Triangle def is formed by connecting the midpoints of the sides of triangle abc.

The circumcenter of a triangle is the point where the perpendicular bisectors of all three sides of the triangle intersect.

To find the circumcenter of a triangle, you can:

Draw the perpendicular bisectors of all three sides of the triangle.

Locate the point where the three bisectors intersect. This is the circumcenter of the triangle.

To find the circumcenter of a triangle with the coordinates of its three vertices, use the circumcenter formula which is (x₁ + x₂ + x₃)/3 and (y₁ + y₂ + y₃)/3 for x and y coordinates respectively.

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By calculating, The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and the sum of three angles is always 180 degrees

Given expression ,

4x-8 = 3x+2

4x-3x = 2 + 8

x = 10

So the sides given in the triangle are 5x+1 , 2x+3 and 5x+2

So put x=10 in the give sides

we get,

5x+1  =  5*10 + 1  = 51

2x+3 = 2*10 + 3  = 20 + 3 =23

5x+2 = 5*10 + 2 = 50 + 2 = 52

The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.

Hence, By calculating, The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.

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The product of expressions ( x + a ) and (x + b ) is equals to the x² + (a - b)x - ab.

Product is an important arithmetic operation. The multiplication or product of algebraic expressions is a method of multiplying two expressions consisting of variables and constants. The product of two factors with the same signs will be positive, and the outcome of multiplying two terms with two, unlike signs, will be negative. We have two algebraic expressions as ( x + a) and ( x - b) and we have to calculate their product.

=> (x + a) ( x - b) = x( x- b) + a(x - b)

=> (x + a) ( x - b) = x² - xb + ax - ab

=> (x + a) ( x - b) = x² + (a - b)x - ab

Hence, required product is x² + (a - b)x - ab .

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Complete question:

What is the product of (x + a )and (x - b )?.

The length of side QR of triangle PQR can be calculated by using the Pythagorean Theorem. The length of QR is equal to the square root of the sum of the squares of the length of the other two sides. Therefore, if the length of sides PQ and PR are 3 units each, then the length of side QR is 8 Start Root 3 End Root units.

The length of side QR of triangle PQR can be determined by using the Pythagorean Theorem. This theorem states that in a right triangle, the sum of the squares of the lengths of the two sides is equal to the square of the length of the hypotenuse. Therefore, for triangle PQR, if the lengths of sides PQ and PR are 3 units each, then the length of side QR can be calculated by taking the square root of the sum of the squares of the lengths of the other two sides. This means that the length of side QR is 8 Start Root 3 End Root units. To calculate this, first, calculate the squares of the lengths of the other two sides by multiplying them by themselves, i.e. 3 x 3 = 9 and 3 x 3 = 9. Then, sum the squares of the lengths of the other two sides, i.e. 9 + 9 = 18. Finally, take the square root of the sum of the squares of the lengths of the other two sides, i.e. Start Root 18 End Root = 8. Thus, the length of side QR is 8 Start Root 3 End Root units.

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Answer:

[tex]\displaystyle 1\frac{2}{5}=\frac{7}{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}[/tex]

Step-by-step explanation:

density is mass/volume.

usually it is expressed as grams/cm³.

the question does not give us the information about the dimensions for density. so, I am going with my assumption.

the volume of a cylinder is

ground area × height

the ground area is a circle, so this is

pi×r²×height

r is the radius and therefore half of the diameter.

so, we have in our case as volume :

pi×(20/2)²×5 = pi×100×5 = 500pi = 1,570.796326... m³

1 m = 100 cm

1 m³ = 100×100×100 = 1,000,000 cm³

so, the volume of our cylinder is then also

1,570,796,326.7948966192... cm³

1 kg = 1000 g ("kilo" means 1000)

1300 kg = 1,300,000 g

so the standard density is

1,300,000/1,570,796,326.7948966192... g/cm³ =

= 0.000827606... g/cm3

The density of the waste is approximately 0.827 kg/m³.

A physical property is known as density gauges a substance's mass per unit volume. It is referred to as the mass-to-volume ratio.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height.

