How do you prove a congruence statement?

Motion that keeps a distance while traveling in a plane is referred to as rigid body motion. There are four types of transformations, also called stiff, congruent, isometric, or similar terms.

The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped. When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.

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The equation for graphing y = 4 in slope-intercept form is y = 4x + 0. This equation can be graphed by plotting the point (0, 4) and then using the slope of 0 to draw a horizontal line that passes through that point.

1. Plot the point (0, 4)

2. Draw a horizontal line that passes through the point (0, 4). This line will have a slope of 0.

Start by plotting the point (0, 4). This point marks the y-intercept of the graph. Then, draw a horizontal line that passes through this point. The slope of this line will be 0, which is necessary for graphing the equation y = 4 in slope-intercept form. The equation for this graph is y = 4x + 0 and the graph should be a straight, horizontal line that passes through the point (0, 4).

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The three categories are interquartile range, standard deviation, and variance. The range of a distribution's middle quintile is known as the interquartile range.

The difference between the highest and lowest values for a certain data set's statistics is the range. Any real number between any two other numbers in the set is considered to be in the range, which is a set of real numbers.

here

The range is the space between the highest and lowest numbers.

The range of a distribution's middle quintile is known as the interquartile range.

Average separation from the mean is known as standard deviation. Variance is defined as the sum of squared deviations from the mean.

Therefore, the three categories are interquartile range, standard deviation, and variance.

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The value of y when x = 17 based on y=156 when x=39 is 68

Based on the given task content; the value of y can be determined by using ratio

y = 156 when x = 39

y = ? when x = 17

Equate the ratio of y to x

156 : 39 = y : 17

156/39 = y / 17

cross product

156 × 17 = y × 39

2,652 = 39y

divide both sides by 39

y = 2,652 / 39

= 68

In conclusion, y is 68 when x = 17 when solved with ratio.

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The first step in solving the equation by distributing is represented by "negative 12 x plus 20 = negative 16".

The correct answer option is option A

-4(3x - 5) = -16

Step 1:

apply distributive property

-12x + 20 = -16

Apply Subtraction equality

-12x = -16 - 20

-12x = - 36

applying division equality

x = -36 / - 12

x = 3

In conclusion, the solution to the equation as solved by Melanie by distributing is x = 3

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Yes AAS and SAA are the same Methods for determining whether two triangles are congruent.

The acronym AAS or SAA stands for "Angle, Angle, Side or Side, Angle, Angle" denoting two angles and a side opposite them. AAS os SAA is one of the five methods for determining whether two triangles are congruent. It states that two triangles are congruent if their vertices are in one-to-one correspondence, that is if two angles and the side that is opposite to one of them in one triangle are congruent to the corresponding angles and the side that is not included in the second triangle. The side that is in opposition to either of the angles that are being used is called the non-include side. In layman's terms, two triangles are congruent if the sides of two pairs of corresponding angles are equal in each triangle.

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Answer:

6' = 12" with a scale of 1

8'= 20" with a scale of 1

6" = 12' with a scale of 1

48" = 146' with a scale of 1

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

6' = 18" with a scale of 0.5

8' = 25" with a scale of 0.5

6" = 24' with a scale of 0.5

48" = 58' with a scale of 0.5

Step-by-step explanation:

Should be right.

The mean of the data 1,2,3,4,5,6,7 is 4.

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

The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;

Mean = Sum of the Given Data/Total number of Data

Mean= 1+2+3+4+5+6+7 / 7 = 28/7 = 4

Hence, The mean of the data 1,2,3,4,5,6,7 is 4.

Complete question: What is the mean value of 1,2,3,4,5,6,7?

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Median is the middlemost value after the data set is sorted in ascending or descending order.

What is median?

The data set's median is the value in the middle.when we will put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them up, and divide by two. Your median will be that value.

so if we given with a data set 2, 1 ,4, 3,2 ,2 ,1

so in order to find the median of a data set we will sort it into ascending order and then find the middle most value as the number of element is odd.

so after sorting the data set is like 1 , 1 , 2 , 2, 2 , 3 , 4 so the middle value is 4 the element which is 2 and hence median of the data set is 2.

