20. Find the length of BC in the figure below.
A- 12
BC ?
E - 16
D - 8

The required value of x and y in the given equation are ,

x= 1,

y = -1 .

The algebraic method to solving simultaneous linear equations is known as substitution method. This method, as the name suggests, involves substituting the value of one variable from one equation into the second equation. This makes it much easier to answer a pair of linear equations by combining them into a single linear equation with only one variable.

The given equations are

0.1x - 0.3y = 0.4                             ...(1)

0.3x − 0.2y=0.5                              ....(2)

Multiply both the equations by 10, we get

x - 3y = 4                                           ...(1)

3x − 2y = 5                                        ...(2)

Multiply (1) by 3

3x - 9y = 12

3x − 2y = 5

Subtracting both the equations

-7y = 7

y = -1

From (1):

x - 3(-1) = 4

x + 3 = 4

x = 4 - 3

x = 1

The required value for x and y is,

x= 1,

y = -1

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The length of DE is 12 unit.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

In Triangle DFC using Trigonometry

sin 45 = B/ H

1/ √2 = DF / 12√2

DF = 12 unit

So, DE= DF + FE

DE = 12 + 9

DE = 12 unit.

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The table of values for y = -128x + 3840 is:

x y

0 3840

5 3200

8 2816

10 2560

30 0

From the question, we have the following parameters that can be used in our computation:

Y= -128x + 3840

Then, we have

x = 0,5,8,10,30​

To find the values of y, we substitute each value of x into the equation and simplify:

This means that the above is the table of values for y = -128x + 3840 when x takes on the values 0, 5, 8, 10, and 30

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Another name for the regression line is the least squares line because it was chosen to make the sum of the squares of the differences between the observed y values ​​and the values ​​predicted by the line as small as possible.

A regression line (LSRL - Least Squares Regression Line) is a straight line that describes how the response variable y changes when the explanatory variable x changes. The line is the mathematical model used to predict the value of y for a given x.

Least squares is a form of mathematical regression analysis used to determine the line of best fit for a data set, providing a visual demonstration of the relationship between data points. Each data point represents the relationship between a known independent variable and an unknown dependent variable.

If the data shows a weak relationship between two variables, the line that best fits this linear relationship is called a least-squares regression line, and it minimizes the vertical distance of the data points from the regression line. The term "least squares" is used because it is the minimum of the sum of squared errors, also known as "variance". In regression analysis, the dependent variable is shown on the vertical y-axis and the independent variable is shown on the horizontal x-axis. These specifications form the equation for the line of best fit, which is determined by the method of least squares.

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the value of x will be 8√2 for the given right-angle triangle.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, Two right-angle triangles one with the height of "x" and a base angle of 45-degree.

Another with a base of 8 and a base angle of 60-degree.

From the cosine rule of trigonometry:

Cos θ = base/(hypotenuse)

Sin θ = height/(hypotenuse)

For the triangle with a base angle of 45-degree

sin 45 = height/(hypotenuse)

1/√2 = x/(hypotenuse)

hypotenuse = x *√2.....(1)

For the triangle with a base angle of 60-degree

cos 60 = base/(hypotenuse)

1/2 = 8/(hypotenuse)

hypotenuse = 16

substitute this value in equation 1

x = 8√2

therefore, the value of x will be 8√2 for the given right-angle triangle.

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Here is an explanation to understand step by step how to do this.

A volume can be determined for any three-dimensional object using formulas that are unique to that item's shape. For instance, the volume of a water bottle indicates how much water it can hold. Understanding an object's volume is crucial since it indicates how much stuff that shape can carry.

Any form or object's volume is directly inversely proportional to the volume of water it displaces when submerged in water because of its link to density. As a result, there are two ways to determine an object's volume: by mathematically calculating it using the formula unique to that shape, or by submerging it in water and measuring the volumetric displacement of the water.

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x, which can be simplified to x < 5

and

-6x – 5 < 10 – x, which can be simplified to -5x < 15, and then x > -3

Therefore, the correct options are:

x < 5

A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The FRF method is a common technique for analyzing the dynamics of structures and systems, it is typically not used as a primary method for determining a system damping ratio by field measurements.

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A pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions. Option D is the correct answer.

