Work out the value of u in the equation below. Give your answer to 1 d.p.
tan 34° = 9/u

a) The diagram is given below.

b) The vertical distance from the woman's eye level to the bottom of the flagstaff is approximately 9.07 meters.

c) The height of the flagstaff is approximately 15.45 meters.

What does an angle mean?

The intersection of the intersecting lines that make up a skew's ends determines both its greatest and smallest walls. Two paths might hypothetically come together at a crossroads. Angle is another outcome of two things interacting. They resemble dihedral shapes the most. A two-dimensional curve can be created by placing two line beams in various configurations between their extremities.

a) Diagram:

           C

           /|

          / |

         /  | h

        /   |

       /    |

      /     |

     /      |

    /       |

   /        |

  /         |

 /ɑ        |

/_____|    

A         B

In this diagram, the woman is standing at point A, the flagstaff is at point B, and the top of the flagstaff is at point C. The angle of elevation from the woman to the top of the flagstaff is angle ɑ, and the angle of depression from the woman to the bottom of the flagstaff is angle β. The distance from the woman to the base of the flagstaff is h.

b) The vertical distance from the woman's eye level to the bottom of the flagstaff can be found using trigonometry. We know that the angle of depression from the woman to the bottom of the flagstaff is 20 degrees, so we can use the tangent function to find the vertical distance:

tan(20) = h / 25

h = 25 * tan(20)

h ≈ 9.07 m

Therefore, the vertical distance from the woman's eye level to the bottom of the flagstaff is approximately 9.07 meters.

c) To find the height of the flagstaff, we can use the tangent function again, this time with the angle of elevation from the woman to the top of the flagstaff:

tan(76) = (h + x) / 25

where x is the height of the flagstaff above the bottom

We know that h is approximately 9.07 m from part b. Rearranging the equation, we get:

x = 25 * tan(76) - h

x ≈ 24.52 m - 9.07 m

x ≈ 15.45 m

Therefore, the height of the flagstaff is approximately 15.45 meters.

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Thus, the area of the rectangular face of the phone is found to be:

Area = 200 sq. in.

Due to the diversity of shapes seen in geometry, geometry is also referred to as the study of shapes.

Dimensions of the face of rectangular face of phone:

Length = 20 inches

width =  10 inches

Area = length x width

Area = 20 x 10

Area = 200 sq. in.

Thus, the area of the rectangular face of the phone is found to be:

Area = 200 sq. in.

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Complete question:

The top face of a phone is a rectangle measuring 20 inches by 10 inches. find the area of the face of the phone.

the factored form of the expression 3x² + 15x - 2xy - 10y is (x + 5)(3x - 2y).

How to solve the expression?

To factor the expression 3x² + 15x - 2xy - 10y, we need to look for common factors and grouping of terms. First, we can factor out 3x from the first two terms and -2y from the last two terms:

3x(x + 5) - 2y(5 + x)

Now we can see that both terms have a common factor of (x + 5), so we can factor it out:

(x + 5)(3x - 2y)

Therefore, the factored form of the expression 3x² + 15x - 2xy - 10y is (x + 5)(3x - 2y).

This expression represents the area of a parallelogram with base x+5 and height 3x-2y. The factored form makes it easier to see the relationship between the dimensions of the parallelogram and the expression for its area. For example, we can see that the area is zero when either factor is zero, meaning that the base or height of the parallelogram is zero. We can also use the factored form to find the dimensions of a parallelogram given its area.

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Therefore, the expression that can be used to determine YK is (48)tanK that is option D.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with straight line segments. Each of these line segments is called a side, and the point where two sides meet is called a vertex. A triangle has three vertices, three sides, and three angles. Triangles can be classified based on the length of their sides and the size of their angles.

