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The first of the three theorems below, known as the Angle-Angle-Side Theorem or AAS Theorem, asserts that two angles and a non-included side of a triangle must be congruent with the corresponding two angles and non-included side of another triangle for the triangles to be considered congruent.

What do you mean by congruent?

Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

Why are triangles congruent?

Two triangles are said to as congruent triangles if their dimensions and shapes match. Two congruent triangles remain congruent even if we flip, rotate, or otherwise alter one of the triangles.

                  Two triangles must have the same angles and, as a result, must be congruent if their sides are equal.

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Answer:

C) 5.25s^2

Step-by-step explanation:

1. Multiply 1.5s x 3.5s = 5.25.

2) Because 1.5 has one s, and 3.5 has another s, these 2 s combine (s+s)=s^2. Meaning there is 2 s in the equation. s^2 happens when you multiply two numbers that each have an s. Multiplication in this problem is brought by the use of parenthesizes surrounding these 2 numbers.

Answer:

The 3x+1 problem, also known as the Collatz conjecture, is a problem in mathematics that remains unsolved. It involves taking a positive integer and repeatedly applying a simple rule to it: if the integer is even, divide it by 2, and if it is odd, multiply it by 3 and add 1. The problem is to determine whether this process will always eventually reach the number 1, regardless of which positive integer is chosen as the starting point. Despite much effort by mathematicians, the 3x+1 problem remains unsolved.

Step-by-step explanation:

The probability that the fourth marble Amy picks is black: This probability cannot be determined without knowing the total number of marbles and the number of black marbles.

The probability that, if Amy picks a black marble in the fourth attempt, she will pick a red or a black marble in the fifth attempt: This probability cannot be determined without knowing the total number of marbles and the number of red and black marbles.

Probability is a measure of the likelihood of an event occurring. To calculate the probability of an event, you need to know the total number of outcomes and the number of outcomes that are favorable to the event. For example, if there are 10 marbles in total and 4 of them are black, the probability that Amy will pick a black marble on the fourth attempt is:

Probability = Number of black marbles / Total number of marbles = 4/10 = 0.4

Similarly, if Amy picks a black marble in the fourth attempt and there are a total of 10 marbles, with 4 of them being black and 6 of them being red, the probability that she will pick a red or a black marble in the fifth attempt is:

Probability = (Number of red marbles + Number of black marbles) / Total number of marbles = (6 + 4) / 10 = 0.8

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The resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.

The concept of an equation in algebra is a mathematical statement that shows the equality of two mathematical equations.

For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are divided by the 'equal' sign.

So, we have the equation:

2x - 3y = 12

Now, solve the equation by taking x as the subject as follows:

2x - 3y = 12

2x = 12 + 3y

x = (12 + 3y)/2

Therefore, the resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.

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Correct question:
How do you work out 2x - 3y = 12?

They are the three methods of mean -  Direct Method. Assumed Mean Method. Step-deviation Method.

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

              A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                    Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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The example of a  hypothesis is: a person is innocent until proven guilty. The statement is true

Here the given situation is

A person is innocent until proven guilty.

The hypothesis test is defined as the test in statistics whereby an analyst tests an assumption regarding a population parameter. In hypothesis test using the data from the different types of t sample and the determine the other parameters of the population

The null hypothesis is defined as the a statement of what the statistician expects NOT to find.

Here the given situation is a person is innocent until proven guilty. Therefore, it is a null hypothesis.

In hypothesis test we assume that null hypothesis until it is proven

Therefore, the given statement true

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No. The GCF of 6 and 35 is 1.

To determine the biggest factor that perfectly divides both 6 and 35, i.e. 1, we must factor each number separately (factors of 6 are 1, 2, 3, 6; while factors of 35 are 1, 5, 7, 35).

What is Factors of 35?

Factors of 35 are the list of integers that we can split evenly into 35. It has a total of 4 factors of which 35 is the biggest factor and the positive factors of 35 are 1, 5, 7 and 35. The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).

Factors of 35: 1, 5, 7 and 35

Negative Factors of 35: -1, -5, -7 and -35

Prime Factors of 35: 5, 7

Prime Factorization of 35: 5 × 7 = 5 × 7

Sum of Factors of 35: 48

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Answer:

45n + 60 = 285

Step-by-step explanation:

n=# of weekday classes (this is an unknown value)

45n= each weekday class is 45 mins long, and when you multiply it by "n" which is the number of weekday classes, you will get a total number of minutes.

