are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

The ratio of the corresponding sides of similar shapes are equal.

Therefore 35/28 = w/8

w× 28 = 35 × 8

w = 35× 8/28

w = 5

therefore the value of w is 5

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The substantive audit sampling technique uses a statistical sampling approach is Sampling or MUS.

Sampling is a powerful tool in auditing as it allows the auditor to make conclusions about the population without having to test all the transactions, balances or data.

Substantive audit sampling refers to the use of samples in an audit process to make conclusions about a population of transactions, balances or other data.

There are three main substantive audit sampling techniques: Stratified Sampling, Attribute Sampling and Monetary Unit Sampling.

Monetary Unit Sampling or MUS is a statistical sampling approach that focuses on the monetary value of transactions.

The auditor will select a sample of transactions and calculate the expected deviation rate.

This technique is used when the auditor is focused on testing material balances and ensuring that they are correct.

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Answer:

Below

Step-by-step explanation:

First position   26 possibilities

 second    25

   third   24

       fourth  10

           fifth   9

              sixth 8          

     multiply all of these numbers together = 11 232 000 possible plates

In (a) and (d), the -1 is a reciprocal, as -1 is being multiplied by f(p) or f(p⁻¹) respectively, and the solutions for p are p = 2 and p = -7/3 respectively. In (b) and (c), the -1 is an inverse, as it is part of the inverse of f(p), and the solutions for p are p = 7 and p = 5/3 respectively.

(a) f(p) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f(p) = 5 and solve for p. We do this by subtracting 2 from both sides of the equation to get 3p = 3, and then dividing both sides by 3 to get p = 1.

(b) f⁻¹(p) = 5 is an inverse and we can solve for p using the equation f⁻¹(p) = 5. To do this, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.

(c) (f(p))⁻¹ = 5 is a reciprocal and we can solve for p using the equation (f(p))⁻¹ = 5. To do this, we first divide both sides of the equation by 5 to get 1/f(p) = 1. Then, we multiply both sides by f(p) to get f(p) = 5. Finally, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.

(d) f (p⁻¹) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f (p⁻¹) = 5 and solve for p. We do this by multiplying both sides of the equation by p⁻¹ to get f(p) = 5p⁻¹. Then, we subtract 2 from both sides to get 3p = 5p⁻¹ - 2, and then multiply both sides by 3 to get 9p = 5p⁻¹ - 6. Finally, we add 6 to both sides to get 9p + 6 = 5p⁻¹, and then divide both sides by 4 to get p = 1.

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The amount of time it would take for both Keith and Donna to complete each lap based on the question is given below:

Factor two numbers 12 and 8:

12= 2. 2. 3

8= 2. 2. 2

Find the LCM,

The LCM of (12,8)=  2. 2. 3. 2 = 24

Hence,

1. It will take 24 minutes for Keith and Donna to meet again at the starting line.

2. Keith will complete 2 laps

3. Donna will complete 3 laps.

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36 motorcycles were repaired during the month.

To solve this problem, we can use the formula for the total number of wheels of a vehicle, which is equal to the number of vehicles multiplied by the number of wheels per vehicle. In this case, the number of wheels per vehicle is 4 since both autos and motorcycles have 4 wheels each. This formula can be expressed as: Wheels = Vehicles × Wheels per Vehicle.

We can substitute the given values of the total number of wheels (336) and the number of wheels per vehicle (4) into the formula, and solve for the number of vehicles (V): Wheels = Vehicles × Wheels per Vehicle → 336 = Vehicles × 4 → Vehicles = 336 ÷ 4 → Vehicles = 84.

Since we know that both autos and motorcycles were repaired, and the total number of vehicles was 84, we can use the information that 120 vehicles were repaired to solve for the number of motorcycles (M) that were repaired.

If the total number of vehicles was 84, and 120 vehicles were repaired, then the number of motorcycles that were repaired must be equal to the difference between the total number of vehicles and the total number of autos, which is 120 - 84 = 36.