Here,

In the right triangle MYK, where MY = 48 units, MK = 73 units, and angle Y = 90 degrees, we can use trigonometric functions to find the length of YK. The trigonometric functions that relate to the sides and angles of a right triangle are:

Sine: sinθ = opposite/hypotenuse

Cosine: cosθ = adjacent/hypotenuse

Tangent: tanθ = opposite/adjacent

To find YK, we need to use the tangent function because we know the opposite and adjacent sides (MY and MK). So, the correct expression to determine YK is: (48)tanK

The other expressions given are:

(73)sinK: This expression would be used to find the opposite side, not YK.

(73)cosK: This expression would be used to find the adjacent side, not YK.

(48)tanM: This expression doesn't relate to the right triangle MYK since there is no angle M in the triangle.

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the equation Y = 1(1-x)² - 5 represents a downward-facing parabola with vertex at (1,-5), which opens upwards, and the value of Y increases as x moves away from 1 in either direction.

What is equation?

An equation is a mathematical statement that contains an equality sign (=) between two expressions. It indicates that the expressions on either side of the equality sign are equal in value. Equations can have variables, constants, coefficients, and operators like addition, subtraction, multiplication, and division. The variables represent unknown values, and the goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.

For example, the equation 2x + 5 = 11 is an algebraic equation, where "x" is the variable, "2" and "5" are constants, and "+" and "=" are operators. The solution to this equation is x = 3, since when we substitute x = 3 into the left-hand side of the equation, we get 2(3) + 5 = 11, which satisfies the equality.

The equation given is Y = 1(1-x)² - 5.

This equation represents a parabola in vertex form, where the vertex is at (1,-5). The coefficient of the squared term is positive, which means that the parabola opens upwards.

When x = 1, the value of Y is -5, which is the minimum value of the parabola. As x moves away from 1 in either direction, the value of the expression (1-x)² increases, causing the value of Y to increase as well.

Therefore, the graph of this equation is a downward facing parabola with the vertex at (1,-5), and it opens upward. As x moves away from 1, the value of Y increases.

In summary, the equation Y = 1(1-x)² - 5 represents a downward-facing parabola with vertex at (1,-5), which opens upwards, and the value of Y increases as x moves away from 1 in either direction.

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The author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

The number of steps a runner takes in a specific length of time is referred to as stride rate and is commonly expressed in steps per second. You can figure it out by dividing the total number of steps you took during a certain amount of time by how long that time period lasted. Stride rate, which is frequently used as a gauge of running effectiveness, is impacted by a variety of variables, including running speed, terrain, and personal running form.

Hence, in the given section, the author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

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The workshop would need to be cleaned in 4 hours 21 workers.

How does division work?

In mathematics, division is the process of dividing a quantity into equal pieces or groups. It is used to determine how many times one number can be divided by another number because it is the inverse of multiplication.

In light of the facts provided, we can apply the following formula to determine how long a task will take to complete:

Work = Time / (rate)

Cleaning the workshop is the continual work in this situation. The rate is the amount of work completed in a given length of time. Assume that all employees work at the same rate, making the rate proportionate to the workforce.

Hence, the rate of work is: if 24 people can clean the workshop in 3.5 hours.

rate=(work)/(time)=(1 workshop)/(3.5 hours * 24 workers)=1/84 workshop per worker per hour

We now need to calculate how long it would take 10 employees to clean the workshop. Let's apply the formula once more:

Time = Work / Rate = (1 Workshop) / (10 Workers * Rate)

Using the earlier rate as a substitute, we obtain:

As a result, cleaning the workshop would require 21 people 4 hours.

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The lengths of the altitude "a", the line segment "b", and the diagonal "c" of the regular hexagon are: a = 3, b = 3√3, c = 6√3.

Since the hexagon is regular, all six sides are congruent to each other, and all six angles are congruent to each other. Let's call the length of each side "s".