+60= we add 60 because that is how many mins it takes for the one class on the saturday. there is only one saturday class which means that you dont need a variable attached to it.

=285

this is the total number of mins from last week.

so, the total number of mins from last week has to equal the 60 min class plus however many 45 min classes there are that week.

45n+60=285

and if you really wanted to know how many weekday classes there were that week, n=5

The another root for the given polynomial is 3 + 2i.

A complex number is defined as a number containing both real and imaginary part which is written as x + iy. The conjugate of a complex number can be obtained by changing the sign of the imaginary part of the number. the product of a complex number and its conjugate is the square of its magnitude.

One of the complex roots of a polynomial is given as 3 - 2i.

Since, all the coefficients of the polynomial P(x) are real.

The another root should be the complex conjugate of the given root.

Thus, the other root is given as below,

3 + 2i

Hence, the additional root is given as 3 + 2i.

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Answer:

--------------------------------

The height of the tower is the leg of the isosceles right triangle, since one of angles is 45 degrees.

The horizontal distance from the to the point where you dropped your keys is same as the vertical distance, 156 meters, because it is the other leg of the triangle.

The vertical asymptotes of the graph of f(x) = (2x² + 7x - 4)/(x² + 5x + 4) is x = -1

The equation of the function is given as

f(x) = 2x² + 7x - 4/x² + 5x + 4

Introduce bracket, to differentiate the numerator and the denominator

So, we have

f(x) = (2x² + 7x - 4)/(x² + 5x + 4)

Next, we plot the graph of the function

The asymptotes are the points on the graph is a line that acts as the limit of another line or curve

From the graph, we have the asymptotes to be

x = -1 and y = 2

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Complete question

What is the vertical asymptote of the graph of f X?

f(x) = 2x² + 7x - 4/x² + 5x + 4

A four-sided geometric object called a trapezoid has one pair of opposing sides that run parallel to one another. Its parallel sides are represented by its two bases, while its non-parallel sides are represented by its two legs. The lateral sides of the trapezoid are another name for the legs.

 We must first locate the location of the trapezoid in order to determine where the grey patch of land will be after the 3 m walkway has been built. The following formula determines the area of trapezoid:

A = (b1 + b2)/2 * h

where h is the height, and b1 and b2 are the bases' lengths.

Inputting the values provided yields:

A is equal to (150m + 100m)/2 * 52m, or 125m * 52m, or 6500m2[tex]m^{2}[/tex].

After the walkway is built, the area of the grey piece of land is equal to the trapezoid's area minus the walkway's area. The walkway is 3 m by 52 m in size, or 156 [tex]m^{2}[/tex].

Therefore, 6500[tex]m^{2}[/tex] - 156[tex]m^{2}[/tex]   = 6344[tex]m^{2}[/tex] is the area of the grey patch of land once the walkway is built.

 So, the area of gray patche of land after construction of the walkway is 6344[tex]m^{2}[/tex].

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The final answers are (1) y = 4.133 + 3.0333x, (2) y = 12.55015 and (3) The prediction made in part b) will be underestimated as the residual value will lie below 0 when x = 5.5.

What is linear regression?

Linear regression analysis predicts the value of one variable based on the value of another. The variable you wish to predict is referred to as the dependent variable. The variable you are using to predict the value of the other variable is known as the independent variable.

1) Give the equation of the least-squares regression line. Define any variables you use.

y = 4.133 + 3.0333x

The constant coefficient is what I used as the y-intercept.

2) Use the model from part (a) to predict the area covered by detergent at 5.5 seconds.

y = 4.133 + 3.0333(5.5)

y = 12.55015

3) The prediction made in part b) will be underestimated as the residual value will lie below 0 when x = 5.5.

Hence, the final answers are (1) y = 4.133 + 3.0333x, (2) y = 12.55015 and (3) The prediction made in part b) will be underestimated as the residual value will lie below 0 when x = 5.5.

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An inconsistent system of equations has no solution, whereas a consistent system has at least one solution.

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If the two triangles have the two congruent side, then the two triangles are congruent.

The term triangle refers the polygon with three side, three vertices, and three edges.

