Two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?.

The function f(x) = 3x + 3 - x is neither even nor odd.

The y-axis of the function k's graph is symmetric. This is apparent because, if we reflect any point on the graph across the y-axis, we will obtain a second point on the graph. For purposes of formal definition, the function k is even since k(-x) = k(x) for every x within the range of k.

If the function f(x) = 3x + 3 - x fits the requirements for even or odd functions, we may determine whether it is even, odd, or neither.

Being symmetric around the y-axis means that an even function has f(-x) = f(x) for every x falling inside its domain.

An odd function is symmetric around the origin, which means that for any x falling within the domain of f, f(-x) = -f(x).

We evaluate f(-x) and f(x) to see if they are equivalent in order to determine whether f(x) is even:

f(x) = 3x + 3 - x = 2x + 3 while f(-x) = 3x + 3 - x = -2x + 3

The function f(x) is not even since f(-x) is not equal to f(x).

We assess f(-x) and -f(x) and see if they are equivalent to determine whether f(x) is odd:

F(x) = -3(x) + 3(x) - (x) = -2x + 3 F(x) = -(3x + 3(x) - x) = -2x - 3

The function f(x) is not weird since f(-x) does not equate to -f(x).

The function f(x) = 3x + 3 - x is therefore neither even nor odd.

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Answer:

\(\frac{3}{4}\) = the slope

Step-by-step explanation:

you have a slope formula to do this problem and you need to learn how to use it.  Watch me.

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

m = \(\frac{-12 - (-18)}{-2 - (-10)}\)

   = \(\frac{-12 + 18}{-2 + 10}\)

   =  \(\frac{6}{8}\)

   = \(\frac{3}{4}\)

Answer:

v = 13/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

(-3v + 1) + 7 - (6v + 6) = -37

Step 2: Solve for v

Answer:

30 Degrees

Step-by-step explanation:

all triangles are 180 degrees, therefore 180-130-20=30

:)

Given:

There are given the two numbers 36 and 487.

Explanation;

According to the question:

We need to find the quotient and remainder. when we divide 487 by 36.

So,

From the concept of quotient:

The quotient is defined for the final results when we divide one number from another number.

Then,

Then,

In the above expression:

Final answer:

Hence, the values of quotient and remainder is shown below:

The probability of inhaling at least one molecule from your last breath is virtually certain, reaching close to 1 or 100%.

The probability of inhaling at least one molecule from your last breath, given that there are approximately 10^22 molecules in your breath and they are thoroughly mixed among 10^44 molecules in the atmosphere, is extremely high. It is essentially certain that you are inhaling at least one of these molecules at any given moment.

The probability of inhaling at least one molecule from your last breath can be calculated by considering the ratio of the molecules in your breath to the molecules in the atmosphere. With approximately 10^22 molecules in your breath and 10^44 molecules in the atmosphere, the probability of inhaling at least one molecule from your last breath can be approximated as 1 - (probability of not inhaling any molecule).

The probability of not inhaling any molecule from your last breath can be calculated by the following formula: (1 - probability of inhaling one molecule)^N, where N is the number of breaths you have taken since your last breath.

However, in this scenario, the number of molecules in the atmosphere is enormously greater than the number of molecules in your breath. This means that even if you take a vast number of breaths, the probability of not inhaling any molecule from your last breath becomes incredibly small, approaching zero. Therefore, the probability of inhaling at least one molecule from your last breath is virtually certain, reaching close to 1 or 100%.

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Theorem 9.11 states that the p-series ∑_(n=1)^∞ 1/n converges if p > 1 and diverges if p ≤ 1.
In the given series, we can see that each term is of the form n^3, which can be written as (n^p)^3 where p=1/3.

Since p=1/3 is less than or equal to 1, we can conclude that the series diverges by applying Theorem 9.11.

Therefore, the given series diverges.
Using Theorem 9.11, we can determine the convergence or divergence of the given p-series. This theorem states that a p-series ∑_(n=1)^∞ 1/n^p converges if p > 1 and diverges if p ≤ 1.

If you meant to write the series as 1/8 + 2/27 + 3/64 + 4/125 + ... (with terms of the form n/n^3), then it is a p-series with p = 3 > 1. In this case, according to Theorem 9.11, the series converges.

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K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.

Therefore, the coordinate of the image of point K is K’(-2, 1).

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The most general solution to the original nonhomogeneous differential equation is y = y_h + yp = c1e^(-2x)cos(x) + c2e^(-2x)sin(x) + 2x - 3e^(-x), where c1 and c2 are arbitrary constants.

