Determine the length of x in the triangle. Give your answer to two decimal places. Most importantly show the steps, please.

The value of m∠1 is 103°. The solution has been obtained by using the angle sum property.

What is the angle sum property?

The angle sum property of a triangle states that the sum of the three internal angles of a triangle is 180 degrees.

We are given that m∠5 = 142° and m∠4 = 65°.

Since m∠5 and m∠2 lie on a straight line so, they form a linear pair.

So,

⇒ m∠5 + m∠2 = 180°

⇒ 142° + m∠2 = 180°

⇒ m∠2 = 38°

We know that sum of angles of a triangle is 180°.

So,

⇒ m∠3 + m∠4 + m∠2 = 180°

⇒ m∠3 + 65° + 38° = 180°

⇒ m∠3 + 103° = 180°

⇒ m∠3 = 77°

Now, since m∠3 and m∠1 lie on a straight line so, they form a linear pair.

So,

⇒ m∠3 + m∠1 = 180°

⇒ 77° + m∠1 = 180°

⇒ m∠1 = 103°

Hence, the value of m∠1 is 103°.

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The complete question and the figure has been attached below.

Question: Find m∠1 if m∠5 = 142° and m∠4 = 65°.

Answer:

The probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98%

Step-by-step explanation:

We want to find the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed, which can be written as P(A|U). Using Bayes' theorem, we have:

P(A|U) = P(U|A) * P(A) / P(U)

We are given P(A) = 0.06 (6% of the labor force is Asian), P(U|A) = 0.05 (among Asians in the labor force, 5% are unemployed), and P(U|not A) = 0.06 (among non-Asians in the labor force, 6% are unemployed).

To find P(U), we can use the law of total probability:

P(U) = P(U|A) * P(A) + P(U|not A) * P(not A)

We know P(A) = 0.06, so P(not A) = 1 - P(A) = 0.94.

Therefore,

P(U) = 0.05 * 0.06 + 0.06 * 0.94 = 0.0602

Now we can substitute all the values into Bayes' theorem:

P(A|U) = 0.05 * 0.06 / 0.0602 = 0.0498

So the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98% (rounded to the nearest percentage with no decimal places).

The amount that she needs to pay on her debt to reach a 25% debt-to-credit ratio is given as follows:

$2,535.

The amount that she needs to pay on her debt reach a 25% debt-to-credit ratio is obtained applying the proportions in the context of the problem.

She has a credit limit of $7,950.00, hence 25% of her credit limit is obtained as follows:

0.25 x 7950 = $1987.5.

She current has $4,522.50 on debts, hence the amount that she needs to pay for the debts to be reduced to $1987.5 is given as follows:

4522.5 - 1987.5 = $2,535.

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Therefore , the solution of the given problem of unitary method comes out to be 14.7 dollars  before taxation, assuming he bought 650 feet of the cheaper rope.

The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.

Here,

To evaluate the prices, we need to use the same units.

Since 0.9144 metres make up one yard, we can convert the cost of the rope at the hardware shop to dollars per metre as follows:

=> 0.89 dollars/yard * 1 yard/0.9144 meters = 0.97 dollars/meter

b) We must change the units to yards or metres in order to evaluate the costs of 650 feet of rope. 650 feet is equivalent to 3 yards, which is:

=> 650 feet x 3 feet per yard = 216.67 yards

The hardware store's price for the cord is:

=>  192.5 dollars ($0.89/yard x 216.67 yards)

At the timber yard, the price of the rope is:

=>  (216.67 yards * 0.9144 meters/yard) * 0.94 dollars/meter = 177.8 dollars.

Jim would therefore save:

=>  192.5 dollars - 177.8 dollars = 14.7 dollars.

before taxation, assuming he bought 650 feet of the cheaper rope.

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The x- and y-intercepts as required to be determined in the task content are; (-4/3, 0) and (0, -4).

As evident in the task content; the given function is; f(x) = - 3x - 4.

The x-intercept represents the value of x when f(x) = 0.

0 = -3x - 4

3x = -4

x = -4 / 3.

The y-intercept represents the value of f(0); hence, we have that;

f (x) = -3(0) - 4

f(0) = -4.

Ultimately, the points which correctly represents the x- and y-intercepts are; (-4/3, 0) and (0, -4).