Here we have to prove that the  two triangles are congruent with two congruent sides.

As we know that the term congruent refers if their sides have the same length and angles have same measure.

Based on these theory, and we have to use the another theory called SAS (Side-Angle-Side) tell that any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, if then the two triangles are said to be congruent.

According to this rule, we have clearly identifies that the given two triangles are congruent.

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Answer:1696.35

Step-by-step explanation:

if you time 7.89 by 215 you get 1696.35

An equation that depicts a straight line on a graph is said to be linear line.

What is linear line?

Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.

A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them.

2x - 3 = 0 and 2y = 8 are few examples of linear lines.

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Answer:

x = ± 2√5

Step-by-step explanation:

4x² - 5 = 75

4x² = 75 + 5

x² = 80 ÷ 4

x² = 20

√x² = ± √20

x = ± 2√5

For unbiased sample by data collection, The method to be used is Survey method.

To answer specified research questions, test hypotheses, and assess results, data collection is the act of acquiring and measuring information on variables of interest in a systematic and defined manner. All academic disciplines, including the humanities, social sciences, business, and natural and applied sciences, share the data collection component of research. Although techniques differ depending on the profession, the importance of ensuring accurate and truthful collection does not change.

The popular data collection methods are:

Survey method of data collection is to be used for collection of unbiased sample. It is so because while planning for a on-site gym for the employees, Survey conducted on the employees working would be the best method for data collection which will increase the efficiency for selection of gym hours.

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The inequality that represents the most no. of music played is,

C ≤ 4,  J ≤ 1 and 4C + 0.25C ≤ 12

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, the radio station plays at most 12 hours of music per day. Let C denotes classical music, J denotes jazz music, and 25% of 4 hours be 1 hour.

The inequality representing this situation is

C ≤ 4 and J ≤ 1.

4C + 0.25C ≤ 12.   (less than or equal to is at most)

4.25C ≤ 12.

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The point that satisfy linear quadratic  system of equation are (1,0) and (4,-3)

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

we have x + y = 1  ......... (i)

y=4x-3-x²...... (ii)

put y=4x-3-x² in equation (i)

x + y = 1

x + 4x - 3 - x^2 = 1

-x^2 + 5x - 4 = 0

(-x + 1)(x - 4) = 0

-x + 1 = 0      

-x = -1            

x = 1              

To find the value of y put x=1 in equation ii

 y = 4x - 3 - x^2

        y = 4(1) - 3 - 1^2

     y = 4 - 3 - 1 = 0

similarly.

x - 4 = 0        y = 4x - 3 - x^2

x = 4             y = 4(4) - 3 - 4^2

                    y = 16 - 3 - 16

                     y = -3

so the point that satisfy linear quadratic  system of equation are (1,0) and (4,-3)

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we have x + y = 1  ......... (i)

y=4x-3-x²...... (ii)

put y=4x-3-x² in equation (i)

x + y = 1

x + 4x - 3 - x^2 = 1

-x^2 + 5x - 4 = 0

(-x + 1)(x - 4) = 0

-x + 1 = 0      

-x = -1            

x = 1              

To find the value of y put x=1 in equation ii

y = 4x - 3 - x^2

y = 4(1) - 3 - 1^2

y = 4 - 3 - 1 = 0

similarly.

x - 4 = 0        y = 4x - 3 - x^2

x = 4             y = 4(4) - 3 - 4^2

                    y = 16 - 3 - 16

                    y = -3

so the point that satisfy linear quadratic  system of equation are (1,0) and (4,-3)

Step-by-step explanation:

The form of a exponential function is

[tex]y = a \times {b}^{x} [/tex]

We know that

[tex]18 = a \times {b}^{ - 0.5} [/tex]

[tex]52 = a \times {b}^{1} [/tex]

If we divide these two we will get

[tex] \frac{26}{9} = b {}^{1.5} [/tex]

[tex] \frac{676}{81} = b {}^{3} [/tex]

[tex] \sqrt[3]{ \frac{676}{81} } = b[/tex]

Solving for a,

[tex]52 = a \times \sqrt[3]{ \frac{676}{81} } [/tex]

[tex]a = 25.64[/tex]

f(0)=a, so

f(0)=25.64

The diaphragm creates a transverse section between the thoracic and abdominal body cavities.

