Are my answers correct?

Are My Answers Correct?

Answers

Answer 1

Answer:

Yes they are both correct.

Step-by-step explanation:

Answer 2

yes they are both correct.


Related Questions

Consider this equation.

7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)


Mia solved the equation and determined that m = 2. Is she correct?
She is incorrect because when substituting 2 for m the result was a true statement.
She is incorrect because when substituting 2 for m the result was a false statement.
She is correct because when substituting 2 for m the result was a true statement.
She is correct because when substituting 2 for m the result was a false statement.

Answers

Answer:

B .  She is incorrect because when substituting 2 for m the result was a false statement.

Step-by-step explanation:

Edge. 2020

Answer:

B

Step-by-step explanation:

Pedaler's peddlers is a bike store that is having there annual sale. Denise wants to buy a bike that originally cost $264. The bike model is on sale for 40% off. What price will Denise pay after the discount?


Plz hurry

Answers

105.6

Convert 40% to 0.4
Then multiply 0.4 by 264
0.4*264= 105.6

What are the answers for these,

What are the answers for these,
What are the answers for these,

Answers

3.5 m = 350 cm

9.072 km = 9072 m

0.07 kg = 70 g

70.4 l = 70400 ml

79 m = 0.079 km

6 g = 6000 kg

5,870 m = 5.78 km

61,900 g = 61.9 kg

What is the equation of the line of reflection? please help, due in 30 minutes!!!

What is the equation of the line of reflection? please help, due in 30 minutes!!!

Answers

Answer:

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.

Step-by-step explanation:

Answer:

The line of reflection in \(y=mx+b\) form is \(y=\frac{1}{3} x-2\)

Step-by-step explanation:

Help please!!!!! Thank you

Help please!!!!! Thank you

Answers

Answer:

C

Step-by-step explanation:

So we know that:

\(f(3)=-2\text{ and } f(4)=-4\)

This is the same as saying we have two coordinates: (3,-2) and (4,-4).

Let's find the equation of the linear function.

First, let's find the slope:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Substitute (3,-2) for x₁ and y₁ and let (4,-4) be x₂ and y₂:

\(m=\frac{-4--2}{4-3}\)

Simplify:

\(m=-2/1=-2\)

So our slope is -2.

Now, use the point-slope form:

\(y-y_1=m(x-x_1)\)

Let's use (3,-2) for x₁ and y₁ and use -2 for m:

\(y+2=-2(x-3)\)

Now, we can figure out the x-intercept.

Recall that the x-intercept is when the graph touches the x-axis.

In other words, the y-value would be 0. It will be (x,0).

So, to solve for the x-intercept, substitute 0 for y and solve for x:

\(0+2=-2(x-3)\)

Simplify and distribute the right:

\(2=-2x+6\)

Subtract 6:

\(-4=-2x\)

Divide both sides by -2:

\(x=2\)

So, our x-intercept is (2,0)

How do I look in a different basis. Find the matrix form of S z

when the base vectors are the eigen kets of S y

. (You know the spin operators and their eigenstates in the S z

basis.)

Answers

The matrix form of S z when the base vectors are the eigenkets of S y is:

⎡ 0.5 0.5 ⎤

⎢ ⎥

⎣-0.5 0.5 ⎦.

What is the significance of the eigenkets of S y in determining the matrix form of S z?

The matrix form of S z, when the base vectors are the eigenkets of S y, can be obtained by considering the spin operators and their eigenstates in the S z basis. Let's denote the eigenkets of S y as |+⟩ and |−⟩, corresponding to the eigenvalues +1/2 and -1/2, respectively. In the S z basis, these eigenkets can be represented as linear combinations of the base vectors |↑⟩ and |↓⟩, which are the eigenkets of S z.

