Proof! Help please *no links*

The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

What are integers ?

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .

According to the Property of Closure, A set has the closure property under a particular operation if the result of the operation is always an element in the set.  If a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”

Hence ,  the set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

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A matrix's inverse can be calculated in a number of stages.

To find the inverse of a matrix, you can use the following steps:

Here is an example:

Find the inverse of the matrix A:

[1 2]

[3 4]

Find the determinant of the matrix: det(A) = 14 - 23 = -2

Find the adjoint of the matrix: adj(A) = [4 -2]

[ -3 1]

Divide the adjoint of the matrix by the determinant: A^-1 = adj(A)/det(A) = [-2 1] / -2 = [1 -1/2]

[ 3/2 -1/2]

Matrix A's inverse is A-1= [1 -1/2].

[3/2 -1/2]

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Since there is a common ratio between each term so this is a geometric sequence.

A unique kind of sequence is a geometric sequence. Every term in the series (aside from the first term) is multiplied by a fixed amount to determine the following term. In other words, we multiply the current phrase in the geometric sequence by a constant term (called the common ratio), and then divide the current term in the geometric sequence by the same common ratio to discover the previous term in the geometric sequence.

Every term in a geometric series is obtained by multiplying the term before it by the same number. [tex]a_{n}=a_{1} r^{n-1}[/tex] is the general phrase for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the word before it.

In 72 36 and 18 if we multiply the previous term by [tex]\frac{1}{2}[/tex] we will get the next term. So r=[tex]\frac{1}{2}[/tex] and hence there is a common ratio so the given sequence is geometric sequence.

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It is said that concept of using 0 numerically came from India. It is said that Aryabhatta used zero as a placeholder number in the 5th century and thus said to invent 0. There are various theories around the invention of 0.

Therefore, the answer is Aryabhatta.

Zero as a symbol and as absence of quantity helps us in calculations. As a placeholder various civilizations have utilized zero, but they didn't develop the idea of zero as a number. In the 7th century, Brahmagupta have noted laws on use of zero numerically.

Zero as a number represents an empty quantity. It is denoted by the arithmetic symbol 0.

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Answer:

The answers are in the picture I attached to this response.

Step-by-step explanation:

(1) The equation of a line, in slope-intercept form, is: [tex]y = mx + b[/tex], where m is the slope, and b is the y-intercept.

⭐ What is the slope (m) mean?

⭐ What is the y-intercept (b) mean?

To find the slope, we need to use the formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](y_1, y_2)[/tex] are coordinates you are given.

In this problem, you are given the coordinates (2,6) and (4,9). Let's substitute these coordinates into the slope formula.

[tex]m = \frac{9-6}{4-2}[/tex]

[tex]m = \frac{3}{2}[/tex]

Now, substitute the value of m into the equation of a line.

[tex]y = \frac{3}{2}x + b[/tex]

All we have to do now is substitute the value of b. We are already given that the line intersects the y-axis at (0,3), which means that (0,3) is the y-intercept.

[tex]y = \frac{3}{2}x + 3[/tex]

⭐ How do we graph this equation?

(3) Start by taking the square root of 44 on a calculator.

You should get an irrational number (a number that's digits never terminate or repeat).

Whenever you have questions like these, you are expected to round the number to the nearest tenth.

[tex]\sqrt{44} = 6.6332495807107996982298654733414\\\\\sqrt{44} = 6.6[/tex]

Choose a place on the number line to start your positive integers (1,2,3 . . .) and plot the point 6.6.

6.6 should be a bit after 6.5, which is in between 6 and 7.

Answer:

The average rate of change is -4

Step-by-step explanation:

The given function is  f(x) = -(3)x1+3

We want to find the average rate of exchange of this function from x=1 to x=3.

This is the slope of the secant line joining the points (1,f(1)) and (3,f(3)).

From the graph, f(1)=2 and f(3)= -6

The average rate of exchange

=f(3)-f(1)/3-1

=-6-2/3-1

=-8/2

=-4

Answer:

[tex]\frac{5}{36} , \frac{6}{49}[/tex]

Step-by-step explanation:

The numerator of these terms is increasing by 1

The denominator is being squared... Look at this

The denominator of the first term is 2² which equals 4

the next denominator is 3² = 9

the next 4² = 16

the next 5² = 25

so, what what's next?

6² = 36   and 7² = 49

Hope I helped! :)

Answer:

The next two terms of the following sequence is 5/36 and 6/49.

Step-by-step explanation:

The pattern in this sequence is that the numerators of the sequence are all positive integers that increase by 1, so I added 1 to each preceding numerator. The denominators of the sequence are consecutive perfect squares (e.g., 4, 9, 16, 25, 36, etc.), so I made each following denominator the next perfect square.