To find a particular solution to the nonhomogeneous differential equation y'' + 4y' + 5y = 10x + 3e^(-x), we can use the method of undetermined coefficients.

First, we find the complementary homogeneous equation by setting the right-hand side to zero: y'' + 4y' + 5y = 0. The characteristic equation is r^2 + 4r + 5 = 0, which has roots r = -2 ± i. Therefore, the general solution to the homogeneous equation is y_h = c1e^(-2x)cos(x) + c2e^(-2x)sin(x), where c1 and c2 are arbitrary constants.

To find a particular solution, we assume that yp has the same form as the nonhomogeneous terms, i.e., yp = Ax + Be^(-x), where A and B are constants to be determined. Substituting this into the nonhomogeneous equation, we get:

y'' + 4y' + 5y = 10x + 3e^(-x)
-Be^(-x) + 4A - 4Be^(-x) + 5Ax + 5Bx = 10x + 3e^(-x)

To satisfy this equation, we set the coefficients of the like terms on both sides equal to each other:

5A = 10, which gives A = 2
-4B + 5B = 3, which gives B = -3

Therefore, the particular solution is yp = 2x - 3e^(-x).

The most general solution to the original nonhomogeneous differential equation is y = y_h + yp = c1e^(-2x)cos(x) + c2e^(-2x)sin(x) + 2x - 3e^(-x), where c1 and c2 are arbitrary constants.

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Answer:

Down below

Step-by-step explanation:

we would figure out the average, which is [(22+40)/2]

62/2=31

31

and that is a vary low score

Answer:

\(2 \times 9 = 3 \times y \\ y = 18 \div3 = 6 \\ 6 \times 3 = x \times 5 \\ x = 18 \div 5 = 3.6\)

In the data of 8 9 9 4 5 5 2, the mean absolute deviation (MAD) is

equal to  0.

The mean absolute deviation (MAD) is a variability measure that indicates the average distance between observations and their mean. MAD uses the data's original units, which simplifies interpretation.

Larger values indicate that the data points are further apart from the average. Lower values, on the other hand, correspond to data points clustering closer to it. The mean absolute deviation is also known as the average absolute deviation and the mean deviation.

Let us find the mean first

8+ 9+ 9+ 4+ 5+ 5+ 2 = 42

Mean = 42/7

         = 6

Now lets find the deviation

(8 - 6) + (9 - 6) + (9 - 6) + ( 4 - 6) + (5 - 6) + (5 - 6) + (2 - 6)

= 0

Now, mean absolute deviation (MAD) = 0/6

                                                               = 0

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6 miles , is the one additional step which Cecil must travel in order to return to starting point A . His move accord expression is

8+(-5)+7+6+(-7)+5+(-8)+6

Let Cecil start from a point A and move toward point B . His movement expression is

8+(-5)+7+6+(-7)+5+(-8)

A →8 <--5 →7→6<--7→5<--8 , here  shows forward steps and shows backward steps

A→8→7→6→5 (B)

Total distance travelled by Cecil from A to B = 26 miles

B→5→7→8

Total distance travelled by Cecil from B to A = 20 miles

Cecil wants to return to the starting point A ,so he must be travel same distance as travelled from A to B i.e. 26 miles .

But Cecil travel from B to A is 20 and not 26 . The difference between the distance travelled by Cecil is (A→B – B→A) = 26-20 = 6 miles

Hence, Cecil required travel distance is 6 miles to return his starting point A.

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The equation in point-slope form is y=-2/7 x-36/7.

To determine the equation of a line in point-slope form, it is necessary to use the slope and a point on the line given. The formula is: y-y₁=m(x-x₁)where m is the slope, and (x₁, y₁) is the point on the line. Firstly, find the slope of the line using the coordinates of the given points, (−4,−4) and (10,−6). slope=m=(y2-y1)/(x2-x1) =(-6-(-4))/(10-(-4))= -2/7 Therefore, the slope of the line is -2/7.

Using the point-slope form, y-y₁=m(x-x₁), we can now fill in the other values using one of the points provided. Let's choose (-4,-4). y-(-4) =-2/7(x-(-4))y+4=-2/7(x+4) Multiply both sides of the equation by 7 to remove the fraction:7y+28=-2x-8 Isolate y on the left side of the equation:7y=-2x-8-28 =-2x-36y=-2/7 x-36/7.

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Answer:

55%

Step-by-step explanation:

First, find the total number of students who voted by adding.

264 + 216 = 480

Next, divide the number of students who voted for candidate A by the total you just found.

