What are the four ways to prove that two triangles are similar?

Yes, it is generally considered appropriate for a 12-year-old to learn algebra. Algebra is a branch of mathematics that involves working with variables and equations to solve problems. It is usually introduced to students in middle school or junior high school, which is around the age of 12 or 13.

According to studies, depending on the teaching technique and intellectual maturity: between 5 and 13. Algebra is a theoretical algebra with fewer techniques for demonstrating tangible lessons.

A youngster who develops abstract comprehension at a young age might learn extremely quickly, but a pupil who has difficulties with abstract notions may struggle well into their adolescence.

It is crucial to recognize that each student learns at a different rate and may have distinct arithmetic talents and weaknesses. It is critical that students receive the necessary support and adjustments in order to study algebra and excel in their math studies.

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The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]

When the vector of constants to the right of the equals sign is not zero, an equation system is said to be non-homogeneous. A broad description of the solutions to a non-homogeneous system is presented in this solution.

General solution for the equation: [tex]y''-y'=t[/tex] , [tex]yp(t)=-t[/tex]

Consider the equation [tex]y''-y'=t[/tex]. The corresponding homogeneous equation has the associated auxiliary equation  [tex]r^2-1=0[/tex] which has [tex]r= -1[/tex]  and [tex]r=1[/tex]  as solutions.

The solution of an n[tex]^{th}[/tex]-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.

Hence the general solution for a homogeneous equation is [tex]y(t)=-t+c_{1}e^t+c_{2}e^-t[/tex]

Combining the general solution [tex]y(t) = c_{1}e^t+c_{2}e^t[/tex] of  [tex]y"-y'=0[/tex]  with the particular solution [tex]y_{p}(t)=-t[/tex] of [tex]y"-y'=t[/tex], we find that the general solution to [tex]y"-y'=t[/tex]  is  [tex]y(t)=c_{1}e^-t+c_{2}e^t-t[/tex]

The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]

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Answer:

Step-by-step explanation:

A direct variation is a linear relationship between variables so they have a constant ratio. It is a special case of the slope-intercept form y =mx +b, where b = 0.

To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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The graph of the line x=-5 is attached below :

An informational shift over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments.

x=-5 denotes that for the given line the value of x cordinate is always same and is equals to -5.

This line passes through point (-5,0)

So for the given line the value of x cordinate is constant and is equal to -5 so it is a vertical line that passes through point (-5,0).

Any straight line that runs from top to bottom or bottom to top is considered to be a vertical line. Standing lines are another name for the vertical lines.

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An object is moved rigidly when it is transferred from one location to another without affecting its size or shape.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

An object is moved rigidly when it is transferred from one location to another without affecting its size or shape. Only a precise movement may generate a correspondence between two forms, and only then can two shapes match.

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Bibliographic citations are the headings on your References page that provide links to the sources you used in your essay.

The entries on your References page that give directions to the sources you cited in your essay are known as bibliographic citations.

Consider them the "address" of a source since they direct readers to a source you cite.

The author's name, the book's title, the publisher's name, and the publication date must all be included in a book citation.

When cited in full, edited books will list the editor's name rather than the author's name.

The appearance of bibliographies can vary depending on the style manual you are using.

Bibliographies often include the page number, title, and an alphabetical list of all the sources you consulted.

A synopsis of the work is also included in annotated bibliographies.

Therefore, bibliographic citations are the headings on your References page that provide links to the sources you used in your essay.

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Whole numbers are closed under addition and multiplication. If we add and  multiply any two whole numbers, the result will be a whole number.

What are Whole numbers ?
The numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Whereas Integer: A counting number, zero, or the negative.

If we add any two whole numbers, the result will be a whole number. For example, 2 + 4 = 6 and 6 is a whole number.

Therefore, whole numbers are closed under addition.

If we multiply any two whole numbers, the result will be a whole number. For example, 2 × 4 = 8 and 8 is a whole number.

Therefore, whole numbers are closed under multiplication.

Also , Whole numbers are not closed under Subtraction and division.

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A point in mathematics is symbolised by a dot (.) and used to indicate an accurate location in space. It lacks all three dimensions—length, breadth, and height. It has no size, in other terms.

Different Points

In geometry, there are several distinct kinds of points:

Converging Points

Collinear refers to something that is parallel. If three or more points lie on a single straight line, they are said to be collinear.

