Derive the formula for the Pythagorean theorem in 3 dimensions. Math help ASAP

The value of height of triangle is 12.3 units.

A triangle is a polygon with three sides, three angles, and three vertices (or corners). It is one of the most fundamental shapes in geometry and has many unique properties that make it a useful tool in mathematics and science.

The sum of the three interior angles of a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the lengths of the other two sides.

Given;

Triangle is right angle

hypotenuse=18 units

Using trigonometric formula

sin43=y/18

.68=y/18

y=12.3

Value of height of triangle is 12.3 units.

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The equation (5)/(6)x+2=(7)/(8) when rewritten without fraction has a representation of 40x + 96 = 42

Given that we have the following

(5)/(6)x+2=(7)/(8)

When the brackets are removed, we have the following equation

5/6x + 2 = 7/8

Multiplying through the equation by 6

So, we have

6 * (5/6x + 2 = 7/8)

When the products are evaluated, we have

5x + 12 = 6 *  7/8

Multiplying through the equation by 8

So, we have

8 * (5x + 12 = 6 *  7/8)

When the products are evaluated, we have

40x + 96 = 42

Hence, the solution is 40x + 96 = 42

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Answer:

median, and mode

Step-by-step explanation:

The total amount allocated to the Department of Health is R145,026,540,000, calculated by multiplying the total expenditure by the percentage allocated to the department expressed as a decimal.

To calculate the total amount allocated to the Department of Health, we need to multiply the total expenditure by the percentage allocated to the department, which is 12.6%.

Then, we must divide the percentage by 100 to get the decimal equivalent:

12.6/100 = 0.126

Next, we can calculate the total amount allocated to the Department of Health by multiplying the total expenditure by the decimal equivalent of the percentage:

Total amount allocated to the Department of Health = 0.126 x R1 149 390bn

Simplifying this expression, we get:

Total amount allocated to the Department of Health = R145,026,540,000

Therefore, the total amount allocated to the Department of Health is R145,026,540,000.

The calculation involves multiplying the total expenditure by the decimal equivalent of the percentage allocated to the department, which gives the amount allocated to the Department of Health.

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Answer:

Hello! Yes, when completing the square, you are essentially transforming a quadratic equation from standard form to vertex form. The vertex form of a quadratic equation is given by:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola and 'a' is a constant that determines the shape and direction of the parabola.

To convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form, we follow these steps:

1. Divide both sides of the equation by 'a' to make the coefficient of x^2 equal to 1.

2. Move the constant term (c/a) to the right-hand side of the equation.

3. Complete the square by adding and subtracting (b/2a)^2 on the left-hand side of the equation.

4. Factor the left-hand side of the equation as a perfect square trinomial.

5. Write the equation in vertex form by identifying the values of 'a', 'h', and 'k'.

Answer:

24pi

Step-by-step explanation:

Step-by-step explanation:

the initial salary is $52,365

increment = $57,128

Raise = $57,128 - $52,365 = $4,763

%raise = $4,763/$52,365 × 100

= 9.1%

Using fractiοn it can be derived that Albertο can run 250.25 miles in 11 days.

In Mathematics, a fractiοn can be defined as the part οf the whοle thing. Fοr example, a cake is divided intο five equal pieces, then each piece is represented by 1/5. There are prοper fractiοns and imprοper fractiοns. The upper value οf a fractiοn is called numeratοr and the lοwer value οf the fractiοn is called denοminatοr.

This is a prοblem based οn fractiοn.

If Albertο runs 3 1/4=13/4 miles each day.[This was a mixed fractiοn. Here it is cοnverted tο imprοper fractiοn.]

Sο in 7 days Albertο can run (7×13)/4 miles

In 11 days he can run (7×13×11)/4 miles.

sο he can run in 11 days = 1001/4 miles.

It is a fractiοnal fοrm. We cοnvert it intο decimal number.

Hence Albertο can run in 11 days 250.25 miles.

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∠ABO and ∠BCO equal to 35

Measure of arc AD = 180 - measure of arc CD = 180 - 125 = 55

m∠AOB = 55 ( measure of central angle is equal to intercepted arc)

∠OAB = 90 degrees (Tangent makes an angle of 90 degrees with the radius)

In triangle AOB ,

∠AB0 = 180 - (90 + 55) = 35 degrees(angle sum property of triangle)

In triangle BOC, ∠BOC = 125,

m∠, BCO = 35 degrees

Answer:

The length and width of the roof can be used to calculate the total square footage of the roof. For example, if the roof is 20 feet long and 10 feet wide, the total square footage would be 200 square feet.

Once the total square footage is known, the number of sheets of plywood needed can be calculated. Each sheet of plywood is 4 feet x 8 feet, or 32 square feet. Therefore, 200 square feet of roof would require (200/32 = 6.25) 6.25 sheets of plywood. In order to cover the entire roof, 7 sheets of plywood would need to be used.

Step-by-step explanation:

The nurse will advise the patient to take 1 ml of medication with each dose.

The physician orders medication at 400 mg po twice daily. The pharmacy supplies medication with a dosage strength of 2 grams per 5 ml.