264/480 = 0.55

Finally, convert the decimal to a percent by multiplying by 100.

0.55 x 100 = 55%

Answer:

1343

Step-by-step explanation:

Answer:

sorry only have an answer for part b :/

Step-by-step explanation:

part b: the y-intercept is 25. it represents the amount of money she paid before her first practice.

Answer:

Each student get 3/4 cups.

Step-by-step explanation:

15÷20=0.75

turn into fraction

3/4

I answer this question before

According to the information, Samuel can stain the deck in 4 hours, and Julio can do it three times faster, in 4/3 hours or 1 hour and 20 minutes.

Let's assume that Samuel can stain the deck in x hours. Then, Julio can do the same job in x/3 hours (since he is three times faster).

Working together, they can stain the deck in 3 hours. Using the concept of work, we can set up the following equation:

1/x + 1/(x/3) = 1/3

Simplifying this equation by finding a common denominator, we get:

3/(3x) + x/(3x) = 1/3

Combining like terms, we get:

4x/(3x) = 1/3

Cross-multiplying, we get:

12x = 3x

Solving for x, we get:

x = 4

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Given that the graph of f(x) = ax² + 3 passes through the point (1,1). We are supposed to find the value of a.Since the point (1, 1) lies on the graph of the function, we can say thatf(1) = 1That is:a(1)² + 3 = 1a + 3 = 1a = 1 - 3a = -2

Therefore, the value of a is -2. Thus, the graph of the function f(x) = -2x² + 3 passes through the point (1, 1).The solution is done in 88 words.

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34.2 is a number that has a 3 with a value that is 100 times greater than the value of 3 in 20.342.

For both integer and non-integer numbers, the decimal numbering system is the accepted system. This is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the term for how numbers are represented using the decimal system.

Given, the number is 20.342.

3 is in the tenth position = 0.1

The value of 3 in 20.342 = 3 × 0.1 = 0.3

We have to find a number that has a 3 value that is 100 times greater than the value of the 3 in 20.342.

100 times greater than the value of 3 in 20.342 = 100 × 0.342

The number is = 34.20

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\(k=60 USD \)

\(q = 30\% = 1 \frac{3}{100} = 1.3\)

\(r=q⋅ k=1.3⋅ 60=78 USD \)

The probability that all three pairwise distances between the points are less than the radius of the circle is 1/12.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Since it doesn't matter where the first point is picked, it can be placed anywhere on the circle.

The following point must be within an arc of 60 degrees on either side, providing a total of 120 degrees and a chance of 1/3. The final point must be situated within 60 degrees of the first two.

If the first two points are apart by 60 degrees, the third point can be placed within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6. If the first two points are the same, the third point can be placed with a maximum degree of freedom of a 120 degree arc and a 1/3 probability.

The chance changes linearly with increasing distance from the first point, up to a maximum of 60 degrees.

As a result, we may find 1/4, the average likelihood we can position the third point based on a fluctuating second point, by averaging the probabilities at either end.

Total probability is 1 × 1/3 × 1/4 = 1/12.

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Answer:

-4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

10 ÷ (2x)

x = -5/4

Step 2: Evaluate

Answer: -4

Step-by-step explanation:

2(-5/4) = -5/2

10/ -5/2 = -4

Hope this helps :)

Answer:

D. 97

Step-by-step explanation:

The reason being is that his average should only be going up if he is dropping his lowest test score. And the only answer that shows his score going up is D.

Answer:

1,645 poles

Step-by-step explanation:

Here, we want to calculate the total number of poles

We can have an arithmetic progression here

Where the last term is the 58 piles , the first term is the top layer which is 12 and the common difference between the piles is 1

Firstly, we calculate the number of stacks which can be obtained using the nth term formula;

Tn = a + (n-1)d

58 = 12 + (n-1)1

58 = 12 + n - 1

58 = n + 11

n = 58-11

n = 47

So we have the stack high up to 47 units

So, using the sum of terms in an arithmetic sequence formula, we have;

Sn = n/2 ( a + L)

where a is the first term 12 and L is the last term 58

Thus, we have

Sn = 47/2( 12 + 58)

Sn = 47/2 * 70

Sn = 1,645

Answer:

x 2 +(29/10)x-(21/10) = 0 Add 21/10 to both side of the equation : x 2 +(29/10)x = 21/10 Now the clever bit: Take the coefficient of x , which is 29/10 , divide by two, giving 29/20 , and finally square it giving 841/400 Add 841/400 to both sides of the equation

Step-by-step explanation:

Answer:

You're right it is E

Step-by-step explanation:

6 to the right and 1 up