The dimension of an item in mathematics is, approximately speaking, the quantity of degrees of freedom of a moving point on the object. To put it another way, a dimension is indeed the amount of distinct factors or coordinates required to define the location of a point that must be on an object. For instance, a point has a dimension of zero; a line has a size of one since a point can only move along a line in one direction (or its opposite); a plane has a dimension of two; etc.

The volume of the wooden board is given by the formula:

V = (l)(b)(h)

V = (2)(6)(14)

V = 168 cubic inches.

The volume of pile of 3 boards has dimensions:

l = 14

b = 6

h = 3(2)

V = 3(168) = 504 cubic inches.

Similarly, piling the boards and changing the height.

The volume of pile of four boards = 4(168).

The volume of pile of 5 boards = 5(168)

The volume of pile of 6 boards = 6(168) = 2(3(168))  = 2(Volume of pile of 3 boards)

Hence, a pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions.

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The spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

The maximum amount of water that one of the spherical tanks of Eindhoven will hold can be found using the formula for the volume of a sphere:

V = (4/3) * π * [tex]r^3[/tex]

where V is the volume of the sphere, r is the radius of the sphere, and π is a constant equal to approximately 3.14159.

According to the Eindhoven website, the diameter of each spherical tank is 30 meters. The radius, therefore, is half of the diameter, which is:

r = 30/2 = 15 meters

Substituting this value into the formula for the volume of a sphere, we get:

V = (4/3) * π * [tex](15)^3[/tex]

V ≈ 14,137 cubic meters

When we round this to the closest integer, we obtain:

Maximum amount of water = 14,137 cubic meters

Therefore, one of the spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

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The magnitude of the vector is calculated by using the formula √((c-a)²+(d-b)²) where A(a,b) and B(c,d) are point on the plane.

A vector is any quantity that has a magnitude as well as directiom and that also follows the vector law of addition.

Let us say that there are any two points on the co-ordinate plane A(a,b) and B(c,d).

Now the magnitude of the vector AB can be found by using the formula,

AB = √((c-a)²+(d-b)²)

and the direction of this vector will be from A to B on the coordinate plane. If we want to find direction, then it is given by, tab A = (d-b)/(c-a)

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Answer:

The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.

Step-by-step explanation:

The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

A. Line of Best Fit

A regression line is a statistical tool used to predict the value of a response variable based on the value of one or more predictor variables. It is also known as a line of best fit because it is used to show the best fit of a given data set. The line of best fit is a straight line that best represents the data by minimizing the sum of the squared distances between the observed data points and the line. The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

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Answer:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes through (0, 1), (2, 4), and (3, 8).

Step-by-step explanation:

Answer:

graph 2

Step-by-step explanation:

I did the assignment

The two lines that are parallel to y = 2x - 1 that pass through the given points are:

a) y = 2x + 1

b) y = 2x

A general linear equation is written in the slope-intercept form as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are parallel if the slopes are equal but the y-intercepts are different.

So, here we want to find lines parallel to:

y = 2x - 1

These lines have the form:

y = 2x + b

a) If we want our line to pass thrugh A(0,1), we can replace the values of the point to get:

1 = 2*0 + b

1  = b

So the line is y = 2x + 1

b) if we want the line to pass through A(1,2) we can replace the values to get:

2 = 2*1 + b

2 = 2 + b

2 - 2 = b

0  =b

So this line is:

y = 2x

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Answer:

(4 × y) - 8 = <26

Step-by-step explanation:

The equation for this problem is:

(Let y = the unknown number)

Therefore, you can use (4 × y) - 8 = <26 as an inequality for this problem.

Answer:

Gram.

Step-by-step explanation:

Commutative property of addition is the property that we used to get the answer for 27+29+31 = 87.

The commutative property of addition says that changing the order of addends does not change the sum. As the first civilization to study fractions, the Egyptians used fractions to address a variety of mathematical problems, including the division of food and supplies and the absence of a bullion currency.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

In the properties used for this question use the properties of the Commutative property of addition

If counted then the final result

31 + 27 + 29

= (30 +1) + (30 - 3) + (30 - 1)

= 3(30) + 1 - 3 - 1

= 90 - 3

= 87

Hence, 27+29+31 = 87

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Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is  aⁿ = a(3)ⁿ and Second  sequence nth formula is  aⁿ = a + (n-1)5.