To find the length of the altitude "a", we can draw a perpendicular bisector from the center of the hexagon to one of the sides. This bisector will bisect the side into two segments of length "s/2", and it will also form a right triangle with "a" as the altitude and "s/2" as one of the legs. Using the Pythagorean theorem, we can solve for "a":

[tex]a^2 + b^2 = 6^2\\a^2 = 6^2 - b^2[/tex]

To find the length of "b", we can draw one of the radii from the center of the hexagon to a vertex. This radius will bisect the angle at the vertex and also bisect the opposite side. This will form two right triangles, each with one leg of length "s/2" and one acute angle of 30 degrees. Using trigonometry, we can solve for "b":

cos(30) = b/6

√3/2 = b/6

b = 3√3

Sin 30 = a/6

1/2 = a/6

a = 3

c = b + b =  3√3 +  3√3 = 6√3

Therefore, the lengths of the altitude "a", the line segment "b", and the diagonal "c" of the regular hexagon are:

a = 3

b = 3√3

c = 6√3

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Use differentials to estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick.Therefore, the estimated amount of metal in the can is 0.001416.

To estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick, we can use differentials.

First, let's calculate the volume of the can. The volume of a cylinder is calculated by the formula

[tex]V = πr^{2} h,[/tex]

where r is the radius of the cylinder, and h is its height.

In this case, the radius is 5 cm and the height is 15 cm, so the volume of the can is

[tex]V = π x (5 cm)^{2}  x 15 cm = 707.1 cm^{3}[/tex]

Next, we need to calculate the volume of the metal. The volume of a rectangular prism is

V = l x w x h,

where l is the length, w is the width, and h is the height. In this case, the length and width are both 10 cm, and the height is 0.1 cm, so the volume of the metal is

[tex]V = 10 cm x 10 cm x 0.1 cm = 1 cm^{3}[/tex]

Finally, we can calculate the amount of metal in the can by dividing the volume of the metal by the volume of the can:

[tex]1 cm^{3} / 707.1 cm^{3}  = 0.001416.[/tex]

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Answer:

To use the line of best-fit equation to estimate the cost of a collection with 1,500 cards, we can substitute 1.5 (since x represents thousands of cards) for x in the equation and solve for y:

y = 39.94x + 3.84

y = 39.94(1.5) + 3.84

y = 59.91

Therefore, based on the store owner's line of best-fit equation, she should expect to pay approximately $59.91 for a collection that has 1,500 cards.

The answer is: $59.91

Step-by-step explanation:

The missing side of a right triangle, from the figure, is 33.1 meters long.

A right triangle has three sides, what are they?

An "opposite" side in a right triangle is the one that is across from a specific angle, while an "adjacent" side is the one that is next to a specific angle. The hypotenuse seems to be the longest side in a right triangle. The sides in right triangles are described with particular terminology.

We can apply the tangent function in order to calculate the length of the missing side if we assume that it is opposite the 43-degree angle that is provided:

tan(43°) = x/34

When we multiply all sides with 34, we get:

x = 34 tan(43°)

Using just a calculator, we determine:

x ≈ 33.1

Rounded to the nearest tenth, we obtain:

x ≈ 33.1

Hence, the missing side of the given triangle is x = 33.1.

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The complete question is in the attached figure.

Answer:

Step-by-step explanation:

1500

+1500

3000

+1500

4500

+1500

6000

+1500

7500

Answer=7500

The increased number is  15/16 by 3/5 of is  345/160.

What is a fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

To solve this problem, we need to follow the steps given in the question.

Step 1: Increase the number 15/16 by 3/5 of it.

We can write this mathematically as:

15/16 + (3/5)*(15/16)

Multiplying 15/16 by 3/5, we get:

(15/16)*(3/5) = 45/80

Adding this to 15/16, we get:

15/16 + 45/80 = 375/320 + 225/320 = 600/320

Simplifying this fraction, we get:

600/320 = 75/40 = 15/8

So, the result of the first step is 15/8.

Step 2: Increase the resulting number by 3/5 of it.

We can write this mathematically as:

(15/8) + (3/5)*(15/8)

Multiplying 15/8 by 3/5, we get:

(15/8)*(3/5) = 45/40

Adding this to 15/8, we get:

15/8 + 45/40 = 300/160 + 45/160 = 345/160

Therefore, the final result is 345/160.