How many milliliters does the nurse advise the patient to take with each dose?

The nurse should advise the patient to take 1 ml of medication with each dose.

To find the number of milliliters, the following formula will be used.

Dose × Volume/Strength

Given, Dose = 400 mg

Strength = 2 grams per 5 ml

Volume = ?

To convert 400 mg to grams, divide by 1000.

400 mg = 400/1000 = 0.4 g

Now, put the values in the formula,

0.4 g × Volume / 2 g/ 5 ml= 5/2 × 0.4/1= 5/2 × 0.4= 1 ml

Hence, the nurse will advise the patient to take 1 ml of medication with each dose.

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Ai Mi's total cost after the discount but before tax would be $33.93. Rounded to the nearest cent, this is equal to $33.94.

Cost refers to the total amount of money, time, effort, or resources that are required to produce or acquire a particular good or service. It can be expressed in monetary terms or other units of measurement depending on the context. Cost plays a crucial role in decision-making for individuals, businesses, and governments.

If Ai Mi has a 13% discount, it means that she will pay only 87% of the total cost of the items.

So, the cost after the discount can be calculated as:

$39 x 0.87 = $33.93

Therefore, Ai Mi's total cost after the discount but before tax would be $33.93. Rounded to the nearest cent, this is equal to $33.94.

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The experimental probability of selecting a red marble is 12/20, which simplifies to 3/5 or 0.6 as a decimal.

The theoretical probability of selecting a red marble can be calculated by dividing the number of red marbles by the total number of marbles:

P(red) = number of red marbles / total number of marbles

In this case, there are 27 red marbles out of 70 total marbles:

P(red) = 27/70

Therefore, the theoretical probability of selecting a red marble is 27/70, which cannot be simplified further as a fraction. As a decimal, it is approximately 0.386.

The slope of the equation A = 8,500 + 350t represents the rate of change of altitude with respect to time. Specifically, it represents the vertical speed of the helicopter in feet per unit of time (in this case, per time interval t).

The slope of the equation is m = -350 and the helicopter is descending at a rate of 350 feet per unit time

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

A = 8,500 - 350t

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = -350

So , it indicates that the altitude is falling at a rate of 350 feet per unit of time (t). The helicopter is falling at a constant rate of 350 feet per unit of time, according to this negative slope

Hence , the slope of the line is m = -350

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The complete question is attached below :

A helicopter is landing, and the pilot monitors her altitude, A, in feet over a set number of time intervals, t . She records her data and all of her data points fit the equation below. A= 8,500 - 350t
What does the slope of this equation represent?

The total number of outcomes that are possible is 186.

There are different ways to solve the problem of finding the total number of outcomes when selecting a letter from the word TROPHY and a day from the month of May. One way is to use the Multiplication Rule of Counting, which states that if there are n1 ways to perform the first task and n2 ways to perform the second task, then there are n1 x n2 ways to perform both tasks.

Let's apply this rule to the given problem.

1. Selecting a letter from the word TROPHY: There are 6 letters in the word TROPHY. Therefore, there are 6 ways to select a letter from the word TROPHY.

2. Selecting a day from the month of May: There are 31 days in the month of May. Therefore, there are 31 ways to select a day from the month of May.

Using the Multiplication Rule of Counting, the total number of outcomes that are possible is the product of the number of ways to perform each task:

Total number of outcomes = 6 x 31 = 186.

Therefore, there are 186 possible outcomes when selecting a letter from the word TROPHY and a day from the month of May.

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The 1st statement is true about the graph. Here the graph is a function with domain {0≤x≤5} and the range {-6≤y≤0}.

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts.

The Latin term datum, which means "something delivered," is where the word data originated.

The development of a research question is followed by the ongoing observational collection of data.

Here in the question,

The graph is a function with domain {0≤x≤5} and the range {-6≤y≤0}.

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The value of length OP is √65

The value of length PQ is √65

The value of length QR is √65

The value of length RO is √65

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is given as ;

d = √ (y2-y1)² + (x2-x1)²

The slope of a line = y2-y1)/x2-x1. This means the value of y2-y1 and x2-x1 have been calculated for each line.

Length OP = √ 4²+7²

= √ 16+49

= √ 65

length PQ = √8²+1²

= √ 64+1

= √65

length QR = √ 4²+7²

= √ 16+49

= √ 65

length RO = √8²+1²

= √ 64+1

= √65

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The diameter of circle C is [tex]x[/tex], which is [tex]5[/tex].

A circle is the collection of all points on a plane that are at a specified distance from another point (the radius) (the centre). A radius is any distance separating a point on a circle from its center. Any two radii are equal in length under the concept of a circle.

A semicircle is a half circle produced by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends.

Since [tex]CE[/tex] is a radius of the circle and the diameter is [tex]30[/tex] units long, we know that [tex]CE[/tex]is half the length of the diameter:

[tex]CE = 1/2[/tex](diameter)[tex]= 1/2([/tex]30 units)[tex]= 15[/tex] units

We are given that [tex]CE = 6x[/tex], so we can solve for [tex]x[/tex]:

[tex]CE = 6x = 15[/tex]

[tex]x = 15/6[/tex]

[tex]x = 2.5[/tex]

Now, we can use the fact that angle [tex]CED[/tex], where [tex]D[/tex] is the center of the circle, is a central angle that intercepts arc [tex]CD[/tex], to find the measure of angle [tex]CED[/tex].

