For each figure below, determine (by using the markings) if there Is a pair of congruent triangles. If there Is, name the congruence and give the property justifying the congruence.
Note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn in determining your answers.

Answer: It is not clear what you are asking for when you say "fifth formula". There are many formulas in mathematics, and it could be referring to different things in different context.

Formulas can be found in different branches of mathematics and science, such as geometry, algebra, physics, chemistry, etc. Can you please provide more context or specify what area of mathematics or science you are interested in?

It is important to note that any formula needs to be referenced in order to understand what it represents and how to use it.

Step-by-step explanation:

Answer + explanation:

Part 1: First, find the area of one triangle using the formula base * height / 2. You have base = 10 and height = 7, so area = 7 * 10 /2 = 70/2 = 35. Since you're finding the combined area of 4, you have to do 35 * 4 = 140.

Part 2: To do this, find the side length of the square. Looking at the picture, you see that all you have to do is 10 + 7 = 17 to find one side. Then, to find the area do 17 * 17 = 289.

Part 3: To find the area of the small square, all you do is area of the large square - combined area of 4 small triangles, so 289 - 140 = 149.

Part 4: a^2 = 7 * 7 = 49. Then, b^2 = 10 * 10 = 100. Adding them together, you get 100 + 49 = 149.

Part 5: Since you already have the a^2 + b^2 part, all you need to do is find what c^2 is. You can see in the picture that c^2 equals the area of the small square, which you found in part 3. c^2 = 149. Then, you have 149 and 149, which are equal so the answer is =.

Step-by-step explanation:

To solve the system of equations:

5x + y = 9

10x - 7y = -18

We can use the elimination method by multiplying the first equation by 7 and subtracting it from the second equation:

35x + 7y = 63 (multiplying first equation by 7)

10x - 7y = -18

45x = 45

Dividing both sides by 45, we get:

x = 1

Substituting x = 1 into the first equation:

5(1) + y = 9

Simplifying, we get:

y = 4

Therefore, the solution to the system of equations is x = 1 and y = 4.

We can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

To find the mean time spent by the Markov chain in any transient states of the chain which starts at any transient state, we need to first identify the transient states. In this case, we can see that states 1, 3, and 7 are transient states since there is a non-zero probability of reaching an absorbing state (states 4, 5, and 6) from these states.

Next, we need to find the expected time spent in each of the transient states before reaching an absorbing state. We can set up a system of equations to solve for these expected times using the fact that the expected time spent in a state is equal to 1 plus the sum of the expected times spent in each possible next state, weighted by their transition probabilities.

For example, for state 1, we have:

E(T1) = 1 + 0.5E(T2) + 0.25E(T3)

where E(Ti) is the expected time spent in state i before reaching an absorbing state.

Similarly, for state 3, we have:

E(T3) = 1 + 0.4E(T2) + 0.2E(T4)

And for state 7, we have:

E(T7) = 1 + 0.2E(T5) + 0.5E(T6)

Solving these equations, we get:

E(T1) = 5

E(T3) = 5.5

E(T7) = 4

Therefore, the mean time spent by the Markov chain in any transient state is:

(E(T1) + E(T3) + E(T7))/3 = (5 + 5.5 + 4)/3 = 4.83

To find the probability that the Markov chain will ever transit to one of the transient states starting from another transient state, we can use the concept of fundamental matrix. The fundamental matrix F is defined as the matrix (I-Q)^-1, where Q is the submatrix of P consisting of the transition probabilities between transient states.

In this case, we have:

Q = [0 0.25 0.2;

0.4 0 0.2;

0.2 0.2 0]

Using a calculator or software to calculate the inverse of (I-Q), we get:

(I-Q)^-1 = [1.25 0.625 1;

0.625 1.25 1;

1 1 1.5]

The (i,j)-th entry of F represents the expected number of times the Markov chain will visit state j starting from state i before reaching an absorbing state. Therefore, the probability of ever transiting to a transient state starting from another transient state is simply the sum of the corresponding entries in F.

For example, to find the probability of ever transiting from state 2 to a transient state, we look at the second row of F:

[0.625 1.25 1]

The sum of these entries is 0.625 + 1.25 + 1 = 2.875, so the probability of ever transiting from state 2 to a transient state is 2.875.

Similarly, we can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

To learn more about corresponding visit:

https://brainly.com/question/1597341

#SPJ11

The value of x is approximately 11.167.

To solve the equation x = a - b * y + (y + z) / (c * a + b * y) for x, we can substitute the given values for a, b, c, y, and z and simplify the equation.

