1/3 (6x +12) - 2(x-7)=19

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer: Vertically shifting it by 3

The transformation of a function is horizontally shrink by a factor of 3 .

Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.

How do you horizontally shrink  by a factor of 3 ?

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The steps for adding and subtracting fractions with whole numbers:

- Write the whole number in the form of a fraction.

- Convert the fractions to like fractions.

- Add/Subtract the numerators while the denominator remains the same.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part of fraction is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

In case of adding and subtracting fractions with whole numbers:

Let us assume that 'a' represents the whole number and \(\frac{x}{y}\) be fraction

First we write the whole number in the form of a fraction.

So, a = \(a = \frac{a}{1}\)

Now we find the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\) and then convert the given fractions to like fractions.

Let m be the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\)

So, the fractions becomes  \(\frac{a}{m} ,\frac{x}{m}\)

Last we Add/Subtract the numerators while the denominator remains the same.

i.e., \(\frac{a\pm x}{m}\)

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The complete question is:

How to add /subtract fractions with whole numbers?

With the help of binomial distribution we can conclude our answer.

acc to our question-

The confidence interval can be found out using,

Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).

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Answer:

c would be the y intercept,

Step-by-step explanation:

The surface area of the open-top rectangular box is 2L^2 + 6Lh.

The surface area of an open-top rectangular box consists of the area of its base and the areas of its four sides. The base is a rectangle with dimensions w (width) and l (length), and the box has a height h.

To calculate the surface area, we need to find the areas of the base and the four sides.

1. The area of the base is given by lw.

2. The four sides of the box consist of two pairs of equal-sized rectangles. Each pair has a width w and a height h, and a length equal to the length of the base, l.

Therefore, the total surface area (SA) can be expressed as:

SA = lw + 2wh + 2lh

Given that the base width is double the base length (w = 2l), we can substitute this into the equation:

SA = lw + 2(2l)h + 2lh

SA = lw + 4lh + 2lh

SA = lw + 6lh

Comparing this expression to the given options, we can see that the correct answer is:

SA = \(2L^2\)+ 6Lh  (option a)

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Answer:

57.5

Step-by-step explanation:

divide 92 by 1.6. I hope this helps

The probability of an event A∪B occurring is the sum of the probabilities of each event occurring independently. When two events are mutually exclusive, the probability of both events occurring at the same time is 0. Therefore, the probability of A∪B occurring is the sum of the individual probabilities of A and B.

P(A∪B) = P(A) + P(B)
Since A and B are mutually exclusive events, the probability of both events occurring at the same time is 0. Therefore, P(A∪B) = P(A) + P(B) = 0.33 + 0.29 = 0.62.

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The simplified value is 8*cos^4(x) = 3+ 4 cos2x + cos 4x.

The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers. This becomes important in several applications such as integrating powers of trigonometric expressions in calculus.

Given:

Using the power reduction identity, we have that:

cos² x= 1/2( 1+ cos 2x)

cos^4(x) = (cos² x)²= (1/2( 1+ cos 2x))²

cos^4(x) =  1/4( 1+ cos² 2x+ 2 cos (2x))

Again, cos² 2x= 1/2( 1+ cos 4x)

cos^4(x) =  1/4( 1+ 1/2( 1+ cos 4x)+ 2 cos (2x))

cos^4(x) =  1/4( 1+ 1/2 +1/2 cos 4x+ 2 cos (2x))

cos^4(x) =  1/4( 3/2 + 2 cos2x + 1/2 cos 4x)

8*cos^4(x) =  8*1/4( 3/2 + 2 cos2x + 1/2 cos 4x)

8*cos^4(x) =  2( 3/2 + 2 cos2x + 1/2 cos 4x)

8*cos^4(x) = 3+ 4 cos2x + cos 4x

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The general solution of the given recurrence equation is Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n.

The given recurrence equation is

Qn-1 + 5Qn-2 + 3Qn-3 = 3

Let's find the characteristic equation of the given recurrence equation:

By assuming Qn = rn,

the characteristic equation can be derived as:

r3 - r2 - 5r - 3 = 0

So, the characteristic polynomial is

(r + 1)(r - 3)2

Let α = -1 and β = 3 (repeated roots)

Now, the solution of the given recurrence equation is:

Qn = Arn + Bnαn + Cnβn

As α = -1 and β = 3 are the roots of the characteristic equation, substitute these values in the above equation.

We have

A(-1)n + Bn(-1)n + Cn(3)n ... (1)

As we are going to find the general solution of Qn, the constants A, B, and C need to be determined.