Answer:

Step-by-step explanation:

solved & got 8.6

The expression represents the number of coins Arthur is x + 80 cents.

The term expression in math refers a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that Arthur has x pennies. His father gave him 6 dimes, and his mother gave him 4 nickels.

And we need to find expression represents the number of coins Arthur has now.

From the given question, here we have to convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

AS we know that one penny = 1 cent, one dime = 10 cents, one nickel = 5 cents and

Therefore, x pennies = x cents

Then 6 dimes = 60cents

Then 4 nickels = 20 cents

Therefore, the Arthur's coins in total is written as,

=> (x + 60 + 40) cents

=> (x + 80) cents.

Therefore, the resulting expression is written as (x + 80) cents.

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Answer:

177x

Step-by-step explanation:

The size and shape of the object or pre-image are not changed by a rigid transformation, sometimes referred to as isometry, when the final picture is returned.

While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.

The size and shape of the object or pre-image are not changed by a rigid transformation, sometimes referred to as isometry, when the final picture is returned. Rigid transformations are any of the three recognized transformations, which include rotation, reflection, and translation.

Triangle = 1/2 X b X h

b= 10

h=5

A = 1/2 X 10X 5

A = 25 unit sq.

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The criterion if any could prove the triangles are congruent are SSS, SAS, ASA, AAS, and RHS congruence properties.

Two triangles are congruent if all the three corresponding sides of two triangles are the same. There are a few more criteria also. Thus, congruent triangles are mirror images to each other. The mathematical symbol represents congruence is ≅.

In the triangles ΔABC, ΔEFG as shown below, we can identify corresponding angles and corresponding sides are equal.

Diagram attached at the end of solution.

ΔABC≅ΔEFG

Corresponding Angles: ∠A≅∠E,∠B≅∠F,∠C≅∠G

Corresponding sides: AB≅EF,BC≅FG,AC≅EG.

Corresponding vertices: A and E,B and F,C and G

Two triangles of the same size and shape are called congruent triangles. When we rotate, reflect, or translate a triangle, its position or appearance seems identical to the other, also called congruent.

Based on the experiments, there are mainly 5 conditions or rules to compare the two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.

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The sum of the squares of three consecutive odd number   11, 13, 15 is 515.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let the second number = x.

so the first number = x-2

the third number = x + 2

according to the question, the sum of the squares of the numbers = 515

so the formula is:

x² + (x-2)² + (x + 2)² = 515

(a-b)² = a² + b² - 2ab

and,

(a+b)² = a² + b² + 2ab

So, let’s apply these to our equation:

x² + x² + 2² -2*2x + x² + 2² + 2*2x = 515

There are three x² and 2*2 = 4 and 2*2x = 4x. Let’s apply all that to the equation,

3x² + 4 - 4x + 4 + 4x = 515

there is a -4x and a +4x, -4x + 4x = 0, so let’s remove that.

3x² + 4 + 4 = 515

3x² + 8 = 515

3x² = 515 - 8

3x² = 507

x² = 507/3

x² = 169

x = √169

√169 (square root(169)) = 13

x = 13

if x = 13, then the first number = 13–2 = 11 and the third number = 13 + 2 = 15

Hence , the sum of the squares of three consecutive odd number   11, 13, 15 is 515.

11*11 + 13*13 + 15*15 = 515

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Answer:

131560.072

Step-by-step explanation:

Because it is increase so we add humdred to the percent and then divide by hundred - 18+100/100 = 1.18

eight years - 1.18 raised to the pwer of 8

worth - 35000

hence it will be - 1.18 raised to the power of 8 x 35000

thank you

Answer:

  1/6 pan

Step-by-step explanation:

You want to know the portion of the whole represented by 1/4 of 2/3.

Todd ate 1/4 of 2/3 of the pan of brownies. That fraction of the original whole amount is ...

  (1/4)×(2/3) = (1·2)/(4·3) = 2/12 = 1/6

Todd ate 1/6 of the entire pan.

Answer:

The scale factor is 60

Step-by-step explanation:

The drawing is measured in inches and the billboard is measured in feet.  First, convert 15 feet to 180 inches.  Then use the ratio [tex]\frac{180}{3}[/tex] to find that the scale factor is 60.  This means the length of the billboard will be 600 inches or 50 feet.

Finding the missing number from the N numbers in the given array arr[] of size N-1 with integers in the range [1, N] is the task. The list must not contain any duplicates.

Java method for locating a missing integer in an array of integers from 1 to N:

Make a temp array temp[] of size n + 1 with a value of 0 for each element.

For each element in the input array arr[i], perform the following.