Therefore, 36 motorcycles were repaired during the month.

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The vertex form of given expression  y=9x² + 9x - 1  is y = 9 ( x + 1/2  )² - 13 / 4

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

y = 9x² + 9x - 1

complete the square for 9x² + 9x - 1

Use the form ax²+ bx +c , to find the values of a,b,c

a = 9 b = 9 c = -1

Consider the vertex form of a parabola

a ( x+d )² + e

Find the value of d using the formula d = b / 2a

d = 9 / 2.9

d = 1 / 2

So, now we have to find the value of e suing the formula

e = c - b²  / 4a

e = -1 - 9*9 / 4*9

e = -13/ 4

Substitute the values a,d and e into the vertex form

9 ( x + 1/2  )² - 13 / 4

So,

y = 9 ( x + 1/2  )² - 13 / 4

Therefore, The vertex form of given expression  y=9x² + 9x - 1  is

y = 9 ( x + 1/2  )² - 13 / 4

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By algebra properties, the radical equation [tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex] has the following extraneous solution: x = - 14.

A solution for a radical equation is extraneous when result leads to an absurdity (i.e. 3 = 4). In this problem, we proceed to show how to solve a radical equation by means of algebra properties. First, write the entire radical equation:

[tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex]

Second, use compatibility with addition:

[tex]3\cdot \sqrt [4]{(x-2)^{3}} = 24[/tex]

Third, use compatibility with multiplication:

[tex]\sqrt [4] {(x - 2)^{3}} = 8[/tex]

Fourth, use a relationship between powers and roots:

[tex](x - 2)^{\frac {3}{4}} = 8[/tex]

Fifth, elevate both sides to 4 / 3 to cancel exponent on left side:

[tex]x - 2 = 8^{\frac {4}{3}}[/tex]

Sixth, solve the power constant:

x - 2 ≈ ± 16

Seventh, apply absolute value properties:

x - 2 = 16 or x - 2 = - 16

Eighth, use compatibility with addition once again:

x = 18 or x = - 14

Ninth, check for extraneous solutions:

x = 18

[tex]3\cdot \sqrt [4]{(18-2)^{3}} = 24[/tex]

24 = 24

x = - 14

[tex]3\cdot \sqrt [4]{(- 14-2)^{3}} = 24[/tex]

NaN

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In linear equation, The resultant speed is 48.27m/s and the bearing is 235.65 degrees. The vertical component is given by vsinθ = 32sin34° = 17.89 miles per hour.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                 Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

OP = 59m/s represents the plane that has a bearing of 214 degrees.

PW = 21m/s represents the wind that is blowing at an angle of N14W.

OW =  represents the resultant vector.

The angle that OP makes with west direction = 270-214=56 degrees. Therefore the angle that OP makes with the vertical is 90-56=44 degrees

In the ΔOPW,  ∠WPO = 14+44=58 degrees.

Using law of cosines, we can find the magnitude of OW

      Using law of sines we can calculate ∠WOP

  21/Sin∠WOP = 48.27/sin58

Therefore sin∠WOP = 21.SIN58/48.27  = = 0.368895

Therefore ∠WOP = sin-1 (0.368895) = 21.65 degrees

Therefore the bearing of OW is 214 + 21.65 = 235.65 degrees.

The resultant speed is 48.27m/s and the bearing is 235.65 degrees.

The horizontal component is given by vcosθ = 32cos34° = 26.53 miles per hour

The vertical component is given by vsinθ = 32sin34° = 17.89 miles per hour.

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The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it properly depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.

the mean of the data = 9.12 oz

The SD = 0.05 oz

The probability of the bag to be less than 9.07 oz

x = 9.07

z = x - mean / SD = 9.07 - 9.12/0.05 = - 1

for z = -ve

Ф(z) = 1 - Ф(-z) = 1 - Ф(1) = 1 - 0.8413 = 0.1587

The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

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The subgroups of S6 include the following abelian groups: Z₁, Z₂, Z₃, Z₆, Z₂ x Z₂, and Z₃ x Z₂

A subgroup of a group is isomorphic to another group if there is a bijective homomorphism between the two groups, meaning there is a one-to-one correspondence between their elements that preserves the group operation. In this case, the subgroup of S6 (the symmetric group on 6 elements) is isomorphic to one of the abelian groups.