Let's solve for A, B, and C by considering the first few terms of the given recurrence equation.

Suppose n = 3 in the recurrence equation Qn-1 + 5Qn-2 + 3Qn-3 = 3, we have

Q2 + 5Q1 + 3Q0 = 3 ... (2)

Now, substitute n = 2 in the general solution (1), we have

Q2 = A(-1)2 + B2(-1)2 + C23 ... (3)

Now, substitute n = 1 in the general solution (1), we have

Q1 = A(-1)1 + B1(-1)1 + C31 ... (4)

Now, substitute n = 0 in the general solution (1), we have

Q0 = A(-1)0 + B0(-1)0 + C30 ... (5)

Now, let's solve for A, B, and C using equations (2), (3), (4), and (5).

Q2 + 5Q1 + 3Q0 = 3:

2A + 5B + 3C = 3A(-1)2 + B2(-1)2 + C23:

A - B + 9C = 3A(-1)1 + B1(-1)1 + C31:

-A - B + 3C = 1A(-1)0 + B0(-1)0 + C30:

A + B + C = 1

On solving the above equations,

we get A = -1/4, B = 1/4, and C = 1/2

So, the general solution of the given recurrence equation is  

Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n

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Answer:

-1

Step-by-step explanation:

6/7-1=11/14 11/14-1=5/7 and so on.

12/14, 11/14, 10/14, 9/14, next term is 8/24 which is simplified to 1/3

We have the equation:

To find the value of y when x = 2, we replace x = 2 in the equation above, we get:

Answer: 20

Two congruent triangles with the same orientation aligned with one above the other. The transformation is -

Option A: reflection over a horizontal line

What is reflection?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

In the figure it is given that -

Both the triangles are equal and congruent to each other.

There is no change in the shape or size of both the images only the place of the image is changed.

One triangle is placed above the another.

This is done over a horizontal plane.

Therefore, the transformation is reflection over horizontal line.

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Step-by-step explanation:

General line equation: y = mx + c

When x = 0, y = 3. => (3) = m(0) + c, c = 3.

When x = -4, y = 5. => (5) = m(-4) + c,

5 = -4m + (3), -4m = 2, m = -0.5.

Hence the answer is y = -0.5x + 3.

Answer:

y=-\(\frac{1}{2}\)+3

Step-by-step explanation:

To write the equation of the line in slope-intercept form, first calculate the slope of the line (m)

m=\(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)

=\(\frac{5-3}{-4-0}\)

=2/-4

=-\(\frac{1}{2}\)

next, calculate b by substituting a point (0, 3) into the equation

y=mx+b

3=(-1/2)(0)+b

b=3

final equation of line is: y=-\(\frac{1}{2}\)+3

Answer:

Step-by-step explanation:To find the scale factor of an original and a scale drawing, set up a ratio of the original length and the length of the drawing. Then simplify the ratio. A scale factor may be expressed by the ratio or by a positive number.A scale factor expresses the relationship between two lengths. It can be expressed as a ratio or a positive number. Let's look at some examples. If the original image is 4 inches, and the scale drawing is 8 inches, we can say that the scale factor is 4:8, but we must simplify that ratio, making it 1:2. We can also write the scale factor as a number by dividing 8 by 4 for a scale factor of 2.

That example is pretty straightforward, but let's look at something a bit more complicated. Let's say we have an original image that is 4 inches and a scale drawing that is 9.5 inches, and we want to find the scale factor. We cannot write the ratio 4:9.5, because ratios do not allow decimals or fractions. We must simplify the ratio. This involves getting rid of the decimal. To do this, we multiply 9.5 by 2 and get 19. What we do to one element of the ratio, we must do to the other, so we multiply 4 by 2 for 8. Our ratio looks like this: 8:19. Because 19 is a prime number, we cannot simplify further. This scale factor of 8:19, then, tells us that for every 8 inches in the original, the scale drawing will have 19 inches. We can also express the scale factor as 2.375 (19 divided by 8).

We'll try one more example. We have an original image that is 1.25 inches and a scale drawing that is 4 inches. Again, we cannot write a ratio with decimals, so we can't leave our scale factor as 1.25:4. We must simplify. This time, we must get rid of the decimal by multiplying each side by 4, so we have 5:16. We cannot simplify this ratio any further, but we can express it by the number 3.2 (16 divided by 5).

Answer:

The answer is C

Step-by-step explanation:

Khan Academy

Answer:

C

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

A visualization technique to view a distribution of the popularity of words in a bag-of-words model is a word cloud.