If (temp[arr[i]] == 0), then temp[arr[i]] is 1.

traverse temp[] and output an element of an array with the value of 0. (This is the missing element).

class GFG; import java.io.*; import java.util.*

public static void findMissing(int arr[], int N)

{

int i;

int temp[] = new int[N + 1];

for (i = 0; i <= N; i++) {

 temp[i] = 0;

}for (i = 0; i < N; i++) {

 temp[arr[i] - 1] = 1;

} int ans = 0;

for (i = 0; i <= N; i++) {

 if (temp[i] == 0)

  ans = i + 1;

} System.out.println(ans);

}

public static void main(String[] args) {

int arr[] = { 1, 3, 7, 5, 6, 2 };

int n = arr.length; // Function call

findMissing(arr, n);

}

}

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A triangular prism and a triangular pyramid with identical bases and heights are related by the fact that the prism's volume is three times that of the pyramid.

When a pyramid and a prism have bases and heights that are equivalent, the pyramid can fit inside the prism. In reality, when this is the case, the pyramid occupies precisely one-third of the prism's volume. This fact enables us to see a correlation between the volumes of a prism and a pyramid when their bases and heights are equal. That is, a prism with an identical height and base has a volume that is 1/3 that of a pyramid.

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Required Conditions for similarity of traingles are:-

What are similar traingle?

Triangles with have the same shape but can distinct sizes are said to be similar triangles. In other words, if two triangles are similar,then they need to follow either of the 2 mentioned condition if  their corresponding sides are proportionately equal and their corresponding angles are congruent.

Conditions for similarity of traingles are:-

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Answer:

-15/4

Step-by-step explanation:

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

  =(3-18)/(-14- -18)

  =-15/4

Answer:

Slope = [tex] \sf \frac{-15}{4} [/tex]

Step-by-step explanation:

Now we have to,

→ find the required slope.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Then the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (3 - 18)/(-14 -(-18))

→ m = -15/(-14 + 18)

→ [ m = -15/4 ]

Hence, the slope is -15/4.

Positive Slope: A slope in which two variables, i.e., variable at x-axis and variable at the y-axis, shows a positive relationship is known as positive slope. In simpler words, a positive slope is one in which the variable x increases with the increase in variable y and/or variable y increases with the increase in variable x.

Negative Slope: A slope in which two variables, i.e., variable at x-axis and variable at the y-axis, shows a negative relationship is known as negative slope. In other words, a negative slope is one in which the variable x increases with the decrease in variable y and/or variable y increases with the decrease in variable x.

A number of absolute values that represent whether a line is steeper or flatter and the direction of the line on the graph are known as a slope or gradient. The slope of a line is fundamental concept in economics and mathematics. It is generally denoted by the letter 'm'. The slope can be calculated by dividing the 'vertical change' with the 'horizontal change' between two distinct points on a line.

There are two main types of slopes which are given below:

Positive Slope: A slope in which two variables, i.e., variable at x-axis and variable at the y-axis, shows a positive relationship is known as positive slope. In simpler words, a positive slope is one in which the variable x increases with the increase in variable y and/or variable y increases with the increase in variable x. Similarly, the variable x decreases with the decrease in variable y, and/or variable y decreases with the decrease in variable x. It means both the variables are complements to each other. A positive slope moves in the upward direction or is upward sloping.

In graphical terms, a positive slope is one in which the line on the graph rises when it moves from left to right. The concept of positive slope can be clearly understood with the help of the supply curve of a producer or firm in economics. The two variables of the curve are price at the y-axis and quantity of goods at the x-axis. Let us assume the firm is producing the goods for profit maximization. Therefore, when the prices of the goods increase, the quantity supplied by the firm of those goods will also increase, while when the prices decrease, the quantity supplied by the firm will decrease.

Negative Slope: A slope in which two variables, i.e., variable at x-axis and variable at the y-axis, shows a negative relationship is known as negative slope. In other words, a negative slope is one in which the variable x increases with the decrease in variable y and/or variable y increases with the decrease in variable x. In the same manner, the variable x decreases with the increase in variable y, and/or variable y decreases with the increase in variable x. This represents an inverse relationship between these two variables. A negative slope moves in the downward direction or is downward sloping.

Graphically, a negative slope is one in which the line on the graph falls when it moves from left to right. One of the best examples of the negative slope of the graph is the demand curve in economics. The two variables of the curve are price at the y-axis and quantity of goods at the x-axis. As we know, the consumers buy a large quantity of a good at a lower price than at a higher price. Therefore, the quantity demanded by the consumers of goods will decrease with an increase in the prices of those goods. On the other hand, when prices of the goods will decrease, the quantity demand will increase.

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When an initial/input value is zero, the output of a function is its initial value.

The starting value represents the input at zero, whereas the rate of change relates to how rapidly the output varies in respect to the input.