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Answer:

RM 300

Step-by-step explanation:

Let's assume that the cost price of the merchandise is "C" in RM.

According to the problem, the marked price of the merchandise is 20% higher than the cost price. Therefore, the marked price can be calculated as:

Marked price = Cost price + 20% of Cost price

Marked price = C + 0.2C

Marked price = 1.2C

The merchandise is sold at 90% of the marked price, which means the selling price can be calculated as:

Selling price = 90% of Marked price

Selling price = 0.9 × 1.2C

Selling price = 1.08C

We are given that the profit after selling the merchandise is RM 24. Profit is calculated as the difference between selling price and cost price. Therefore, we can write:

Profit = Selling price - Cost price

24 = 1.08C - C

24 = 0.08C

Solving for C, we get:

C = 24/0.08

C = 300

Therefore, the cost price of the merchandise is RM 300.

The probability that less than 10 of the entry forms will include an order is 0.0193, rounded to four decimal places.

The company has received 14 entries in the sweepstakes, and they know that the probability of receiving a magazine subscription order with an entry form is 0.5. Now, we want to find the probability that less than 10 of the entry forms will include an order.

To find the probability that less than 10 of the entry forms will include an order, we need to add up the probabilities of getting 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 orders. We can use the binomial probability formula to calculate these probabilities:

P(X = x) = (n choose x) x pˣ x (1 - p)ⁿ⁻ˣ

where P(X = x) is the probability of getting x successes, n is the number of trials, p is the probability of success, and (n choose x) is the number of ways to choose x successes from n trials.

We can also use a calculator or spreadsheet to do the calculations.

P(X = 10) = (14 choose 10) x p¹⁰ * (1 - p)¹⁴⁻¹⁰ = 0.0193

After adding up the probabilities for 0 to 9 orders, we get a probability of approximately 0.0193.

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On solving the linear equation in two variables, the duration of Plan A workout is 1.5 hours and the duration of Plan B workout is 2 hours.

According to the question, the total hours of Plan A workouts on Friday and Saturday are (8 + 2) = 10,

and the total hours of Plan B workouts are (3 + 5) = 8.

If the duration of Plan A workout is "x" hours, then the duration of Plan B workout is "y" hours.

According to the question, the total hours spent in Plan A workouts is 10, and the total hours spent in Plan B workouts is 8. So, we can write two equations as:

8x + 3y = 1510x + 5y = 8By

solving these equations, we get:

x = 1.5y = 2

Therefore, the duration of Plan A workout is 1.5 hours, and the duration of Plan B workout is 2 hours.

Therefore, the answer is: Duration of Plan A workout is 1.5 hours and that of Plan B workout is 2 hours

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Answer:

a. x > -1

b. x >= -2

c. x <= 3

d. x <= 0

Step-by-step explanation:

the value of f(5) is 10, which is option (b) ,  the value of f(-2) is -12, which is option (d).  To find the value of f(5) using synthetic substitution, we first set up the synthetic division table as follows:

5 | 3  -9  -20

   |||___

   |   |   |

We write the coefficients of the polynomial in the top row of the table and the root (in this case, 5) outside the division symbol. We then bring down the first coefficient (3) and multiply it by the root to get 15, which we write below the second coefficient (-9). We add 15 and -9 to get 6, which we then multiply by the root to get 30, which we write below the third coefficient (-20). We add 30 and -20 to get 10, which is the remainder. Therefore, the value of f(5) is 10, which is option (b).

6) To find f(-2) using synthetic substitution, we set up the synthetic division table as follows:

-2 | 1   0   8   24

  |_|||

  |    |   |   |

We write the coefficients of the polynomial in the top row of the table and the root (in this case, -2) outside the division symbol. We then bring down the first coefficient (1) and multiply it by the root to get -2, which we write below the second coefficient (0). We add -2 and 0 to get -2, which we then multiply by the root to get 4, which we write below the third coefficient (8). We add 4 and 8 to get 12, which we then multiply by the root to get -24, which we write below the fourth coefficient (24). We add 12 and -24 to get -12, which is the remainder. Therefore, the value of f(-2) is -12, which is option (d).