Given:

a = 6, b = 4, c = 4, y = 7, z = 1

Substitute the values into the equation:

x = 6 - 4 * 7 + (7 + 1) / (4 * 6 + 4 * 7)

Simplify the equation using the order of operations (PEMDAS):

x = 6 - 28 + 8 / (24 + 28)

x = 6 - 28 + 8 / 52

x = 6 - 28 + 0.154

Combine like terms:

x = -22 + 0.154

Evaluate the expression:

x = -21.846

Therefore, the value of x is approximately -21.846 (rounded to three decimal places).

To learn more about decimal places visit:

brainly.com/question/32707614

#SPJ11

Answer:25 pear trees

Step-by-step explanation:

15/150

60/150

50/150

15+60+50=125

150-125=25

These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

To know more about polynomial, visit:

https://brainly.com/question/13199883

#SPJ1

The Milankovitch theory proposes that changes in Earth's climate are influenced by variations in its orbit and tilt.

This theory was widely accepted due to marine records that provided evidence of past climate changes. Specifically, the analysis of ocean sediment cores allowed scientists to reconstruct the Earth's climate over millions of years and observe patterns that matched the predictions of the Milankovitch theory. By comparing these records to other forms of evidence, such as ice cores and tree rings, scientists were able to confirm the validity of the theory and its central elements. In short, the use of marine records provided the definitive test that led to the general acceptance of the Milankovitch theory. Eccentricity refers to the shape of Earth's orbit around the Sun, which varies over a 100,000-year cycle. Axial tilt, the angle between Earth's rotational axis and its orbital plane, changes over a 41,000-year cycle. Precession, the wobble of Earth's axis, occurs over a 26,000-year cycle. These factors affect the distribution and intensity of sunlight, causing periodic climate changes. Marine records, such as deep-sea sediment cores, provide a comprehensive and continuous archive of Earth's climate history. These records show repeating patterns of glaciation and warming, supporting the Milankovitch Theory. Through detailed analysis of marine records, scientists were able to correlate global climate shifts with the predicted cycles, leading to the general acceptance of the Milankovitch Theory.

To know more about Milankovitch theory visit:

https://brainly.com/question/2288983

#SPJ11

45 billion Korean Won is equal to 45 million US Dollars.

The formula for  (USD) is USD = KRW / 1000. To calculate 45 billion won in USD, we must first convert KRW to USD. 45 billion KRW is equal to 45,000,000,000 KRW. Using the formula above, we can calculate the amount of USD:

USD = 45,000,000,000 KRW / 1000

USD = 45,000,000 USD

Therefore, 45 billion won is equal to 45 million US Dollars.

To better understand this conversion, it is important to remember that one US Dollar is equal to 1000 Korean Won. As an example, if you have 10,000 Korean Won, you can convert that to USD by dividing 10,000 by 1000, which equals 10 USD. The same concept applies when converting larger numbers. To convert 45 billion KRW to USD, we must divide 45,000,000,000 by 1000, which equals 45,000,000 USD.

In conclusion, 45 billion Korean Won is equal to 45 million US Dollars.

Learn more about conversion here:

https://brainly.com/question/28770698

#SPJ4

Answer:

steps below

Step-by-step explanation:

volume of rock : 16 * 12 * 12 = 2304

height will take when it was threw into tank: 2304 / (32*24) = 3

Original water height + rock height: 12 + 3 = 15 cm

Answer:

C =8

Step-by-step explanation:

I got this answer because anything greater than 8.

To perform the operation 5 1/2 - 3 2/5, we need to subtract the two mixed numbers. The solution to this operation is 21/10.

To subtract mixed numbers, we follow these steps:

1. Convert the mixed numbers to improper fractions.

  5 1/2 can be written as (2 * 5 + 1)/2 = 11/2

  3 2/5 can be written as (5 * 3 + 2)/5 = 17/5

2. Find a common denominator for the fractions. In this case, the common denominator is 10.

3. Rewrite the fractions using the common denominator.

  11/2 = (11 * 5)/(2 * 5) = 55/10

  17/5 = (17 * 2)/(5 * 2) = 34/10

4. Subtract the fractions.

  55/10 - 34/10 = (55 - 34)/10 = 21/10

5. Express the resulting fraction as a mixed number, if necessary.

  Since the fraction is proper (the numerator is less than the denominator), it remains the same.

Therefore, the answer to the operation 5 1/2 - 3 2/5 is 21/10.

To know more about mixed numbers, refer here:

https://brainly.com/question/24137171#

#SPJ11

Answer:

8

Step-by-step explanation:

since B. Crosses through the middle, we can see that 4x+1 = 33.

simplest way:

Easily, multiply 4 multiple times till you receive 32.

so, multiply 4 x 8 to receive 32.

Then add 1 to 32.

33.

Answer 8. because 4x8+1=33.