Since the diameter of the silo is 20m, the radius is 10m. Therefore, the volume of the silo is:

V = π(10m)²(5m) = 500π m³

Since the silo is full to the top with 1300kg of waste, the density of the waste is:

density = mass/volume

density = 1300kg/(500π m³)

density ≈ 0.827 kg/m³

Therefore, the density of the waste is approximately 0.827 kg/m³.

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Answer:r=6,7

Step-by-step explanation:3(6)<4(6)-6= 18<24-6= 18<18

3(7)<4(7)-6= 21<28-6= 21<22

15 bottles of Mango juice cost AED 30

Will this solve this question by the unitary method

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

What would he pay for 15 bottles of mango juice if 8 bottles cost AED 16?

so,

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

8 bottle=AED16 So I bottle of mango juice costs AED 2.

2x15=30

So,15 bottles of Mango juice cost AED 30

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The value of x=3 and y=1 is the solution.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

given equations are,

2x-y=5 and 3x+2y=11

Let  2x-y=5 ----[1]

,  3x+2y=11 ----[2]

Now, solving [1] and [2] by substitution method,

Substitute the value of x from [1] in [2],

x= [tex](\frac{5+y}{2})[/tex]

3x+2y=11

3[tex](\frac{5+y}{2})[/tex] + 2y = 11

[tex](\frac{15+3y}{2})[/tex] + 2y = 11

[tex](\frac{15+3y+4y}{2})[/tex] = 11

15 + 7y = 22

7y = 22 - 15

7y = 7

y = 1

Substitute the value of y=1 in [1],

2x - y = 5

2x - 1 = 5

2x = 6

x = 6 / 2

x = 3

Therefore, The value of x=3 and y=1.

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Answer:

Step-by-step explanation:

Answer: 1/4

Add: 3/4 + 1/6 = 3 · 3 / 4 · 3 + 1 · 2 / 6 · 2 = 9/12 + 2/12 = 9 + 2/12 = 11/12

Subtract:  1 - 2/3 = 11/12 - 2/3 = 11/12 - 2 · 4 / 3 · 4 = 11/12 - 8/12 = 11 - 8/12 = 3/12 = 3 · 1 / 3 · 4 = 1/4

Answer:

constants because

7 > 57>5

There u go

If consonants to vowels has a ratio of 7:5, this means there are 7 consonants for every 5 vowels.  There are more consonants in the word.

The sentence which describes a situation which can be represented by the equation 4 ÷ 1 1/3 is,  "4 divided by the fraction number 11 by 3"

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

An equation,

⇒ 4 ÷ 1 1/3

Mathematically, it represents that,

4 is divided by fraction number 11 by 3

or

Product of 4 and reciprocal of 11 divided by 3

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Answer:

x=210

Step-by-step explanation:

supplementary angles add up to 180 so to find x in this problem we have to keep in mind that it is gonna be divided by 2. So first subtract 75 from 180 which equals 105. Then because x is going to be divided by 2 we are going to multiply 105 by 2 so when it’s eventually divided the 2 angles equal 180. So x= 210 and 210/2 = 105 and 105+75=180.

8² = 64 , 5² = 25 and 13² = 169 . A number that has been multiplied by itself produces a square number.

8² = 8 × 8 = 64 , 5² = 5 × 5 = 25 and 13² = 13 × 13 = 169 . Informally: A square number, perfect square, or simply "a square" is what is produced when you multiply an integer (a "whole" number), positive, negative, or zero, times itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.

Similar to numbers like 2, 3, 5, 6, 24, 13, 125, etc., 12, however, is not a square. Consequently, its simplicity is somewhat usual. nevertheless, are 4, 16, 25, 81, 121, and other numbers. It is incorrect to say that the number 14 is a perfect square because it cannot be written as the product of two equal numbers. If n is a number, then n2 stands in for n.

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Answer: 140 mph

Step-by-step explanation:

3 1/2+40=140 mph

The number of miles traveled in 3(1/2) hours is 140 miles.

We have,

Speed is the ratio of the given distance and time.

It shows how fast an object is moving at a given time.

The formula of speed is used.