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Therefore , the solution of the given problem of angles comes out to be the regular polygon has a 230 centimeter circumference.

The largest and smallest walls of a skew are determined by the point at which the lines that make up its ends meet. At a junction, it's possible that two routes will cross. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

All of the edges and angles make up a regular polygon. If a regular polygon's exterior angle is 18 degrees, then the internal angle is:

180 minus the external angle is the interior angle.

180 degrees minus 18 degrees is the interior angle.

Angle inside equals 162 degrees

Sum of internal angles is equal to (n - 2)°, or 180°.

=> (n - 2) × 180 = n × 162

When we simplify and solve for n, we obtain:

=> 180n - 360 = 162n

=> 18n = 360

=> n = 20

The regular polygon in the example has 20 edges.

Given that the length of each side is 11.5 centimeters, the polygon's circumference is as follows:

Circumference is equal to the sum of the lengths of all the edges.

=> Circumference = 20.1 centimeters.

=> 230 centimeters is the circumference.

Consequently, the regular polygon has a 230 centimeter circumference.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Correct option is A, It is not function, because for each input there is not exactly one output.

A function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), where each input is associated with exactly one output. In other words, a function is a set of ordered pairs (x, y) such that no two ordered pairs have the same first element (x-value) and different second elements (y-value).

A function can be represented in different ways, including as a table of values, as a graph, or using a formula or rule. For example, the function f(x) = 2x + 1 represents a rule where each input value x is multiplied by 2 and then 1 is added to the result to obtain the output value f(x).

Functions are important in mathematics and in many fields such as physics, engineering, and economics, where they are used to model and analyze various phenomena.

To determine whether the relation represents a function, we need to check whether for each input (x-value), there is exactly one output (y-value).

Looking at the given points, we can see that the x-values 3/4 and 3 both have more than one corresponding y-value (-2 and -1/2, respectively). Therefore, the relation does not represent a function because for each input there is not exactly one output.

The answer is: No, because for each input there is not exactly one output.

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Bob has 4,000 grams of sand, which is equivalent to 4,000/1,000 = 4 kilograms of sand.

His brother has one kilogram of sand.

Therefore, his brother has 1/4 = 0.25 kilograms of sand.

There is evidence of a negative correlation between systolic blood pressure and heart rate because the sample correlation is -0.057. This value indicates that there is a small negative correlation between systolic blood pressure and heart rate.

There is evidence of a negative correlation between systolic blood pressure and heart rate. In a sample of 200 patients, a sample correlation of -0.057 was found. Correlation is a statistical measure used to assess the degree to which two variables are related to one another. A correlation coefficient ranging from -1 to 1 is used to represent this relationship. A negative correlation exists when two variables move in opposite directions.

It means that as one variable increases, the other variable decreases or vice versa.In the given case, there is evidence of a negative correlation between systolic blood pressure and heart rate because the sample correlation is -0.057. This value indicates that there is a small negative correlation between systolic blood pressure and heart rate. Systolic blood pressure is the amount of pressure exerted by blood against the walls of the arteries when the heart pumps. It is the top number in a blood pressure reading.

When your heart beats and pushes blood out, the systolic pressure is created.Heart rate is the number of times your heart beats per minute. It is also known as the pulse rate. It represents the number of times your heart contracts and relaxes with each heartbeat.

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Answer:

A

Step-by-step explanation:

He shouldn't of added the "^1" to c because its changed the value to c^5 in the final step when it should really be c^4

Therefore, the area of the trapezoid is 84cm².

A trapezoid (also known as a trapezium) is a four-sided geometric shape with two parallel sides and two non-parallel sides that meet at two endpoints. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the two bases is the height of the trapezoid. The formula for finding the area of a trapezoid is (base1 + base2) x height / 2. The formula for finding the perimeter of a trapezoid is the sum of the lengths of all four sides.