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Answer:

To find the quotient of 3/4 and 5/6, divide each number by 2: 3/4 = 1/2 and 5/6 = 3/4. Therefore, the quotient is 1 1/9.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

See attached image below

Answer:

Step-by-step explanation:

[tex]Equation 1\\y-2x=-2\\Equation 2\\8x=-3y-48[/tex]

To begin, solve equation 1 for y:

[tex]y=2x-2[/tex]

Then substitute 2x-2 for y in equation 2:

[tex]8x=-3(2x-2)-48[/tex]

Now solve for x:

[tex]8x=-3(2x-2)-48\\8x=-6x+6-48\\8x=-6x-42\\(8x)+6x=(-6x-42)+6x\\14x=-42\\\frac{14x}{14}=\frac{-42}{14}\\x=-3[/tex]

Substitute this x-value into equation 1:

[tex]y=2x-2\\y=2(-3)-2\\y=-6-2\\y=-8[/tex]

So, the ordered pair that best represents the solution to this system of equations is (-3,-8).  This can be proven by substituting these values for x and y into the original equations:

[tex]y-2x=-2\\(-8)-2(-3)=-2\\-8-(-6)=-2\\-8+6=-2\\-2=-2[/tex]

and

[tex]8x=-3y-48\\8(-3)=-3(-8)-48\\-24=24-48\\-24=-24[/tex]

The system of linear equations 2x – y = 7 and y = 2x + 3, has no solution.

Linear equations are those with a degree of 1. ax + by = c is the formula for linear equations in two variables, where a, b, and c are constants. We shall substitute the value of y in order to solve the system of linear equations.

Let equation (1) be 2x - y = 7 and equation (2) be y = 2x + 3

Enter the value of the equation y = 2x + 3 in equation (1).

2x - (2x+3) = 7

2x - 2x - 3 = 7

             -3 = 7

which is not true.

Therefore, there is no solution.

Correct Question:

What is the solution to the system of equations 2x – y = 7 and y = 2x + 3?

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There is no mode in the data set 1, 2, 3, 4, 5,6,7,8,9.

A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

Given that,

Data set= 1, 2, 3, 4, 5,6,7,8,9

By the definition of mode, it is clear that the most observed data in a data set will be the mode of that data set. And this can be zero also. And it can be more than zero.

In statistics, the mode is the most commonly observed value in a set of data. And for the normal distribution, the mode is always the same as the mean and median. But in many cases, the modal value of a data set will differ from the average value in the data.

If we take our question then 1, 2, 3, 4, 5, 6,7,8,9.

Here, no term is repeated more than once.

So, there is no most observed term.

So, there is no mode in this data.

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Answer:

C) 395 grams

Step-by-step explanation:

Box B = 350g and is lighter than box A, 45 gram

Box A = Box B +45

350 + 45 = 395 grams

So, the answer is C

The age of Ally and Burke is

1/2    [1   1 ]   [6 ]  -   [16]

     [  -1    1]   [  26]   [ 10]

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Algebraic expressions fall into three main kinds, including: Numeral Expression.

Binary Expression

Expression of a polynomial.

Let the age of Ally be x years

Then age of Burke will be x+6 years

Given, Sum of their age is 26

Therefore x+x+6=26

2x=26 - 6

x = 10

Thus the age of Burke is 10 years

Now age of Ally will be x + 6= 10 + 6 = 16

That is

1/2[1   1 ] [6 ]  - [16]6

  [  -1    1] [  26]   [ 10]

Therefore the age is of ally is 16 and burke is 10

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Answer: ΔDEB ≅ ΔCEA; SAS

Step-by-step explanation:

          Using the diagram below, we can see that these two triangles share an angle, meaning that angle in both triangles is congruent. Next, we see dashed lines representing congruence for two of the other sides. This means these two triangles are proved congruent by SAS;

    S = Side

    A = Angle

    S = Side

          See attached for a visual.

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example'

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that [tex]X[/tex] is less than or equal to is 0.1,

the probability that [tex]X[/tex] is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that [tex]X[/tex] is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that [tex]X[/tex] is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

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Answer:

1.6

Step-by-step explanation:

Goold helped!!!

The correct answer is the error made by the students of statistics is of Type 1 error.

As the question states that,

The news article that claim the number of student who believes that their online courses are as good as  or superior to traditional face-to-face instruction = 90%.

The two types of error known are:

Type I error  :  Reject the null hypothesis when the null hypothesis is true.

Type II error  : Fail to reject the null hypothesis, when the null hypothesis is NOT true.

From the question,

The hypothesis that the student test is H₀ : p = 0.90, Hₐ : p < 0.90 .

Here, p<0.90 means that College student disagree with the statement.

The student had rejected the null hypothesis,

and concluded that p <  0.90 , when in fact the null hypothesis is true .

The correct answer is Type 1 error.