It is known that the number of subgroups of a finite group is bounded above by the number of its elements, so there are only finitely many possible subgroups of S6 to consider. The most common abelian groups are the cyclic groups Zₙ, and any group that is isomorphic to a direct sum of cyclic groups is also abelian.

It is known that the subgroups of S6 include the following abelian groups: Z₁, Z₂, Z₃, Z₆, Z₂ x Z₂, and Z₃ x Z₂. These are the only abelian groups that can be isomorphic to subgroups of S6. Note that there may be non-abelian subgroups of S6 as well.

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A histogram is a graph used to represent the frequency distribution of a few data points of one variable.

Histograms often classify data into various “bins” or “range groups” and count how many data points belong to each of those bins.

Option (b)  is correct.

Because, virtually all the common causes variations with time

Option (c) special and command variation

Which are two important variation

Option (a) location is the correct option here as histogram can not show the location.

Because, histogram shows shape and spread of data, also it shows variation over time. hence the correct option is a according to histogram data.

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Therefore , the solution of the given problem of triangle comes out to be sides are a = 10 and b=5√3.

Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.

Here,

Given :

A right triangle is :

=> 5 , b and a

has 30 degree angle .

=> Sin 30° = 5/a

=> 1/2 = 5/a

=> a = 10

Thus,

Using pythagoras theorem ,

=> 10² = 5² + b²

=> 100 -25 = b²

=>  b² = 75

=> b = 5√3

Thus , sides comes out to be a = 10 and b=5√3

Therefore , the solution of the given problem of triangle comes out to be sides are a = 10 and b=5√3.

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The equation representing the relationship between the number of balls of dough (b) and the amount of flour (f) would be b = f / 2.5.

To find the relationship, we need to determine how much flour is used per ball of dough. We know that Cam uses 12 1/2 cups of flour to make 5 balls of dough, so we can calculate the amount of flour per ball of dough by dividing the total amount of flour by the number of balls of dough: 12 1/2 cups / 5 balls = 2 1/2 cups per ball.

Therefore, the equation representing the relationship between the number of balls of dough (b) and the amount of flour (f) would be: b = f / 2.5, where f is the amount of flour used in cups and b is the number of balls of dough.

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The equation used is 3 (x - 5) = 60, the cost of each rashguard at full price is $25

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Price of rash guard on sale =$5

Number of rashguard miguel purchased= 3

Now, Let the full price of each rashguard be x,

Rashguards sell for $5 less than full price;

x - 5

Miguel purchases 3 rashguards and pays a total of $60;

3 (x - 5) = 60

x - 5 = 60 / 3

x - 5 = 20

x = 20 + 5

x = 25

Therefore, the algebraic solution for x will be 25;

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This does not make sense as x is a discrete variable, so it cannot take on a value of 3.5.

A binomial variable is a discrete variable, meaning it can only take on certain values. In this case, x can take on values from 0 to 10 (inclusive). Since 3.5 is not one of these values, it does not make sense to calculate the probability that x equals 3.5.

This does not make sense as x is a discrete variable, so it cannot take on a value of 3.5.

A binomial variable is a discrete variable, meaning it can only take on certain values that are determined by the given parameters. For example, if the binomial variable x is defined as the number of heads in 10 flips of a coin, then x can only take on values from 0 to 10 (inclusive). Since 3.5 is not one of these values, it does not make sense to calculate the probability that x equals 3.5.

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The average Honda beat the Dodge but couldn't pass the Smart Car, and the Mini couldn't pass the Audi, so the Audi won the race.

The Honda was able to defeat the Dodge but was unable to pass the Smart Car, so it was the Audi that arrived first in the race.