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Answer:

Step-by-step explanation:

9. sin 18 = x/21

 x = 21* sin 18

  x = 6.5

10. tan 55 = 29/x

  x* tan 55 = 29

x = 29/tan 55

x = 20.3

11. sin 23 = x/25

  x = 25 * sin 23

  x = 9.8

12. sin 47 = 33/x

  x * sin 47 = 33

 x = 33/sin 47

  x = 45.1

The area of the shaded region of the composite shape is: 21.03  cm²

The formula for the area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Area of given triangle = ¹/₂ * 14 * 14 = 98 cm²

Area of sector is given by the formula:

θ/360 * πr²

Area of sector = 45/360 * π * 14 * 14

= 76.97 cm²

Thus:

Area of shaded portion = 98 cm² - 76.97 cm² = 21.03  cm²

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Answer:

Step-by-step explanation:

The discriminant value (denoted by Δ) of a quadratic equation in the form of ax² + bx + c = 0 is given by the expression b² - 4ac.

For the quadratic equation m² + 18m + 17 = 0, a = 1, b = 18, and c = 17. Substituting these values into the expression for the discriminant, we get:

Δ = b² - 4ac

Δ = (18)² - 4(1)(17)

Δ = 324 - 68

Δ = 256

Therefore, the discriminant value of the quadratic equation m² + 18m + 17 = 0 is 256.

Answer:

Step-by-step explanation:

b

After answering the presented question, we can conclude that The answer for the following expression will be as follows  [tex]4.4 X 10^3 = 4400[/tex]

In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.

The answer for the following expression will be as follows

[tex]4.4 X 10^3 = 4400[/tex]

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The upper and lower interval estimate are often describe as associated with a specific level of confidence.

In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.

The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.

The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.

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Answer:

a)  Area of inner square = 58 cm²

b)  Area of inner square = (2x² - 2xy + y²) cm²

Step-by-step explanation:

To calculate the area of a square, multiply the length of one of its sides by itself. This can be expressed as A = s², where A is the area and s is the side length of the square.

To calculate the area of a triangle, halve the product of its base and height. This can be expressed as A = (1/2)bh, where A is the area, b is the base and h is the height of the triangle.

The easiest way to calculate the area of the inner square is to subtract the areas of the 4 congruent triangles from the area of the outer square.

[tex]\hrulefill[/tex]

The outer square has a side length of 10 cm. Therefore its area is:

[tex]\implies \sf A_{outer\;square} = 10^2 = 100 \; cm^2[/tex]

Each corner triangle has a height of 3 cm and a length of (10 - 3) cm.

Therefore, the area of one triangle is:

[tex]\implies \sf A_{triangle}=\dfrac{1}{2} \cdot 7 \cdot 3=10.5\;cm^2[/tex]

Therefore, the area of the inner square is:

[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=\sf 100-(4 \cdot 10.5)\\&=\sf 100-42\\&=\sf 58\; cm^2\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The outer square has a side length of y cm. Therefore its area is:

[tex]\implies \textsf{A$_{\sf outer\;square}$} = y^2 \; \sf cm^2[/tex]

Each corner triangle has a height of x cm and a length of (y - x) cm.

Therefore, the area of one triangle is:

[tex]\begin{aligned}\implies \sf A_{triangle}&=\dfrac{1}{2} \cdot (y-x) \cdot x\\\\&=\dfrac{1}{2}x(y-x)\;\sf cm^2\end{aligned}[/tex]

Therefore, the area of the inner square is:

[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=y^2-4\left(\dfrac{1}{2}x(y-x)\right)\\\\&=y^2-2x(y-x)\\\\&=y^2-2xy+2x^2\\\\&=(2x^2-2xy+y^2)\; \sf cm^2\end{aligned}[/tex]

76 is m<BFD in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

 m<AFC + m<BFD = 180°

   (7x-8)° +   m<AFC = 180°

   (5x+6)° +  m<BFD =  180°

(7x-8)° = (5x+6)

 2x = 12

    x = 14

m<BFD=(5x+6)°

       = 5 * 14 + 6

        = 70 + 6

          = 76

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The value of the fraction x/y is 3/25 and option b is the correct answer.

An expression for a portion of a whole is a fraction. In general, the whole can be any particular object or value, and the fraction might be a piece of any quantity out of it.

The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.

The given equation is:

5x + y / y = 8/5

Divide the terms individually at the left side of the equation:

5x/y + y/y = 8/5

5 (x/y) + 1 = 8/5

5 (x/y) = 8/5 - 1

5 (x/y) = 3/5

x/y = 3/25

Hence, the value of the fraction x/y is 3/25 and option b is the correct answer.

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Answer:

a. aₙ=(aₙ₋₁ x 0.98) + 1150

The inequality that has a dashed boundary line when graphed is:

y > 3x + 1

In mathematics, an inequality is a statement that two quantities are not equal or do not have the same value. In other words, it is a statement that compares two values, expressing that one value is greater than, less than, or not equal to the other value. An inequality is denoted by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

In mathematics, a dashed boundary refers to a boundary line that is graphed as a dashed line rather than a solid line. The use of a dashed line is typically used to indicate that the boundary itself is not included in the set of solutions of an inequality or equation.