To find the area of a trapezoid, you can use the formula:

[tex]A = (B1 + B2) * h / 2[/tex]

where A is the area of the trapezoid, B1 and B2 are the lengths of the parallel sides (also called bases), and h is the height (the perpendicular distance between the bases).

Using the values, you provided:

[tex]B1 = 8cm\\B2 = 16cm\\h = 7cm[/tex]

Plugging these values into the formula, we get:

[tex]A = (8cm + 16cm) * 7cm / 2[/tex]

[tex]A = 24cm * 7cm / 2[/tex]

[tex]A = 168/2cm^{2}[/tex]

[tex]A = 84cm^{2}[/tex]

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After answering the provided question, we can conclude that Therefore, equation the function [tex]f(x) = x^3 + 3[/tex]is neither even nor odd.

In mathematics, an equation is a statement that states the equivalence of two expressions. An equation consists of two sides separated by an algebraic equation (=). For instance, the argument "2x + 3 = 9" states that the sentence "2x + 3" equals the number "9". The purpose of solving equations is to find the value or amounts of the variable(s) that always allow the equation to be true. Equations can just be simple or complicated, regular or nonlinear, and contain one or more variables. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used extensively in mathematics, including algebra, calculus, and geometry.

We must investigate the symmetry features of the function[tex]f(x) = x^3 + 3[/tex] to determine if it is even, odd, or neither.

If f(-x) = f(x) for every x in its domain, a function is even.

If f(-x) = -f(x) for every x in its domain, the function is odd.

If a function meets none of these requirements, it is neither even nor odd.

[tex]f(-x) = (-x)^3 + 3 = -x^3 + 3\\f(x) = x^3 + 3\\f(-x) = -x^3 + 3\\f(x) = x^3 + 3\\f(-x) = -x^3 + 3\\-f(x) = -(x^3 + 3) = -x^3 - 3\\[/tex]

Since f(-x) ≠ -f(x), f(x) is not odd either.

Therefore, the function [tex]f(x) = x^3 + 3[/tex]is neither even nor odd.

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my because he was poor liké kiss

The y-intercept of a line in the xy-plane is (0,1) as shown in attached graph given int the question.

To find the y-intercept of a line in the xy-plane, we need to find the point where the line intersects the y-axis. The y-axis is the vertical axis that runs through the origin and is perpendicular to the x-axis. This means that the y-intercept is the value of y when x is equal to zero. Therefore, we can read off the y-intercept directly from the equation of the line. To find the y-intercept of a line in the xy-plane, we need to find the point where the line intersects the y-axis. The y-axis is the vertical axis that runs through the origin and is perpendicular to the x-axis.

In the given graph we can see that the line intersects the point 1 on y axis.

Therefore, y-intercept of a line in the xy-plane is (0,1).

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AC=FC is the additional information needed to prove the triangles congruent using the SSS postulate. So, option (b) is correct:

According to the SSS postulate, if three sides of one triangle are congruent with three sides of another triangle, the triangles are congruent. Therefore, we need to ensure that the included angles are also congruent to prove the triangles congruent.

Option (a) states that angle A is congruent to angle F, and angle D is congruent to angle B. While this is true, it is not sufficient to prove the triangles congruent using the SSS postulate alone.

Option (c) suggests that nothing else is needed to prove the triangles congruent using the SSS postulate. However, as explained above, we need to ensure that the included angles are congruent as well.

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[tex] \sqrt{ \frac{2}{9} } - 3 \sqrt{ \frac{8}{9} } + \sqrt{ \frac{32}{9} } [/tex]

[tex] \frac{ \sqrt{2} }{3} - 3( \frac{2 \sqrt{2} }{3}) + \frac{4 \sqrt{2} }{3} [/tex]

[tex] \frac{ \sqrt{2} - 6 \sqrt{2} + 4 \sqrt{2} }{3} = - \frac{1}{3} \sqrt{2} [/tex]