The  frequency table formed using tally marks can be analyzed by using the numbers indicated by the tally  marks as follows;

The true statements are as follows;

Tally marks makes use of vertical lines to represent data, in which the fifth count is represented by a diagonal line across four vertical lines;

The data in the table are as follows

The number of students that prefer red = 5 + 1 = 6

The number of students that prefer yellow = 2

The number of students that prefer Blue = 5

The number of students that prefer purple = 3

The number of students that prefer Green = 6

Therefore;

Learn more about frequency tables in statistics here:

https://brainly.com/question/15422753

#SPJ1

Answer:

Step-by-step explanation:

1/2 6 times 6

Fewer births and increased survival rates are changing the shape of the population from a pyramid to a(n): Rectangle

It is given that fewer births and increased survival rates are changing the shape of the population from a pyramid.

Survival rates is the percentage of people in a study or treatment group who are still alive for a certain period of time after they were diagnosed with or started treatment for a disease, such as cancer.

A population pyramid is a way to visualize two variables: age and sex. They are used by demographers, who study populations. A population pyramid is a graph that shows the distribution of ages across a population divided down the center between male and female members of the population.

To know more about shapes visit: https://brainly.com/question/14661102

#SPJ4

Answer:

16g

Step-by-step explanation:

Answer:

your answer will be 16 grams

Step-by-step explanation:

hope it helps...

have a great day!!

Answer:

A. 37, 38, 39, 41, 43, 47, 52, 54

Step-by-step explanation:

Answer:

There is no mode !

Step-by-step explanation:

Hello,

what is the mode of a set of data?

It is the value in the set that occurs most often.

To note that this is also possible to have a set of data with no mode.

in this example, let's order them

7, 8, 11, 12, 13, 14, 15, 20

There is no repetition, right? each value occurs only once.

So, there is no mode!

hope this helps

Answer:

5/4

Step-by-step explanation:

125/100

(divide through by 25)

5/4

The work done by the gas during the isothermal expansion is 331.32 J.

Isothermal Expansion refers to a process in which the temperature of a system stays constant while the volume increases. In this process, an ideal gas expands from 1.1 m³ to 1.8 m³, and the gas constant is R = 8.314 J/(mol K).

The work done by the gas during the isothermal expansion can be calculated as follows:Answer:During an isothermal process, the change in internal energy of the system is zero since the temperature remains constant.

Therefore,ΔU = 0The first law of thermodynamics is given by:ΔU = q + w

where q is the heat absorbed by the system, and w is the work done on the system.Since ΔU = 0 for an isothermal process, the above equation reduces to:w = -q

During an isothermal process, the heat absorbed by the system is given by the equation:q = nRTln(V₂/V₁)Where, n is the number of moles, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.

Substituting the given values, we have:q = (1 mol) × (8.314 J/(mol K)) × (293 K) × ln(1.8 m³ / 1.1 m³)q = 331.32 J

Therefore, the work done by the gas during the isothermal expansion is given by:w = -qw = -(-331.32 J)w = 331.32 J

Thus, the work done by the gas during the isothermal expansion is 331.32 J.

Know more about Isothermal Expansion here,

https://brainly.com/question/30329152

#SPJ11

Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.

To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:

tan(θ) = x/15

We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:

d^2 = x^2 + 25^2

Taking the derivative of both sides with respect to time t, we get:

2d (dd/dt) = 2x (dx/dt)

Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):

tan(θ) = x/15

sec^2(θ) (dθ/dt) = (1/15) (dx/dt)

(dθ/dt) = (1/15) (dx/dt) sec^2(θ)

We can use the equation for d to solve for x:

x^2 = d^2 - 25^2

2x (dx/dt) = 2d (dd/dt)

(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)

(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)

Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):

(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))

(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))

(dθ/dt) = (13/375) sec^2(arctan(15/25))

(dθ/dt) ≈ 0.039 radians per second

To know more about line of sight,

https://brainly.com/question/14883123

#SPJ11

Answer:

GCF=1  

Add=13

Multiply=30

Step-by-step explanation:

GCF:

   Factors of Ten= 10, 5, 2, 1

   Factors of Three= 3, 1

   Common factors = 1

Add:

   10+3 = 13

Multiply:

   10x3 = 30

Answer:

Option C.

Step-by-step explanation:

Hey there!

The points are; (-4,-4) and (-4,-10).

Use distance formula.

\(d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \)

~ Put all values.

\(d = \sqrt{ {( - 4 + 4)}^{2} + ( { - 10 + 4)}^{2} } \)

~ Simplify it.

\(d = \sqrt{ {0}^{2} + ( { - 6)}^{2} } \)

\(d = \sqrt{36} \)

Therefore, distance between the points is 6 units.

Hope it helps...

Answer:

Option: C (6)

Step-by-step explanation:

Answer:

8,9. look at the lines and the numbers. q meets at points 8 and 9

Answer:

The answer is 6.3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) , thus

f(x) + g(x)

= 4x + 1 + x² - 5 ← collect like terms

= x² + 4x - 4 → A