Speed = Distance / Time

From the given statement, make an expression.

1 hour = 40 miles

Multiply 3(1/2) on both sides.

3(1/2) hours = 3(1/2) x 40 miles

Simplify the mix fraction.

3(1/2) hours = 7/2 x 40 miles

Simplify the fraction.

3(1/2) hours = 7 x 20 miles

3(1/2) hours = 140 miles

Thus,

The number of miles traveled in 3(1/2) hours is 140 miles.

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You will need 2.8 canisters.

To determine this, you need to know the quantity of breadcrumbs required for one meatloaf and how many meatloafs you are planning to make. Since the breadcrumbs are sold by the canister, you will also need to know the quantity of breadcrumbs in one canister. With this information, you can calculate the total quantity of breadcrumbs required for all the meatloafs and divide it by the quantity of breadcrumbs in one canister to find out how many canisters you need to buy.

The solution of the given expression 9x² + ( 4y / z ) will be 4763.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 9x² + ( 4y / z ) and the values are x=23, y=3, and z=6.

The expression will be solved as below,

E = 9x² + ( 4y / z )

E = 9 x ( 23 ²) + ( 4 x 3 ) / ( 6 )

E = 4761 + 2

E = 4763

Hence, the solution will be 4763.

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The distance between points A(-6,7) and B(-1,-5) is 13 units.

We know that the distance formula.

According to distance formula distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given points A(-6,7) and B(-1,-5)

Let us assume that  (x₁, y₁) = (-6, 7)

and (x₂, y₂) = (-1, -5)

Also, d represents the distance between points A(-6,7) and B(-1,-5)

Using above distance formula,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-1 - (-6))^2 + (-5 - 7)^2]}\\\\\Rightarrow d = \sqrt{[(-1+6)^2 + (-12)^2]}\\\\\Rightarrow d = \sqrt{[(-5)^2 + (-12)^2]}\\\\\Rightarrow d = \sqrt{25+144}\\\\\Rightarrow d = \sqrt{169}\\\\\Rightarrow d = 13~units[/tex]

Therefore, the distance between points A and B is 13 units.

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The complete question is:

What is the distance between points A(-6,7) and B(-1,-5) on the coordinate plane?

The method for density is d = M/V, where d is density, M is mass, and V is extent. Density is usually expressed in devices of grams in keeping with cubic centi meter.

The common density of granite is between 2.65 and 2.75 g/cm3 (one hundred sixty five and 172 lb/cu feet), its compressive energy usually lies above hundred MPa (29,000 psi), and its viscosity close to STP is 3–6·1020 Pa·s.

GRN = GL * GW * GT/12 * a hundred seventy five

GRN is the Granite Weight (lb)

GL is the granite period (ft)

GW is the granite width (feet)

GT is the granite thickness (in)

The density of granite is high and tiers from 2.sixty three to two.75 g according to cm3. Its resistance to strain is between 1.000 and 1.4 hundred good enough in step with cm2.

Rock density can be very sensitive to the minerals that compose a particular rock kind. Sedimentary rocks (and granite), which can be rich in quartz and feldspar, have a tendency to be less dense than volcanic rocks.

Therefore, The method for density is d = M/V, where d is density, M is mass, and V is extent.

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The equation of the function is y = 10 * sin(x/2pi) + 5.

What is the sinusoidal function?

The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.

The graph of a sinusoidal function can be represented by the equation:

y = A * sin(B(x - C)) + D

where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.

The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.

The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.

So the frequency is 1/2π.

The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.

The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.

So the equation of the function is:

y = 10 * sin(1/2pi (x - 0)) + 5

y = 10 * sin(x/2pi) + 5

where x is entered in radians.

Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.

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Answer:

Dylan's budget is $250, and she is buying pumpkins for $20 each and balloons for $2 each. We can represent the total cost of the pumpkins as 20x and the total cost of the balloons as 2y. The inequality that represents all possible ways she could buy pumpkins and balloons within her budget is:

20x + 2y <= 250

To find the maximum number of balloons she could buy, we can use the equation above and set x = 0, and then solve for y.