A list's values are added together to get the average values, also known as the group's mean, which is then multiplied by the maximum population of list items. Similar progression trends can be seen in math. The average of the actual numbers 5, 8, and Nine is 3, while a mean of the actual numbers 5, 7, & 9 is 4, and indeed the number 21 times three (there now multiple 3 numbers) equals seven. This is demonstrated by the following equation.

Here,

Given :

First sequence :

=> 7,21,63 ....

We can see it is a type of geometric progression:

As,

=> 21/7 = 3

=> 63/21 = 3

So, it's nth formula is :  aⁿ = a(3)ⁿ

And

Second sequence :

=> 3, 8, 13,....

it is a type of arithmetic progression:

As,

=> 8 -3 =5

=> 13 -8 = 5

So, it's nth formula is :  aⁿ = a + (n-1)5

Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is  aⁿ = a(3)ⁿ and Second  sequence nth formula is  aⁿ = a + (n-1)5.

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Answer:

  65 cm

Step-by-step explanation:

You want the perimeter of the shape that results from removing a 60° sector from a circle.

The curved edge of the shape is 5/6 of the circumference of the circle.

  5/6C = 5/6(2πr) = 5/6·2·π·(9 cm) = 15π cm ≈ 47 cm

Each straight edge of the shape has a length equal to the radius. Then the straight edges have a total length of ...

  2r = 2(9 cm) = 18 cm

The perimeter of the shape is the sum of the length of its curved edge and the lengths of the straight edges:

  P = 47 cm + 18 cm = 65 cm

The perimeter is about 65 cm.

__

Additional comment

A total circle is 360°, so 1/6 of the circle is 60°. The size of a sector of a circle can be described by the angle measure of its central angle. Here, that means the removed portion is a 60° sector.

The domain of the given function in the graph will be x ≤ -1.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, a function as we can see in the graph,

Since The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values.

The y-axis on a graph represents the possible output values or range.

thus, in the given graph the domain of the function will be All real values smaller than -1.

therefore, the domain of the given function in the graph will be x ≤-1.

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Answer:

B) 5

Step-by-step explanation:

   AB = 4 units

  BC = 3 units

Use Pythagorean theorem to find the length of AC,

                AC² = AB² + BC²

                      = 4² + 3²

                       = 16 + 9

                       = 25

                  [tex]AC = \sqrt{25}\\\\[/tex]

                 AC = 5 units

Answer: 20

Step-by-step explanation: The volume formula for a rectangular pyramid is [tex]\frac{lwh}{3}[/tex] so the initial volume would be 540. Since you are dilating it by 1/3 the length, with, and height are all shrinking by 1/3. 1/3*1/3*1/3 is 1/27 so that means the final thing will be 1/27 of its original size.

Answer:

So, first let's understand what a scale factor is. A scale factor is a number that tells you how much you need to multiply the size of an object to make it bigger or smaller. In this case, the scale factor is 1/3, which means we're going to make the pyramid one third of its original size.

Now, let's talk about how we can find the volume of the pyramid. The formula for the volume of a pyramid is:

Volume = (1/3) x base area x height

The base area is the area of the rectangle at the bottom of the pyramid, which we can find by multiplying the length and width:

Base area = 9 cm x 12 cm = 108 square cm

The height of the pyramid is given as 15 cm, so we can substitute these values into the formula:

Volume = (1/3) x 108 square cm x 15 cm

Volume = 540 cubic cm

So the volume of the original pyramid is 540 cubic cm. But we need to find the volume of the pyramid after it is dilated by a scale factor of 1/3. To do this, we need to multiply the original volume by the scale factor cubed. The reason we cube the scale factor is because we're scaling in three dimensions (length, width, and height).

Scale factor cubed = (1/3) x (1/3) x (1/3) = 1/27

Volume of dilated pyramid = 540 cubic cm x 1/27

Volume of dilated pyramid = 20 cubic cm (rounded to the nearest whole number)

So the volume of the pyramid after it is dilated by a scale factor of 1/3 is 20 cubic cm.

Using distributive property, the expression 55x+5 can be written as 5(11x+1).