Incongruent Points

If three or more points do not lie on the same line, they are said to be non-collinear. There isn't a single straight line that can be drawn that goes through each of these points.

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Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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Answer: The first one is correct

Step-by-step explanation: 4x(-2)=-8; The car used 8 gallons of gasoline.

Answer:

  b)  process b

Step-by-step explanation:

You have 2 of machine A, each of which can do its process in 1 minute; 1 of machine B, which takes 2 minutes to do its process; and 3 of machine C, each of which takes 3 minutes to do its process.

In 6 minutes, the 2 of machine A can produce 2 × 6/1 = 12 units.

In 6 minutes, the 1 of machine B can produce 1 × 6/2 = 3 units.

In 6 minutes, the 3 of machine C can produce 3 × 6/3 = 6 units.

Process B produces the fewest units in equivalent time, so process b is the bottleneck.

__

Additional comment

The production quantity of a given machine is ...

  (production time)/(time/unit) = units

This will be multiplied by the number of machines doing the process.

For comparison purposes, we used a production time of 6 minutes here.

The graph of the given function is attached below.

What is a absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x > 0 and f(x) = -x if x 0.

Given function is g(x)= - 2|x -5|-4.

Finding some points on the graph:

Putting x = 5

g(5)= - 2|5 -5|-4

g(5) = -4

Putting x = 0

g(0)= - 2|0-5|-4

g(0) = -2 ×5 - 4

g(0) = -14

Putting x = 10

g(10)= - 2|10 -5|-4

g(10) = -2 ×5 - 4

g(10) = -14

The points on the graph are ( 5,-4), (0,-14), (10,-14).

Plot the points and joint them.

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The multiplicative rate of change of the exponential function represented in the table is given as follows:

1.5.

For an exponential function, when x is increased by one, the output variable y is multiplied by a constant, called multiplicative rate of change of the exponential function.

Then, given a table of values, the rate of change is obtained by the division of two outputs(output with the greater input divided by output with the smaller input) when their inputs have a difference of 1.

Thus, for the table, the rate of change is obtained as follows:

6.75/4.5 = 1.5.

(the difference of the inputs is of 2 - 1 = 1).

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The equivalent expression is (3⁴/7³)³ = 3¹²/7⁹

Define Power Rule for Exponents

The Power Rule for Exponents:  (aⁿ)ˣ= aⁿ*ˣ .

To raise a number with an exponent to a power, multiply the exponent times the power.

Negative Exponent Rule: x⁻ⁿ = 1/xⁿ.

Given expression is,

(3⁴/7³)³

We need to find equivalent expression,

⇒ (3⁴/7³)³

first, split up exponent 3 to both Numerator and denominator as ,

⇒ (3⁴)³ / (7³)³

Now, power of a power can be done as product as,

⇒ 3¹² / 7⁹

Hence,the equivalent expression is (3⁴/7³)³ = 3¹²/7⁹

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Answer:

550

Step-by-step explanation:

3/4 x 1000 = 750

The parking lot has 750 cars and trucks.  Subtract out the 200 cars and we are left with 550 trucks.

The set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.

You must take the following actions to determine the standard deviation of a set of observations:

Mean: (32 + 28 + 29 + 30 + 31) / 5 = 30

Deviations: 32 minus 30 = 2, 28 minus 30 = 2, 29 minus 30 = 1, 30 minus 30 = 1, etc.

Squared deviations are as follows: 22 = 4, (-2)2 = 4, (-1)2 = 1, and 02 = 0.

Sum of squared deviations: (Sum of squared deviations) / (number of observations) = 10 / 5 = 2

Standard deviation is square root of sum of squared deviation.

so, [tex]\sqrt{2}[/tex] is 1.41.

As a result, the set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.

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Answer: answer 74 hope it help

Step-by-step explanation:

9x9= 81

3x3x3 27

27-20=7

81-7=74

Answer: (3x+4)(3x−5)

Step-by-step explanation:

Beverage containing 160 calories and 40 grams of sugar will be equal to 18 teaspoons.

Like other carbs, sugar has nutritional value.

Carbohydrates contain roughly 4 calories per gram.

A teaspoon of sugar has 20 calories and approximately 5 grams of carbohydrates.