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The perimeter of the triangle is 5x + 12 inches

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

Lengths = 7 inches, 4x + 1 and x + 4

The perimeter of a triangle is the sum of the side lengths

so, we have

Perimeter = sum of side lengths

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

Perimeter = 7 + 4x + 1 + x + 4

Evaluate the sum

Perimeter = 5x + 12

Hence, the perimeter is 5x + 12

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a) 7 in

b) 72 steps

Step-by-step explanation:

Angle of elevation formula:  

where  is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.

a)  Given:

b)  Given:

1st floor = 21 feet

2nd floor = 21 feet

⇒ Total height = 21 + 21 = 42 feet

1 foot = 12 inches

⇒ 42 feet = 42 x 12 = 504 inches

Using vertical rise of 7 in per step found in part (a):

Number of steps = 504 ÷ 7 = 72

Increased accuracy

Using unrounded vertical rise of 12tan(32):

Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step

The formula for finding the asymptote of a hyperbola is

y-k =+/- b/a( x-h)

Hyperbola

A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.

An asymptote of the curve y = f(x) or in the implicit form: f(x, y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

In Mathematics, infinity is the concept describing something larger than the natural number. It generally refers to something without any limit. This concept is predominantly used in the field of Physics and Math which is relevant in a number of fields.

The quintessential example of asymptotes are the vertical or horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant.

In the cartesian system, the coordinate plane is divided into four equal parts by the intersection of the x-axis (the horizontal number line) and the y-axis (the vertical number line). These four regions are called quadrants because they each represent one-quarter of the whole coordinate plane.

The formula for finding the asymptote of a hyperbola is

y-k =+/- b/a( x-h)

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An asymptote of the curve y = f(x) or in the implicit form: f(x, y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

The quintessential example of asymptotes are the vertical or horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant.

The expected value to pick a package is $.1125.

To find the expected value, you need to multiply the value of each package by the probability of selecting it and then add up all of these values.

The probability of selecting one of the $.70 packages is 20/40 = 1/2, since there are a total of 40 packages and 20 of them are worth $.70. The expected value of selecting one of these packages is $.70 * (1/2) = $.35

The probability of selecting one of the $.60 packages is 15/40 = 3/8, since there are a total of 40 packages and 15 of them are worth $.60. The expected value of selecting one of these packages is $.60 * (3/8) = $.22.5

The probability of selecting one of the $.30 packages is 5/40 = 1/8, since there are a total of 40 packages and 5 of them are worth $.30. The expected value of selecting one of these packages is $.30 * (1/8) = $.0375

The expected value of selecting one package at random is therefore $.35 + $.22.5 + $.0375 = $.61.25. However, you have to pay $.50 to pick a package, so the net expected value is $.61.25 - $.50 = $.1125.

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Picking a bundle is anticipated to be worth $.1125.

You must multiply the value of each package by the likelihood that it will be chosen before adding up all of these values to arrive at the expected value.

Given that there are a total of 40 packages and 20 of them are valued at $.70 each, the likelihood of choosing one of the $.70 packages is 20/40 = 1/2. Selecting one of these packages has an expected value of $.70 * (1/2) = $.35.

Given that there are 40 products in total and 15 of them are worth $.60 each, the probability of choosing one of the $.60 packages is 15/40 = 3/8. Choosing one of these packages will result in a value of $.60 * (3/8) = $.22.5.

There are a total of 40 packets, and 5 of them are worth $.30, hence the likelihood of choosing one of the $.30 packages is 5/40 = 1/8. By choosing one of these packages, the predicted value is $.30 * (1/8) = $.0375.

Therefore, $.35 + $.22.5 + $.0375 = $.61.25 is the expected value of choosing one package at random. The net expected value is $.61.25 - $.50 = $.1125 due to the fact that you must pay $.50 to choose a bundle.

Answer: 30 sq ft

Step-by-step explanation: The area of a triangle can be calculated using the formula A = 1/2 * b * h, where A is the area, b is the base, and h is the height. In this case, the base of the triangle is 7 1/2 feet and the height is 8 feet, so the area is calculated as follows: A = 1/2 * 7.5 * 8 = 30 square feet. Therefore, the area of the triangle is 30 square feet.

Answer:

[tex]30sq ft[/tex]

Step-by-step explanation:

Since the electrician charged $360 on a particular job, the number of hours that this electrician worked for is 4 hours.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being charged by this electrician;

T = mh + b

Where:

Therefore, the required linear function that represents the total amount of money that is being charged by this electrician per hour is given by this mathematical expression;

T = 80h + 40

When the total amount of money is $360, the number of hours worked by this electrician can be calculated as follows;

360 = 80h + 40

80h = 360 - 40

80h = 320

Time, h = 320/80

Time, h = 4 hours.

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