A common technique for visualizing the distribution of the popularity of words in a bag-of-words model is the word cloud.

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Answer:

n = 81

Step-by-step explanation:

The left angle in the upper triangle and 44° are Alternate angles and congruent.

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

n is an exterior angle of the upper triangle, thus

n = 44 + 37 = 81

-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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Answer: x = 150

Step-by-step explanation:

See the liner pair of angle 70 will be 110 degrees.

Then using angle sum property third angle will be

Third angle = 180 - 150

Third angle of the triangle = 30

Now linear pair of the 30 degree angle

30+x = 180

x = 180-30

x = 150

Therefore answer is option e x = 150.

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The measure of the value of angle x is 150°, and the correct option is E

Linear pair of angles are formed when two lines intersect each other at a single point.

The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.

BY applying linear pair angles;

\(\rm \angle 1+\angle 2=180\\\\70 +\angle 2=180\\\\ \angle 2=180-70\\\\ \angle 2=110\\\\\)

The sum of the three angles is 180.

\(\rm \angle 1+\angle 2+ \angle 3=180\\\\ 110+40 +\angle 3=180\\\\150+\angle 3= 180\\\\\angle 3=180-130\\\\\angle 3=30\)

The measure of the value of angle x is;

\(\rm 30+x = 180\\\\x = 180-30\\\\x = 150\)

Hence, the measure of the value of angle x is 150°, and the correct option is E.

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Answer:

120 pounds = 54.5 kilogram

Step-by-step explanation:

We know that,

1 kilogram=2.2 pounds

or

1 pound = (1/2.2) kilogram

We need to convert 120 pounds to kilograms.

\(120\ \text{pounds}=\dfrac{120}{2.2}\ \text{kilogram}\\\\=54.5 \text{kilogram}\)

So, there are 54.5 kilograms in 120 pounds.

Total number of outcomes (n) = 2

Let E be the event of getting a yellow colored side of the coin.

Therefore, n(E) = 1

Therefore, P(E) = n(E)/n = 1/2

Answer:

1/2

Hope it helps.

If you have any query, feel free to ask.

Answer:

144.5 in ^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h  where the b1 and b2 are the lengths of the bases and h is the height

A = 1/2 ( 9.7+24.3) * 8.5

  = 1/2 ( 34)*8.5

   =144.5

Answer:

same. me too❤

Answer:

slope is 2.

Step-by-step explanation:

(1,1) which is x¹and y¹

(3,5)which is x²and y²

so,

by using the formula,

slope= y2-y1over x2-x1

= 3-1over 5-1

= 2 over4

=2.

Using proportions, it is found that there would be 500,000 mites.

The rule of three is:

1 dust mite - \(2.5 \times 10^{-4}\) m.

x dust mites - \(1.25 \times 10^2\) m

Applying cross multiplication:

\(2.5 \times 10^{-4}x = 1.25 \times 10^2\)

\(x = \frac{1.25 \times 10^2}{2.5 \times 10^{-4}}\)

\(x = 500000\)

There would be 500,000 mites.

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Descriptive statistics are those that involve gathering, arranging, and summarizing data.

Brief informational coefficients known as descriptive statistics are used to sum up a given data set, which may be a sample of a population or a representation of the entire population. Measures of the central tendency or measures of variability make up descriptive statistics (spread).

A descriptive statistic's main function is to summarize data. Only the data set from which they were derived are statements made by descriptive statistics; they never extend further than the data you have.

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This integral will give us the desired area of the region bounded by the curve f(x) = 25 - x^2 and the x-axis within the interval [-5, 5].

To calculate the area of the region bounded by the curve f(x) = 25 - x^2, we can set up a definite integral over the desired interval.

The function, f(x) = 25 - x^2, represents a downward-opening parabola centered at the origin with a vertex at (0, 25).

To get  the area, we need to consider the portion of the curve that lies above the x-axis. This corresponds to the region we want to find the area of.

Since the curve is symmetric about the y-axis, we can focus on the positive x-values.

To determine the interval, we need to get the x-values where the curve intersects or touches the x-axis. Solving the equation 25 - x^2 = 0 gives x = ±5.

Therefore, the interval we are interested in is [-5, 5], which represents the portion of the curve above the x-axis.

The definite integral that yields the area of the region is:

∫[from -5 to 5] (25 - x^2) dx

Evaluating this integral will give us the desired area of the region bounded by the curve f(x) = 25 - x^2 and the x-axis within the interval [-5, 5].

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