The Mini was then forced to settle for defeating the Smart Car after failing to pass the Audi. The Audi was the only vehicle that was able to stave off the competition and maintain its lead all the way to the finish line, making it the eventual race winner. Following the Audi in that order, the Honda, Dodge, Smart Car, and Mini were all overrun by the vehicle in front of them before the Mini was able to surpass the Smart Car and finish in fourth place.

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The line of reflection would be x+y =4, Hence the correct option is C.

The equation of a line's standard form is given as follows:

[tex]y = mx+c[/tex]

Where m is the slope and c is the y-intercept of the line.

The slope can be determined by

[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Now, Along its diagonals should be reflected in order to reflect it back to itself.

The diagonals will pass through the points [tex]A(3, 1)[/tex] and [tex]C( 1,3)[/tex]

Hence, The slope of the line is,

[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

[tex]m =\dfrac{(3 - 1)}{(1 - 3}[/tex]

[tex]m =\dfrac{(2)}{(- 2)}[/tex]

[tex]m = - 1[/tex]

Hence, The equation of the line AC,

[tex](y - y_1) = m(x-x_1)[/tex]

It passes through the point (1,3)

[tex](y - 3) = -1( x-1 )[/tex]

[tex]y - 3 = -x +1[/tex]

[tex]y +x =4[/tex]

Therefore, Option C is true.

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Both a and b are knights. This is the only possible answer because, according to the native's statements, a said they were both knights, and b said a was a knave. However, this contradicts what a said, so they must both be knights.

Knights are members of the nobility or military class in medieval Europe, typically depicted as armored warriors on horseback. They were typically sworn to serve their lord and protect his lands and people. Knights were expected to uphold a code of honor and show courage and loyalty in battle.

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A direction field for this system of linear differential equations can be drawn by plotting the values of x' for various values of x.  As t → ∞, the solutions approach either the equilibrium point (1,0) or (3,0).

a) A direction field for this system of linear differential equations can be drawn by plotting the values of x' for various values of x, and then using arrows to indicate the direction of the solution curves at each point.

In general, the solution curves will approach the equilibrium points, which are points where x' = 0. In this case, there are two equilibrium points: (1,0) and (3,0). The solutions that start near the equilibrium point (1,0) will approach it as t → ∞, and the solutions that start near the equilibrium point (3,0) will approach it as t → ∞.

b) As t → ∞, the solutions approach either the equilibrium point (1,0) or (3,0), and thus they settle down to a constant value.

c) The general solution of the system of equations can be found using the matrix exponential:

x(t) = e^(At)x₀

where x₀ is the initial condition and A is the matrix:

A = (3 -4| 1 -1)

The matrix exponential can be found using a variety of methods, including diagonalization and Jordan form. Once the matrix exponential is found, the general solution can be written in terms of x₀, which represents the initial condition.

--The question is incomplete, answering to the question below--

"x' = [tex]\left[\begin{array}{cc}3&-4\\1&-1\end{array}\right] x[/tex]

(a) draw a direction field and sketch a few trajectories.

(b) describe how the solutions behave as t → [infinity].

(c) find the general solution of the system of equations."

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Answer: [tex]x=3.5, y=4.25[/tex]

Step-by-step explanation:

[tex]3x+2y=19 \implies 6x+4y=38\\\\(6x+4y)-(2x+4y)=38-24 \implies 4x=14 \implies x=3.5\\\\\therefore 3(3.5)+2y=19 \implies 2y=8.5 \implies y=4.25[/tex]

Answer:  to label the point D on the number line, you can represent it as a real number and write it alongside the number line with an arrow pointing to its corresponding position. For example:

----|-----D---->|------

Where "D" is the label for the point and the arrow indicates its position on the number line.

Step-by-step explanation:

this is the answer

(x+x+10)*2=4x+20

Using the area of the rectangle and circle, the shaded area is equal to 6.88 squared units

To determine the area of the shaded region, we can simply find the area of the rectangle and the area of the circle.