20(0) + 2y <= 250

2y <= 250

y <= 125

The maximum number of balloons she could buy is 125.

Most linear systems will have exactly one solution. Nevertheless, it is possible that there are no solutions or infinitely many. (but It is not possible that there are exactly two solutions of a linear system.)

Let's assume a system of two linear equations, then, there are three possibilities of solutions.

The possibilities are:

Two parallel lines

e.g. y = 3x + 1

y = 3x − 2 (with the same slope, different intercepts)

Two (distinct) intersecting lines

As we know two straight lines cannot meet at two points. Two points determine only one line (not two lines).

e.g. y = 3x + 1

y = 5x − 2 (different slopes)

These equations have the same line as their graphs

If two lines do have two points in common, then "the lines coincide" (which really means "there is only one line".) In this case, we say, "the two lines are the same".

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The coordinates of the point dividing the segment in the ratio 3:1 will be ( 38 / 4, 6 / 4).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that point A is (2,0) and point B is (2,12) and the line is divided in the ratio of 3:1. the coordinate of the point will be calculated as,

Point = { ( mx₂ + nx₁ ) / ( m + n ) }, { ( my₂ + ny₁ ) / ( m + n ) }

Point = { ( 3 x 12 0 + ( 1 x 2 ) / ( 3 + 1 )], { ( 3 x 2 ) + 0 ) / ( 3 + 1) }

Point = { 38 / 4, 6 / 4 }

Hence, the coordinates of the point dividing the segment by a factor of three will be (38 / 4, 6 / 4).

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Percentage of scores must fall within 4 standard deviations of the mean according to Chebyshev's theorem is 93.75%

Chebyshev's theorem states that the proportion of the data set that lies between k standard deviations from the mean be calculated with the formula below.

1 − 1/k²

which in this case is,

=1 − 1/4²

= 1− 1/16

=15/16

=0.9375

which is 93.75%.

According to probability theory, Chebyshev's inequality ensures that no more than a specific percentage of values can deviate significantly from the mean given a large class of probability distributions.

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

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The domain of the trigonometric equation y = cosec ( x ) is given by the relation domain of y = cosec ( x ) is  x∈R , x≠π⋅n , n∈Z

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

y = cosec ( x )   be equation (1)

On simplifying the equation , we get

y = 1 / sin ( x )

Now , the domain and range of the function will be related to the sine function and range of the sine function -1 ≤ y ≤ 1

The domain of y = cosec ( x ) is every value in the domain of sine with the exception of where sin ( x ) = 0. Since the reciprocal of 0 is undefined. So we solve sin ( x ) = 0 and get x = 0 + π⋅n where n∈Z.

Therefore , the domain of y = cosec ( x ) is  x∈R , x≠π⋅n , n∈Z

Hence , the domain is x∈R , x≠π⋅n , n∈Z

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The perimeter of each shape are as follows:

a. 4x + 18 units

b. 6y + 4x units

c. 5x units

d. 16x + 12 units

The area of the square is 9x² units²

The perimeter of a shape is defined as the total length of its boundary. In other words, the perimeter of a shape is the sum of the whole sides of the figure.

Therefore, let's find the perimeter of the shapes as follows:

a.

perimeter = x + 9 + x + 9 + x + x

perimeter = 4x + 18

b.

perimeter = 3y + 3y + 2x + 2x

perimeter = 6y + 4x

c.

perimeter = 2x + 2x + x

perimeter = 5x

d.

perimeter = 4x + 1 + 2x + 3x + 5 + 2x + 1 + 3x + 5 - 2x + 4x + 1 - (2x + 1)

perimeter = 16x + 12

Area of the square = l²

where

Therefore,

Area of the square = (3x)²

Area of the square = 9x²

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Answer:

47:3

Step-by-step explanation:

47 pizzas had thick crust and 3 had thin crust

The range in statistics for a given data set is the difference between the highest and lowest values.

As a result, the range can also be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.

To find the range in statistics, we need to arrange the given values or set of data or set of observations in ascending order.

For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, The range in statistics for a given data set is the difference between the highest and lowest values.

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