Given the diagram above, m2Z is:
180°
120°
60°
30°

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.

The product of two number is 17,20,740, When one number is 1785 and other number is 39,460.

To find the other number, we can divide the product of the two numbers by the known number:

Other number = 17,20,740 ÷ 1785

We can simplify this calculation by factoring out common factors from both numbers. First, we can factor 1785 into its prime factors:

1785 = 3 x 3 x 5 x 7 x 2

Next, we can factor 17,20,740:

17,20,740 = 2^2 x 5 x 7 x 11 x 13 x 17 x 19

We can then cancel out any common factors in the numerator and denominator. In this case, we can cancel out one factor of 5, one factor of 7, and two factors of 2:

Other number = (2 x 11 x 13 x 17 x 19) ÷ (3 x 3 x 5 x 7 x 2)

Simplifying this expression further, we get:

Other number = (2 x 11 x 13 x 17 x 19) ÷ (3^2 x 5 x 7)

Other number = 39460

Therefore, the other number is 39,460.

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Answer:

a. x > -1

b. x >= -2

c. x <= 3

d. x <= 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression (6)(2)^(n-1) means to multiply 6 by 2 raised to the power of n-1. For example, when n = 3, we have:

(6)(2)^(n-1) = (6)(2)^(3-1)

= (6)(2)^2

= (6)(4)

= 24

On the other hand, the expression 12^(n-1) means to raise 12 to the power of n-1. For example, when n = 3, we have:

12^(n-1) = 12^(3-1)

= 12^2

= 144

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 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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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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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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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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Step-by-step explanation:

Area of a trapezoid =

     height  ( 9 m)   times the average of the bases (10+14)/2 m

          9 x (10+14)/2 = 108 m^2

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 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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The missing length KL in ΔLKJ is x = 22.

Similar triangles are two triangles that have the same shape but may have different sizes.

Corresponding angles are equal and corresponding sides are proportional to each other. 

Since the triangles are similar, the corresponding sides are in proportion.

We can set up the proportion:

LJ/RP = KJ/QP

Substituting the given values, we get:

28/42 = x/33

Cross-multiplying and simplifying, we get:

42x = 28 × 33

42x = 924

x = 924/42

x = 22

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Answer:

The numbers are 0 and 1

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The value of x in terms of the length of the chord BC is x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees

Draw a diagram of the circle and label the given points and segments.

Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. Identify any angles or lengths that can be determined from the given information.

Use the tangent-chord theorem: Since AD is tangent to the circle, we can use the tangent-chord theorem to find that angle ADB is equal to angle ABD.

This implies that triangle ABD is an isosceles triangle.

Use the properties of isosceles triangles: Since triangle ABD is isosceles, we know that angle BAD is equal to angle ADB.

We also know that the sum of the angles in a triangle is 180 degrees.

Therefore, angle ABD is equal to (180 - 2x) degrees.

Use the angle sum property: Since A, B, C, and D are points on the circle, angle BAC is equal to half of the central angle BOC.

Therefore, angle BOC is equal to 2 * angle BAC.

Use the angle subtraction property: Since angle ABD is an exterior angle of triangle BCD, we know that angle ABD is equal to the sum of angles BCD and BDC.

Therefore, (180 - 2x) degrees is equal to (2 * angle BAC) + angle BDC.

Use the angle sum property again: Since B, C, and D are points on the circle, angle BDC is equal to half of the central angle BOC.

Therefore, angle BDC is equal to angle BAC.

Substituting this value into the equation from step 6, we get (180 - 2x) degrees

= (2 * angle BDC) + angle BAC

= 2 * angle BAC + angle BAC

= 3 * angle BAC.

Therefore, angle BAC is equal to (180 - 2x) / 3 degrees.

2 * angle BAC = 2 * (180 - 2x) / 3 degrees.

Use the chord length formula: Using the chord length formula, we can find that BC

= 2 * r * sin(angle BOC / 2), where r is the radius of the circle.

Substituting the value of angle BOC from step 9, we get BC = 2 * r * sin[(2 * (180 - 2x) / 3) / 2]

= 2 * r * sin[(180 - 2x) / 3] .

Solve for x:

We need to express x in terms of BC, so we can use the formula from step 10 to get 2 * r * sin[(180 - 2x) / 3] = BC.

Solving for x gives x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees.

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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]

Answer:

p=18

Step-by-step explanation:

if 4(p-7) = 44,

Then you can use distributive property to solve

4p-28=44

add 28 to both sides. So,

4p=72

Divide 4 from both sides.

p= 18.

Answer:

Step-by-step explanation:

1500

+1500

3000

+1500

4500

+1500

6000

+1500

7500

Answer=7500

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 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:

1:1:1

Step-by-step explanation:

The ratio of orange to black to green cars is 1:1:1.

The evaluated expression  [tex]\frac{4^{x} }{2^{x} }[/tex] for x = 3 is 4.

An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication and division.

Therefore, to evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Hence, let's evaluate the expression as follows:

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

Therefore,

[tex]\frac{4^{3} }{2^{3} } = \frac{64}{16}[/tex]

Therefore,

64 / 16 = 4

Hence, the evaluated expression is 16.

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The coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).

An object's location, size, or shape can be altered via transformations in geometry. Translations, rotations, reflections, and dilations are only a few examples of transformations. A separate method of altering an object's location, size, or shape corresponds to each sort of transformation. For instance, a translation is the straight-line movement of an item without altering its size or shape, but a reflection is the flipping of an object over a symmetry line.

The coordinates of the triangle are S(-4, 4), R(-4, 1) and T (-2, 1).

For the given transformations the new coordinates are:

S(-4, 4) translates to (-4-1, 4-5) = (-5, -1) and reflects to (5, -1)

R(-4, 1) translates to (-4-1, 1-5) = (-5, -4) and reflects to (5, -4)

T(-2, 1) translates to (-2-1, 1-5) = (-3, -4) and reflects to (3, -4)

Hence, the coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).

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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.

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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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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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

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.

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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