The formula of area of the rectangle;

Assuming the width is half the length

Area of rectangle = length * width

Area of rectangle = 8 * 4

Area of rectangle = 32 squared units.

Area of circle = πr²

r = radius of the circle

In this problem, the diameter of the circle is the width of the rectangle or rather, the diameter of the circle is half the length of the the rectangle.

d = 8 / 2 = 4 units

radius = diameter / 2

radius = 4 / 2 = 2 units

Substituting the values into the formula

A = πr²

A = 3.14 * 2²

A = 3.14 * 4

A = 12.56 squared units.

The non-shaded area = 2 * 12.56 = 25.12 squared units.

The shaded area = area of rectangle - non-shaded area

The shared area = 32 - 25.12

The shaded area = 6.88 squared units.

b.

The approximated area to the nearest tenth is 6.9 squared units

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Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation:

Answer:

A = 20, therfore B = 180

Step-by-step explanation:

Technically it's 17 but that is a really awkward scale so I had to round up. This really annoys me because if there was one more box you could had the scale 15 and it would've looked so much nicer but unfortunate you're short one

Answer:

Let's call the radius of the cylinder and cone "r".

The surface area of the cylinder is: 2πr(r + h) = 2πr^2 + 2πrh

The surface area of the cone is: πr(l + r) = πrl + πr^2

The total surface area of the solid object is the sum of the surface area of the cylinder and the cone: 2πr^2 + 2πrh + πrl + πr^2 = (2π + π)r^2 + 2πrh + πrl

We are given that the total cost of painting the solid object is Rs. 2851.20 and the rate of painting is Rs. 140 per 100 sq cm.

So the total surface area of the solid object is: 2851200/140 = 20580 sq cm

Now we can substitute the values we know into the equation for the total surface area: 20580 = (2π + π)r^2 + 2πrh + πrl

We also know that the height of the cylinder is 28 cm and the slant height of the cone is 17 cm.

We can use the Pythagorean theorem to find the height of the cone: h^2 + r^2 = (l/2)^2

Solving this equation for h, we get: h = √(l^2/4 - r^2)

Now we can substitute the given values and solve for the height of the cone:

h = √(17^2/4 - r^2) = √(289/4 - r^2)

We don't have any information about the radius of the cylinder and cone, so we cannot solve for h in terms of r, but we can find the height of the cone by assuming the value of radius.

Let's assume the radius of the cylinder and cone is 5cm.

h = √(289/4 - 5^2) = √(289/4 - 25) = √(289/4 - 25) = √(64) = 8cm

So, the height of the cone is 8cm.

Please note that this is a theoretical height as it is based on the assumption of radius being 5cm, the actual height of the cone may be different if the radius is different.

Answer:

(-41)/6 or -6 5/6 as a mixed fraction

Step-by-step explanation:

Simplify the following:

1 + 2/3 - (8 + 1/2)

Put 8 + 1/2 over the common denominator 2. 8 + 1/2 = (2×8)/2 + 1/2:

1 + 2/3 - ((2×8)/2 + 1/2)

2×8 = 16:

1 + 2/3 - (16/2 + 1/2)

16/2 + 1/2 = (16 + 1)/2:

1 + 2/3 - ((16 + 1)/2)

16 + 1 = 17:

1 + 2/3 - 17/2

Put 1 + 2/3 - 17/2 over the common denominator 6. 1 + 2/3 - 17/2 = 6/6 + (2×2)/6 + (3 (-17))/6:

6/6 + (2×2)/6 + (3 (-17))/6

2×2 = 4:

6/6 + 4/6 + (3 (-17))/6

3 (-17) = -51:

6/6 + 4/6 + (-51)/6

6/6 + 4/6 - 51/6 = (6 + 4 - 51)/6:

(6 + 4 - 51)/6

6 + 4 = 10:

(10 - 51)/6

10 - 51 = -(51 - 10):

(-(51 - 10))/6

| 5 | 1

- | 1 | 0

| 4 | 1:

Answer:  (-41)/6