The diaphragm is one of the important muscle involved in respiration, or breathing. It is a dome-shaped muscle is found just beneath the lungs and heart. It constantly contracts as you breathe in and out.

Thoracic diaphragm is the diaphragm which is present in the thorax and serves as an important anatomical landmark.

It acts as a separation between  the thorax, or chest, from the abdomen.

It contracts to enlarge the thoracic cavity and reduce the intrathoracic pressure so that lungs may expand and fill their alveoli with air during respiration.

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The area of an isosceles right triangle that has one leg that measures 4 cm is 8 cm ^ 2.

One leg of the isosceles triangle is 4 cm.

Since the given isosceles triangle is also a right triangle, the base of the isosceles would also be equal to the height of the triangle which is 4 cm.

Area of a triangle = 1 / 2 × base × height

Therefore, the area of an isosceles right triangle that has one leg that measures 4 cm is:

1 / 2  × 4 cm × 4 cm = 8 cm ^ 2.

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Answer:

0,1,2

Step-by-step explanation:

you have to go in numerical order starting from zero and going forward with no fractions.

The 7 types of hazards in the home are Psychosocial  Risks,Physical

Dangers , Chemical Dangers, Biological risks, Constrained Areas,

Changing Equipment and Biohazards

Psychosocial  Risks

Physical dangers include a subgroup called psychosocial hazards. For some workers, these risks might be more severe or restrictive than for others. Poor management or a lack of feedback may be the cause of these risks.

Physical Dangers

Environmental and occupational hazards are two different categories of physical risks. These include unguarded machines, heat, cold, vibration, noise, and temperature extremes. Engineering controls can lessen some physical dangers.

Chemical Dangers

Toxic, flammable, explosive, self-reactive, oxidizing, or corrosive compounds are considered chemical dangers. Chemical risks can have negative health impacts and need special handling techniques and equipment.

Biological risks

Many workplaces have biological risks, which can be harmful to people. They include waste debris, food, fungi, food, hair, skin, and saliva.

Constrained Areas

Flammable gases can accumulate in small places. These gases tend to gravitate toward lower elevations, yet they can rise to the surface if a lid is closed or if they are hanging in the air.

Changing Equipment

For workers, the moving machinery hazard provides a distinct set of mechanical risks. Injuries caused by it include crushing, shearing, tangling, air being ejected, striking, abrading, and trapping.

Biohazards

There are many danger thresholds for biohazards. Agents of biohazard level I pose little risk to people. On the other hand, biohazard class II agents may be extremely contagious and may result in serious sickness if consumed or dispersed through the air.

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The symbol "≪" means "much less than," and the symbol "≫" means "much greater than."

These symbols are used to express a strong inequality between two values. For example, if you wanted to say that the value of x is much less than the value of y, you could write "x ≪ y." Similarly, if you wanted to say that the value of x is much greater than the value of y, you could write "x ≫ y."

The symbols "≪" and "≫" are used in mathematics to express a strong inequality between two values. They are similar to the familiar inequality symbols ">" (greater than) and "<" (less than), but they indicate a greater degree of inequality.

For example, if you wanted to say that the value of x is much less than the value of y, you could write "x ≪ y." This means that x is much smaller than y, and the difference between the two values is significant. Similarly, if you wanted to say that the value of x is much greater than the value of y, you could write "x ≫ y." This means that x is much larger than y, and the difference between the two values is significant.

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The question is -

What does ≪ mean in math?

The inequalities that match each region are given as follows:

a) x + y ≥ 5. (Option E).

b) y ≤ x + 2. (Option A).

c) y ≥ 4. (Option D).

For item a, we have that values to the right of the line are shaded, meaning that the line is the lower bound of the interval.

The line is decreasing and has an intercept of 5, hence it is given as follows:

y = 5 - x.

As the line is the lower bound of the inequality, the inequality is defined as follows:

y ≥ 5 - x

x + y ≥ 5.

For item b, the line has an intercept of 2, hence it is given as follows:

y = x + 2.

It is an increasing line, and the values to the right of the line are shaded, meaning that the line is the upper bound and the inequality is given as follows:

y ≤ x + 2.

For item c, the lower bound is the horizontal line y = 4, hence the inequality is described as follows:

y ≥ 4.

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Answer:x=98

Step-by-step explanation:you add each corner

its a joke srry