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

Expression           Property         Equivalent expression

3(2+x)                 Distributive                  6+3x

2+(3+4)              Associative                  (2+3)+4

24x+18y             Distributive                 8(3x+y)

4x+5x                Commutative              5x+4x

5+2+3               Commutative               3+2+5

(5x.3y).2           Associative                  5x.(3y.2)

12-3x                Distributive                   3(4-x)

6+3                  Commutative                 3+6

(2x.3y).5z         Associative                  2x(3y.5z)

4(5-2y)             Distributive                   20-8y

y+0                  Identity                             y

a.b                  Commutative                   b.a

3x.1                  Identity                            3x

(a+b)+c           Associative                   a+(b+c)

55x+5            Distributive                   5(11x+1)

8(y-2)             Distributive                    8y-16

2x+5y             Commutative                5y+2x

Therefore, using distributive property, the expression 55x+5 can be written as 5(11x+1).

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The method for determining the similar relationship between the parameters of two equations has been explained below.

The relationship between parameters in two equations depends on the specific equations and parameters involved. In general, parameters are constants or variables that are used to define or modify the behavior of a mathematical or physical system.

If two equations have the same parameters, then changes in those parameters will affect the behavior of both equations in the same way and if they have different parameters, then changes in those parameters may affect the behavior of the equations differently. In general, to determine the relationship between parameters in two equations, you would need to analyze the equations and their specific parameters to understand how they are related.

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Answer:

1 cake

Step-by-step explanation:

12 slices = 2 cakes

6 slices = 1 cake

Answer: Let's use algebra to solve this problem.

Let C be Clot's present age and S be Soup's present age. Then, according to the problem:

One year ago, Clot was C-1 years old, and four times Soup's age at that time was 4(S-1).

Clot's age one year ago was one-third of four times Soup's age, so we have:

C - 1 = (1/3) * 4(S - 1)

Simplifying this equation, we get:

C - 1 = (4/3)(S - 1)

C = (4/3)(S - 1) + 1

One year from now, Clot will be C + 1 years old, and Soup will be S + 1 years old. The sum of their ages will be 21, so we have:

(C + 1) + (S + 1) = 21

C + S + 2 = 21

C + S = 19

Now we have two equations with two unknowns. We can substitute the expression for C from the first equation into the second equation to get an equation in terms of S:

(4/3)(S - 1) + 1 + S = 19

Simplifying and solving for S, we get:

S = 6

Substituting S = 6 into the equation C + S = 19, we get:

C + 6 = 19

C = 13

Therefore, Clot's present age is 13 and Soup's present age is 6.

Step-by-step explanation:

Using normal distribution we know that 7.78% of travelers reported spending less than $1,200 for a 12-day getaway.

Asymmetric probability distribution about the mean, known as the normal distribution or the Gaussian distribution, would indicate that data close to the mean occur more frequently than data far from the mean.

The "bell curve" is a visual representation of the normal distribution.

Currently, in response to the query:

The z-score can be calculated using the formula:

z = (x - μ)/σ

It averages $1,755:

μ = $1,755

$390 is the standard deviation:

σ = 390

The trip doesn't cost more than $1200:

x = $1200

Replace the values in the z-score formula:

z-score = (1200 - 1,755)/390 = -1.42

Use the z-negative table's normal distribution:

P(z < 1,200) = 0.07782

P(x < 1,200) = P(z < 1,200)

P(x < 1,200) = 0.07782

P(x < 1,200) = 7.78%

Therefore, using normal distribution we know that 7.78% of travelers reported spending less than $1,200 for a 12-day getaway.

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Correct question:

If the data are normally distributed with a standard deviation of $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.

Therefore, we would anticipate finding 150,000x golden fish throughout the entire lake based on the class average.

Volume is the measure of room within a particular 3D entity in mathematics. For illustration, a fish aquarium measures three feet long by one foot wide by two feet high. The capacity is calculated by multiplying the length, the breadth, and the height, or 3x1x2, that also equals six. The fish aquarium therefore has a 6 cubic foot capacity.

Let's say the class average is "x" yellow fish per liter of water.

If the sample contained 500 liters of water, we can estimate the number of yellow fish in the sample as:

500 * x = 500x

Now that we have an approximation, we can use it to determine the anticipated number of yellow fish in the 150,000,000-liter pool as a whole.

The expected number of yellow fish in the whole lake would be:

(500x / 500) * 150,000,000 = 150,000x

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Answer:

210 students

Step-by-step explanation:

We want to find 75% of 280, which means we want to find 75 out of every 100 students who voted. We can do this by multiplying 280 by 75% (or 0.75).

280 x 0.75 = 210

So, 210 students voted for the Chiefs to win the Super Bowl.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

Answer:

Step-by-step explanation:

75% = .75

280 x .75 =210

Answer = 210