Since the diameter of the circle is a straight line, it forms a [tex]180[/tex] degree angle at its endpoints. Therefore, angle [tex]CED[/tex] is half of this angle, which is:

angle [tex]CED = 1/2(180 degrees) = 90[/tex]degrees

We are given that angle [tex]CED[/tex] is [tex]30[/tex] degrees, so we can set up an equation:

angle [tex]CED = 30 = 6x[/tex]

Simplifying and solving for [tex]x[/tex]:

[tex]6x = 30[/tex]

[tex]x = 30/6[/tex]

[tex]x = 5[/tex]

Therefore, [tex]x[/tex] is equal to [tex]5[/tex].

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The initial amount is worth $ 1538.46

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that may be added over time.

Simple interest is calculated as a percentage of the principal amount and is usually expressed as an annual rate.

The formula to calculate simple interest is:

Simple Interest = Principal x Rate x Time/ 100

Here we have

You are going to receive $2,000 in 6 years from now

The annual simple interest rate is 5%

Let 'P' be the initial or principal amount

Using the formula, I = PTR/100

Simple interest will gain on 'P' at 5% for 6 years

=> I = P(6)(5)/100  

=> I = 0.3P

And total amount = P + 0.3P = 1.3P

It is given that after 6 years we get $ 2000

=> 1.3P = 2000

=> P = 1538.46

Therefore,

The initial amount is worth $ 1538.46

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The box of cereal now weighs approximately 0.9 pounds and 1.3 pounds.

To estimate the weight of the cereal in the box now, we must subtract the amount of cereal used during the week from the total weight of the box when Kiara bought it.

The total weight of the box when Kiara bought it is 1 7/16 pounds. To convert this fraction to a decimal, divide the numerator (7) by the denominator (16): 7/16 = 0.4375.

The amount of cereal used during the week is 1/2 of a pound. To convert this fraction to a decimal, divide the numerator (1) by the denominator (2): 1/2 = 0.5.

Subtract the amount of cereal used from the total weight of the box: 0.4375 - 0.5 = -0.0625.

Since the result is negative, we can approximate the weight of the cereal in the box now as 0.9 pounds. We can also round the result to the nearest hundredth: 0.4375 - 0.5 = -0.0625 = 0.94 pounds.

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Kaleb and Gage are standing approximately 12.72 feet apart from each other based on their angles of elevation to a basketball hoop that is 10 feet high.

Let's assume that Kaleb and Gage are standing on the same line perpendicular to the basketball hoop. Let's also assume that the distance between Kaleb and the hoop is x, and the distance between Gage and the hoop is y.

Using trigonometry, we can set up two equations based on the angles of elevation:

tan(40) = 10/x

tan(30) = 10/y

Solving for x and y:

x = 10/tan(40) ≈ 12.72 feet

y = 10/tan(30) ≈ 17.32 feet

Therefore, Kaleb and Gage are standing approximately 12.72 feet apart.

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Line segment BD is 12 units

Using the pythagorean theorem a^2 + b^2 = c^2

what number is 3.5% more than 26?

Answer:

Step-by-step explanation:

3.5%=0.035

0.035*26=0.91

26+0.91=

26.91

Answer:

a normal distribution

According to the question, Tyler's playlist has 36 songs. Noah's playlist has one-quarter as many songs as Tyler's playlist. then Noah's playlist has 9 songs.

     Let the number of songs on Noah's playlist be represented by x.

     To solve the question, we'll set up an equation, which is given as:

                      36 / 4 = x

      Simplifying the above equation we get:

                         9 = x

     Therefore, Noah's playlist has 9 songs.

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Step-by-step explanation:

Triangle Area = 1/2 base * height

  14.5              = 1/2   8 * height

     3.625 ft = height

To break even, Carrollton Molding Company needs to sell 1602 plastic handles per week.

Carrollton Molding Company molds plastic handles for certain Southwire products. It costs them $0.30 to make each handle plus $2082 per week to keep their molding machine operating.

The company sells each handle for $1.30.The break-even point (BEP) is defined as the point at which total revenues equal total costs. The company must sell enough units to cover all of its fixed and variable costs to reach the break-even point. The formula to calculate the break-even point is:

Break-even point = Fixed costs / (Selling price per unit - Variable costs per unit)Given, Fixed costs = $2082Selling price per unit = $1.30Variable costs per unit = $0.30Substituting these values in the formula to calculate the break-even point, Break-even point = $2082 / ($1.30 - $0.30)Break-even point = $2082 / $1.00Break-even point = 2082So, Carrollton Molding Company needs to sell 2082 units to break even.

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Answer

8/60 = 2/15

Step-by-step explanation: to get 60 times it by 4 so 8/60 then simplify it by 4 to get 2/15

Answer:

Step-by-step explanation: