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"If in two triangles, sides of one triangle are proportionate to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and consequently the two triangles are comparable," asserts the Side-Side-Side (SSS) criteria.

Take a look at the triangles below.

- We can see that all three pairs of the sides of these triangles are congruent. - This is also known as "side-side-side" or "SSS." According to the SSS criteria for triangle congruence, two triangles are congruent if they have three pairs of congruent sides.

SSS Congruence Rule Theorem

When one triangle's three sides are identical to the corresponding three sides of another triangle, two triangles are said to be congruent.

The aforementioned theorem will now be proven.

Given: [tex]\triangle A B C[/tex] and [tex]\triangle P Q R[/tex] such that AB=PQ, BC=QR and AC=PR.

To prove: [tex]\triangle A B C \cong \triangle PQR[/tex]

Construction: Let BC be the longest side of [tex]\triangle A B C[/tex] and so QR is the longest side of [tex]\triangle P Q R.[/tex]

Draw PS so that [tex]\angle R Q S=\angle C B A[/tex] and [tex]\angle Q R S=\angle B C A[/tex].

Join SQ and SR.

In [tex]\triangle ABC[/tex] and [tex]\triangle SQR[/tex],

BC=QR Given

[tex]\angle C B A=\angle R Q S[/tex] By construction

[tex]\angle B C A=\angle Q R S[/tex] By construction

[tex]\triangle A B C \cong \triangle SQR[/tex] By ASA congruence

[tex]\angle A=\angle S[/tex] By CPCTC

AB=SQ By CPCTC

AC=SR

Now, AB=PQ and AB=SQ => PQ=SQ

Similarly, AC=PR and AC=SR => PR=SR

Hence, [tex]\triangle ABC \cong \triangle PQR,[/tex]

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The equation of the line that passes through the given points will be equal to  11x -9y + 101 = 0.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the data in the question,

Use the equation of the line passing through the point (x₁, y₁) with slope m will be:

y - y₁ = m(x - x₁)

Slope, m = 11/9

And, the points are (-1, 10)

Now,

y - 10 = 11/9(x + 1)

9y - 90 = 11x + 11

11x - 9y + 11 + 90 = 0

11x -9y + 101 = 0

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The perimeter of triangle def similar to triangle abc is 22 cm.

Perimeter is the total distance around a object.

Note: The ratio of the perimeters of two similar figures is equal to the ratio of their corresponding side lengths.

To calculate the perimeter of triangle def, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for P'

Hence, the perimeter of triangle def is 22 cm.

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Answer:

4

Step-by-step explanation:

For each kilogram of mass, [tex]0.2+4(0.1)=0.6[/tex] milligrams are needed.

Thus, [tex]0.6(10)=6[/tex] milligrams are needed.

This is equal to 4 mL

Answer:

  4 ml

Step-by-step explanation:

You want to know how many mL of medicine is needed for 5 days when the dose is 0.1 mg/kg per day and the concentration is 1.5 mg/mL. The dose on the first day is double that for the rest of the days.

The dose on the first day is equivalent to the dose for 2 days, so we can simply add 1 day to the time period: 5 +1 = 6 days of 0.1 mg/kg/day.

The total amount required will be ...

  (0.1 mg/kg/day) × (10 kg) × (6 days) = 6.0 mg

At a concentration of 1.5 mg/mL, the quantity required is ...

  (6.0 mg)/(1.5 mg/mL) = 4.0 mL

For 5 days, the dog will need 4.0 mL of medicine.

__

Additional comment

Each day except the first, the dog should receive 2/3 mL of medicine. On the first day, the dog should get 4/3 mL.

The wax mixtures that will create the same shade of pink are

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

Red wax = 12 mL

White wax = 5 mL

When these parameters are represented as a ratio, we have the following representation

Ratio = Red wax : White wax

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

Red wax : White wax = 12 mL : 5 mL

Remove the units

So, we have

Red wax : White wax = 12 : 5

Multiply the ratio by 3

So, we have

Red wax : White wax = 36 : 15

Multiply the ratio by 5

So, we have

Red wax : White wax = 60 : 25

Hence, the wax mixtures are (d) and (e)

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Complete question

A pink crayon is made with 12 mL of red wax for every 5 mL of white wax. Which of the following wax mixtures will create the same shade of pink?

(A) 10 mL of red wax mixed wit 24 mL of white wax

(B) 48 mL of red mixed with 12 of white wax

(C) 13 mL of red mixed with 6 mL of white wax

(D) 36 mL of red mixed with 15 mL of white wax

(E) 60 mL of red mixed with 25 mL of white wax

Answer: c. 16:20

Step-by-step explanation:

30/5=6

24/4=6

The last expression is equivalent to √5³.

What equation contains an expression?

The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.

                    It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.

                   [tex]= ( 5^{1/8} * 5^{3/8} )[/tex]

                   [tex]= ( 5^{1/8} * 5^{3/8} ) \\= 5^{(1/8 + 3/8)}[/tex]

                    [tex]= 5^{4/8}[/tex]

                    [tex]= 5^{(1/2)}[/tex]

                   [tex]= [5^{(1/2)}]^{3}[/tex]

    Because of the "Power of a power property"

                                    = [tex]5^{3/2}[/tex]

The last expression is equivalent to √5³.

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Two or more shapes are said to be similar if they have common corresponding properties of sides and/ angles. Thus the error made is option D.

Similar shapes are two or more given shapes that have some common properties with respect to their corresponding sides or angles. So that if on comparing each corresponding sides or angles, and are related, then they are similar. Note that similarity does not imply congruency.

Comparing the sides and angles of the given triangles ΔLMN and ΔQRS, it can be seen that;

Angle Side Angle (ASA) similarity relation implies that the included side between two pairs of congruent angles are similar. Thus, the error made in the diagram is explained in option D.

Option D. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.

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Answer:

24

Step-by-step explanation:

You need to work out 16% of 150

10% of 150 = 15

1% 0f 150 = 1.5

so, 6% of 150 = 1.5 x 6 = 9

16% = 10% + 6%

so, 16% = 15+9

24 = 16%

Therefore there are 24 left handed students in Year 9.

The required cost of hosta and ornamental grass is $6 and $3.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
let the cost of each hosta be x and ornamental grass be y,
According to the question,
For
Trevon,
5x + y = 33 - - - - - (1)

For, Scott,
x + 12y = 42 - - - - - - (2)

Solving equations 1 and 2 by substitution method,
x=6, y=3

Thus, the cost of hosta and ornamental grass is given as $6 and $3.

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The 17th hole would be 255 yards long.

What are ratio and proportion?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

hole = c yards

1.5 / 40 = 8.5 /c

1.5 * c = 45 * 8.5

1.5 * c = 382.5

c = 255 yards

Hence, the 17th hole would be 255 yards long.

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Answer:-96

Step-by-step explanation:

The relationship between the volume of pyramid and prism is that when a pyramid and prism have the same base and height, volume of prism is 1/3rd the volume of prism.

The volume of the cylinder is 1/3rd the volume of the cone.

The volume of the sphere is 2/3rd the volume of the cylinder with same radius and height equal to the diameter.

Pyramid is said to have a polygonal base and flat triangular faces, which are connected to a common point called apex.

Prism is a combination of flat faces, identical bases and cross-sections being equal.

Cylinder has two parallel bases joined by curved surface through a fixed distance.

Cone has a circular base and a curved surface tapering till the apex.

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Exponents that are positive go to the right. Exponents with negative signs shift to the decimal to the left. A result is stated in scientific notation when it is a power of ten multiplied by a number that is greater than or equal to one but less than ten.

One approach is to fully write out each number after it has been converted from scientific notation, then calculate the total of the two values and translate the result back into scientific notation.

Therefore, The 2, 4, 5, and final 0 in the number 0.2540 are all significant because they come after the decimal point and follow numbers. Scientific notation does not consider exponential digits to be significant; 1.12106 has three significant digits, 1, 1, and 2.

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We can factor using the rational root theorem by a rational number, both the leading coefficient and the constant term must be divisible by the fraction's denominator.

The rational root theorem, also known as the rational root test, is an algebraic principle that states that for a polynomial equation with one variable and integer coefficients to have a solution (root) that is a rational number, both the leading coefficient and the constant term must be divisible by the fraction's denominator.

A particularly helpful theorem is the theorem of rational roots.

It explains how to get a list of potential solutions for a polynomial function with integer or whole number coefficients by ranking the factors of the constant, or last term, over the factors of the coefficient of the leading term.

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Answer:

q alguien me explique y pueden ser español

Answer:

The coordinate of the midpoint is (\frac{11}{2},\frac{-13}{2}  )\\ with endpoints B(9,−8) and C(2,−5)

Step-by-step explanation:

The inverse of a 2x2 identity matrix is also a 2x2 identity matrix. This is because the identity matrix is its own inverse.

An identity matrix is a square matrix with all primary diagonal members set to one and all other elements set to zero. The letter "In" or just "I" is used to indicate it. Any matrix will produce a given matrix if it is multiplied by the identity matrix. . The components of the provided matrix stay the same.

The 2x2 identity matrix is a square matrix with 1s on the main diagonal and 0s everywhere else. It has the following form:

[1 0]

[0 1]

The inverse of this matrix is also a 2x2 identity matrix with the same form:

[1 0]

[0 1]

Therefore, the inverse of a 2x2 identity matrix is also a 2x2 identity matrix.

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The equation of the line that passes the points (1, - 6) and (- 5, - 3) is - (1 / 2) · x - 11 / 2.

According to Euclidean geometry, a line can be constructed by setting two points on a plane. By analytical geometry, lines are described by polynomials of the form:

y = m · x + b

Where:

The slope can be found by means of secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

If we know that (x₁, y₁) = (1, - 6) and (x₂, y₂) = (- 5, - 3), then the equation of the line is:

m = [- 3 - (- 6)] / (- 5 - 1)

m = 3 / (- 6)

m = - 1 / 2

b = y - m · x

b = - 6 - (- 1 / 2) · 1

b = - 6 + 1 / 2

b = - 11 / 2

The equation of the line is - (1 / 2) · x - 11 / 2.

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The answer is True. If two vertical angles are congruent, then two lines cut by a transversal will be parallel.

Vertical angles are angles that are opposite each other and share the same vertex. They are congruent angles, meaning that they have the same measure. When two angles are congruent, the sides of the angles are parallel. This means that the two lines cut by a transversal will also be parallel.

The formula for this is that if two angles are congruent, then the lines cut by a transversal are parallel. This is also known as the Angle-Angle-Angle (AAA) Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This means that the lines cut by a transversal are parallel.

In other words, if two angles of a triangle are congruent, then the two sides of the triangle that make those angles are parallel. This is because the two angles are congruent, meaning that they have the same measure. Therefore, if two vertical angles are congruent, then two lines cut by a transversal will be parallel.

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The function 4x+7 does not have a horizontal asymptote.

The horizontal asymptote of a function is a horizontal line that the graph of the function approaches as the x-values get larger or smaller.

In this case, the function 4x+7 does not have a horizontal asymptote. This is because the function is a linear function (a function of the form y = mx + b) and all linear functions have a slope (in this case, the slope is 4) but no horizontal asymptotes.

If you are given the graph of a function and you want to find its horizontal asymptotes, you can look at the degree of the function (the highest exponent of the variable). If the degree of the function is less than the degree of the denominator of the function, then the function will have a horizontal asymptote at y = 0.

If the degree of the function is equal to the degree of the denominator, then the function will have a slant asymptote (a line that the graph approaches as the x-values get larger or smaller). If the degree of the function is greater than the degree of the denominator, then the function will not have any horizontal or slant asymptotes.

--The question is incomplete, answering to the question below--

"What is the horizontal asymptote of y = 4x+7?

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The mean of given numbers is 4.

To find: mean of given numbers.

Given data : 2, 3, 4, 5, 6

Average is the arithmetic mean. also called as mean .

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here, sum of observations =20

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data

Total number of observations=5

The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.

Substituting values in above formula,

Mean=[tex]\frac{20}{5}[/tex]=4

Therefore, the mean is 4.

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The idea is to find the sum of integers between 1 and 100 using the n×(n+1)/2 where n is the array’s size and subtract the actual sum of array

Python is a popular computer programming language used to create software and websites, automate processes, and analyze data. Since Python is a general-purpose language, it may be used to develop a wide range of applications and isn't tailored for any particular issues.

Python code for computing sum

Find the missing number in a given array

def getMissingNumber(arr):

  # get the array's length

  n = len(arr)

  # actual size is `n+1` since a number is missing from the list

  m = n + 1

  # get a sum of integers between 1 and n+1

  total = m * (m + 1) // 2

 # the missing number is the difference between the expected sum and

  # the actual sum of integers in the list

  return total - sum(arr)

if __name__ == '__main__':

  array_input = input("Enter a list of integers separated by spaces: ")

  array = [int(x) for x in array_input.split()]

  print('The missing number is', getMissingNumber(arr))

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The inverse formula is [tex][(f o f^{-1}) (x) ] =[( f^{-1} o f ) (x)] = x[/tex]

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The inequality that represents this scenario is 0.08B >= 57.

To get the promotion, Carolina needs to spend at least $75 on paintballs and the entrance fee. The entrance fee is a fixed cost of $18, so we need to find the number of paintballs that Carolina needs to buy in order to reach a total cost of $75 or more.

The cost of the paintballs is calculated using the formula 0.08B, where B is the number of paintballs that Carolina buys. We can use this formula to write an inequality that represents the scenario described in the problem.

The total cost of the paintballs and the entrance fee is calculated using the formula 0.08B + 18. This formula represents the total cost of the paintballs and the entrance fee for any number of paintballs that Carolina buys.

To find the number of paintballs that Carolina needs to buy in order to reach a total cost of $75 or more, we can set the total cost equal to $75 and solve for B:

0.08B + 18 >= 75

0.08B >= 57

B >= 712.5

The inequality 0.08B >= 57 represents the scenario described in the problem. It states that the number of paintballs that Carolina needs to buy in order to reach a total cost of $75 or more is greater than or equal to 712.5.

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The question is -

Carolina goes to a paintball field that charges an entrance fee of $18 and $0.08 per ball. The field has a promotion that says, "Get $10 off if you spend $75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion, Let B represent the number of paintballs that Carolina buys. What inequality describes this scenario?​

Utilize the standard normal curve to calculate probability as follows:

(A) Go to the row that contains the first two digits of your z score.

(B) Go to the column with the third digit of your z-score.

(C) Find the value at the row and column intersection of the previous stages.

The horizontal axis is approached by the standard normal curve as it stretches continuously in both directions without ever being touched by it.

The center of the bell-shaped, z=0 standard normal curve.

Between z=3 and z=3, almost the entire region under the standard normal curve is located.

Find the z-score of the data value and use a Z-Score Table to find the area under the normal curve in question.

A Z-Score Table is a chart that displays the percentage of values (or area percentage) on a standard normal distribution that is to the left of a specified z-score.

To determine probability, use the ordinary normal distribution.

(A) Go to the row that has your z score's first two digits.

(B) Cross over to the column that has your z score as the third digit.

(C) Find the value at the point where the preceding steps' row and column overlap.

Therefore, utilize the standard normal distribution to calculate probability as follows:

(A) Go to the row that contains the first two digits of your z score.

(B) Go to the column with the third digit of your z-score.

(C) Find the value at the row and column intersection of the previous stages.

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The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.

To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.

In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.

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The question is -

Which congruence theorem can be used to prove EB = BD, AE = CB, ∠ A = ∠ C = 90°?

Age demography is important that young people are poised to move into their prime reproductive years.

Demography is a measure of the characteristics or changes in population. Births, deaths, age , marriages, immigration, and periodic census records provide important information in making informed decisions about national policy.

Governments, businesses, and non-governmental organizations use demographic data to learn about population characteristics for many purposes, including policymaking and economic market research.

Age Demographics: In the demographics, it is defined as common to divide the population into three broad age groups, children and youth (under 15) and working-age population (15-64) and elderly population (Ages 65 and Over)

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