Thus, if x = 0 in a function, the initial value is defined. It serves as the scenario's beginning point in real life.

A linear equation's y-intercept is frequently thought of as initial value of the function.

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The given equation can be expressed as xy²+7xy+5y-3=0.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. In English, a well-formed formula with two expressions joined by an equals sign is referred to as an equation; however, cognates of this word in other languages may have slightly different meanings. For instance, the French definition of an equation is one or more variables.

Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved. Equations can be classified as either conditional equations or identities.

Given,

(3/y)-5=x(y+7)

(3-5y)/y=(xy+7x)

3-5y=xy²+7xy

xy²+7xy+5y-3=0

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(A) The expression for each plane are as follows;

B). The equation to show when the two planes would be at the same altitude is; 700 + 16x = 424 + 22x.

It follows from the task content that the initial altitudes of plane A and B are 700 and 424 respectively.

Hence, since plane A gains altitude at 16 meters per second; The expression for the altitude after x seconds is;

Also, since plane B gains altitude at 22 meters per second; The expression for the altitude after x seconds is;

Therefore, when the two planes are at the same altitude; the equation which is true is;

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The expression to find the total number of slices of pizza is 2 + 3

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

Initial slices of pizza = 2

Additional slices of pizza = 3

This means that

The expression to find the total number of slices of pizza is

Total number of slices of pizza = Initial slices of pizza + Additional slices of pizza

Substitute the known values in the above equation, so, we have the following representation

Total number of slices of pizza = 2 + 3

Hence, the expression is 2 + 3

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The matrix will not have an inverse if the determinant is 0; in this case, it is referred to as singular.

An inverse function is a function that gives back the initial value for which an output was provided by another function. The inverse function of y, or [tex]f^{-1}(y)[/tex], will return the value x if f(x) is a function that produces the value y.

Put negatives in front of b and c, swap the locations of a and d, then divide the result by the determinant to determine the inverse of a 2×2 matrix (ad-bc).

Not every matrix of size 2 by 2 has an inverse matrix. The matrix will not have an inverse if the determinant is 0; in this case, it is referred to as singular. Inverses exist only for non-singular matrices.

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Put negatives in front of b and c, swap the locations of a and d, then divide the result by the determinant to determine the inverse of a 2x2 matrix (ad-bc).

Hence, Put negatives in front of b and c, swap the locations of a and d, then divide the result by the determinant to determine the inverse of a 2x2 matrix (ad-bc).

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The graph that represents the equation y = 3/2x² - 6x is

B. The graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7)

The shape of a quadratic function's graph. is a U-shaped curve,

The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of the quadratic function, is where the parabola will open up.

The vertex is the highest point on the graph or the maximum value if the parabola opens downward.

In the problem the graph opens up and points are plotted and attached, the graph shows that option is the correct choice

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In Microsoft Excel 2007, a maximum of 1,048,576 rows may be used. 15.784 columns. A spreadsheet in Excel is composed of columns and rows.

Row refers to a group of objects placed next to or across from one another. A column is defined as a vertical arrangement of objects based on category. The arrangement is done from left to right. The setup is created from top to bottom. The sum is shown on the far right.

here

The rows are horizontally arranged and designated by the numbers 1, 2, 3, and 4.

The letters that go horizontally down the columns are identified by the letters A, B, C, D, etc.

When a column and a row cross, cells are what result.

In Microsoft Excel 2007, 1,048,576 rows is the maximum number permitted. 15,384 rows.

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The triangle transitive congruent is proved by considering that if one triangle is congruent to second triangle and second triangle is congruent to third one, then the first triangle is congruent to third triangle.

The transitive property states that if one geometry is congruent with another, and the second is congruent with a third, then the first is also congruent with the third.

Statement : If triangle ABC is similar to triangle PQR and triangle PQR is similar to triangle EFG , then triangle ABC is similar to triangle EFG.

Given, ∆ABC ≅ ∆PQR and ∆PQR ≅ ∆EFG

RTP -> ∆ABC ≅ ∆EFG.

Proof : ∆ABC ≅ ∆PQR, SSA Congruence which implies, AB = PQ --(1)

PR = AC --(2)

and angle ABC = angle PQR --(3)

∆PQR ≅ ∆EFG, AAS Congruence which gives

Angle PQR = Angle EFG --(4)

PQ = EF --(5)

Angle PRQ = Angle EGF --(6)

from (3) and (4) we get,

angle ABC = Angle EFG --(7)

from (1) and (5) we get , AB = EF --(8)

angle BAC = angle FEG = 40° --(9)

Now, from (7) , (8), (9) we conclude that the triangle ABC is Congruent to triangle EFG by ASA Congrauance postulate i.e ∆ABC ≅ ∆EFG.

Hence proved.

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