In the given question,

The inequality that has a dashed boundary line when graphed is:

y > 3x + 1

The reason for this is that when graphed, the boundary line of the inequality y > 3x + 1 is a straight line, but it is dashed instead of solid. This is because the inequality is strict, meaning that the boundary line itself is not included in the set of solutions. On the other hand, if the inequality had been y ≥ 3x + 1, the boundary line would have been a solid line because the inequality is non-strict and includes the boundary line itself as a solution.

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Answer:

Step-by-step explanation:

Me personally, I think buffets are the best because you can take as music food as you much, without being charged for much! But thats only for some buffets. If you go to a chinese buffet, they might lower the price allowing you to get as much food as you please!

The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.

Let us assume the number of coach tickets purchased is x.

And the number of first-class tickets purchased is y.

Now,

Including Sarah, a total of 11 people took the trip.

Thus,

[tex]x + y = 11 [/tex]

The cost of coach tickets and first-class tickets are $210 and $1200 respectively.

The total budget for airfare for the trip is $10,230.

Therefore,

210x + 1200y = 102309

21x + 120y = 1023

Solving both the equations, we get.

x=3

y=8

Thus, The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.

Callie will need a total of 112 feet of fence for the triangle DFG.

We can find the amount of fence needed by finding the relationship between both triangles and find the missing side.

The sum of all the sides of the triangle will be known as the perimeter of the triangle. we can use this knowledge to find the amount of fence needed.

Both triangles are similar and are in the ratio of 1:7To find the missing side of triangle DFG, we multiply the corresponding side of triangle BAC by 7 to find the missing side.

This will give us 7 x 7 = 49ft

To find the amount of fence needed for triangle DFG we add all the sides of triangle DFG which will be 49 + 35 + 28.

The total will be 112ft.

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Therefore, the total purchase price is $734.78.

Profit is the financial gain obtained by subtracting the cost (or expenses) of producing and selling goods or services from the revenue generated from their sale. In other words, profit is the amount of money that is left over after all expenses have been paid, including the cost of goods sold, operating expenses, taxes, and any other costs associated with running a business.

Profit can be calculated using the following formula:

Profit = Revenue - Cost

by the question.

To calculate the total purchase price, we need to calculate the tax and add it to the sum of the prices of the diamond necklace and the gold pendant.

The tax on the diamond necklace is:

572.95 * 0.065 = 37.24

The tax on the gold pendant is:

113.76 * 0.065 = 7.40

The total tax is the sum of these two taxes:

37.24 + 7.40 = 44.64

We also need to add the city tax, which is 0.5 percent of the total price:

(572.95 + 113.76) * 0.005 = 3.43

The total purchase price is the sum of the prices of the diamond necklace and the gold pendant, the state tax, and the city tax:

572.95 + 113.76 + 44.64 + 3.43 = 734.78

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Given:-

Solution:-

p³+10+m-m

put the value of p nd m in eqⁿ :

━━━━━━━━━━━

hope it helps⸙

The value of expression at m = 8 and p = 3 is,

⇒ 37

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ p³ + 10 + m - m

Now,

Put m = 8 and p = 3 in above expression, we get;

⇒ p³ + 10 + m - m

⇒ 3³ + 10 + 8 - 8

⇒ 27 + 10

⇒ 37

Thus, The value of expression at m = 8 and p = 3 is,

⇒ 37

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The slope of the function is -29 and the y-intercept is the point (0, 2).

What is function ?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range).

To find the slope and y-intercept of the function p(x) = 2 - 29x, we can write it in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

So, by comparing p(x) = 2 - 29x with y = mx + b, we can see that:

m = -29 (the coefficient of x)

b = 2 (the constant term)

Therefore, the slope of the function is -29 and the y-intercept is the point (0, 2).

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The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.

The height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.

area of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel bases.

we shall represent the height of the trapezoid with the letter h so that:

21 cm² = 1/2 × (5 + 9) cm × h

21 cm² = 1/2 × 14 cm × h

21 cm² = 7 cm × h

divide through by 7 cm

h = 21 cm²/7 cm

h = 3 cm

Therefore, the height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.

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Answer:

Step-by-step explanation:

To find the maximum height of the ball, we need to find the vertex of the parabolic function h(t) = -t^2 + 8t + 32. The vertex represents the highest point of the parabolic curve.

The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = -1 and b = 8, so we have:

x = -b/2a = -8/(2(-1)) = 4

Therefore, the vertex occurs at time t = 4.

To find the y-coordinate of the vertex, we evaluate the function at t = 4:

h(4) = -4^2 + 8(4) + 32 = 16 + 32 = 48

Therefore, the ball reaches a maximum height of 48 feet above the ground.