As per the question,

The beverage contains 160 calories,

160 calories will be equivalent to (160/20) = 8 teaspoons. (As 1 teaspoon of sugar contains 20 calories)

Along with it, the beverage also contains 40 grams of added sugar.

The 40 grams of added sugar divided by the 4 grams of sugar per teaspoon resulted in 10 teaspoons of added sugar.

As in a drink, 160 calories and 40 grams of added sugar are present.

So, the total teaspoons of sugar will be = 8 + 10 = 18 teaspoons.

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The three correct answers that describe the given transformations are;

A) To create g, the graph of f is shifted 5 units up.

C) The graph of f is steeper than the graph of g.

F) The y-intercept of g is 5 units above the y-intercept of f.

We are given the equations as;

f(x) = x

g(x) = ¹/₃(f(x)) + 5

For a function f(x) we define a vertical translation (or vertical shift) of n units as:

g(x) = f(x) + n

If n is positive, the translation is upwards

If n is negative, the translation is downwards.

Thus, the graph of f was shifted 5 units upwards.

Now, the equation of a line in  slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus;

y-intercept of f(x) = 0

y-intercept of g(x) = 5

Thus;

y -intercept of g is 5 units above y-intercept of f.

Now, the steeper the line, the higher the slope. Thus, function f has a higher slope than function g and so function f is steeper than function g.

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The formula for 3 consecutive numbers is n + 1, n + 2, and n + 3, where n is an integer.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

(n + 1) and (n + 2) will be the next two consecutive integers if n is an integer. Let n, for instance, be 1. Its consecutive integers are either 2 or 3, or 1 + 1 + 2.

Thus, the formula is:

n, n+1, n+2, n+3,…

consecutive Even Numbers:

The endings of even numbers are 0, 2, 4, 6, or 8. Zero, two, four, six, eight, ten, twelve, and so on are examples of consecutive even numbers.

consecutive Odd numbers:

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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The missing reason in the flowchart would be SAS.

Option (D) is correct.

What is the SAS congruence theorem?

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

In the given figure,

Side RC ≅ Side TN ---- Given

Side HX ≅ Side XK ----Given

Angle RHK ≅ Side HKN --- Vertical angles are congruent.

Hence, ΔRHX ≅ NKXΔ ----- (SAS congruence)

Hence, the missing reason in the flowchart would be SAS.

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Using the concept of functions option A [tex](f-g)(y)=2y^{2}-3y-1[/tex] is true by solving both the functions f(y) and g(y).

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. A relation f between a set A (the function's domain) and a set B is how a function is defined in mathematics (its co-domain). For any A and B, f = {(a, b) | for all a ∈ A, b ∈ B}

According to the given question we have given two functions f (y) and g (y), then:

(f - g) (y)=f(y)-g(y)

We have:

[tex]f(x)=5y^{2} -2y+1[/tex]

[tex]g(y)=-3y^{2}-y-2[/tex]

Subtracting both the above functions we have:

[tex](f-g)(y)=2y^{2}-3y-1[/tex]

Hence option A [tex](f-g)(y)=2y^{2}-3y-1[/tex] is true by using the concept of functions.

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The missing number in a given integer array of 1 to 100 can be found using the PHP array_diff() function.

This function compares two array and returns the difference. To find the missing number, we first need to create an array that contains all numbers from 1 to 100. We then create another array with the given integers. Using array_diff(), we can compare the two arrays and the difference will be the missing number.

To use the array_diff() function, we first need to create the two arrays. For example,

$array1 = range(1,100);

$array2 = array(1,2,3,4,5,6,7,8,9);

The first array is containing all numbers between 1 and 100 and the second array is containing the given integers.

The next step is to use the array_diff() function. The syntax for this is

The result of this will be an array containing the missing integer.

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Answer:

u =10 v=13

in order in order for the triangles to be congruent the sites with vehicle in this case if the you equals to 10 in the both sides then the sides opposite to the right angle will be equal and if the is equal to 13 it will mean that the sides along with the right angle would be equal which makes a triangle congruent

The level of a line's slope indicates its steepness.

A line with a slope of 1/3 has a perpendicular line with a slope of -3. The product of the slope is equal to -1 when two lines are perpendicular.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

That is to say,

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