The first step is to express |+⟩ and |−⟩ in terms of |↑⟩ and |↓⟩. We have:

|+⟩ = (1/√2)(|↑⟩ + |↓⟩)

|−⟩ = (1/√2)(|↑⟩ - |↓⟩)

Next, we need to find the matrix elements of S z with respect to these eigenkets. The matrix elements are given by the inner products between the eigenkets and the S z operator. We know that S z|↑⟩ = +1/2|↑⟩ and S z|↓⟩ = -1/2|↓⟩. Using these relations, we can compute the matrix elements:

⟨+|S z|+⟩ = (1/√2)(⟨↑| + ⟨↓|)(+1/2)(|↑⟩ + |↓⟩)

= (1/√2)(1/2)(⟨↑|↑⟩ + ⟨↑|↓⟩ + ⟨↓|↑⟩ + ⟨↓|↓⟩)

= (1/√2)(1/2)(1 + 0 + 0 + 1)

= 1

Similarly, we find ⟨+|S z|−⟩ = 0, ⟨−|S z|+⟩ = 0, and ⟨−|S z|−⟩ = -1. These values can be arranged in matrix form:

⎡ 1 0 ⎤

⎢ ⎥

⎣ 0 -1 ⎦

Therefore, the matrix form of S z, when the base vectors are the eigenkets of S y, is given by:

⎡ 1 0 ⎤

⎢ ⎥

⎣ 0 -1 ⎦

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PLs help i really need it will give brainliest and thanks and 5 stars

PLs help i really need it will give brainliest and thanks and 5 stars

Answers

Answer:

(5-2t)<-4

Step-by-step explanation:

The midnight temprature is 5 °C and the temprature is decreasing at the rate of 2°C per hour . If T is the hours past midnight then after t hours the temprature will be ( 5t-2t) . If the temprature is colder than -4°C right now , then your inequality can be written like 5t-2t<-4

Explique, de forma resumida, o significado dos números que expressam porcentagens nas orações a seguir. A) 10% dos alunos de uma escola não têm animal de estimação. B) 19% dos livros de uma biblioteca precisam ser catalogados. C) Segundo a Pesquisa Nacional por Amostra de Domicílio (Pnad), divulgada pelo Instituto Brasileiro de Geografia e estatística (IBGE), 51% da população brasileira é constituída por mulheres.

Answers

Answer:

Hola como esta xd lol what

Sally and anne went to the movies. they each purchased a drink. they also bought one popcorn and one veggie cup to share. each woman’ total is modeled with this expression: 9 1.34 1 2 (3.50 1.74) how would you simplify the expression? explain your steps.

Answers

Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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Terrance kicks a soccer ball at his game. Solve the given equation to find the times, t, when the ball is kicked and when it lands back on the ground, in seconds.

-16t^2 + 40t =0

how many seconds is terrance’s ball in the air?
A. 1 second
B. 16 seconds
C. 4 seconds
D. 2.5 seconds

Answers

Answer:

2.5 seconds for plato

Step-by-step explanation:

2.5 seconds is Terrance’s ball in the air

What is an quadratic equation?

We define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = \(ax^{2} +bx+c\), where a, b, and c are numbers and a cannot be 0.

Example of quadratic equation is y = \(x^2 + 3x + 1.\)

Given quadratic equation

\(-16t^{2} +40t =0\)

⇒ \(16t^{2} -40t=0\)

⇒ \(8(2t^{2}-5t)=0\)

⇒ \(2t^{2}-5t=0\)

⇒ \(t(2t-5)=0\)

⇒ \(t_{1} =0\) and \(t_{2}=\frac{5}{2} =2.5\)

T = \(t_{2}-t_{1} =2.5-0 = 2.5\)

2.5 seconds is Terrance’s ball in the air

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friend functions may directly modify or access the private data members. group of answer choices true false

Answers

Friend functions may directly modify or access the private data members. group of answer choices are true.

Q: Can friend functions modify or access private data members directly?

A friend function in C++ is a function that is not a member of a class but has access to its private and protected members. It is declared with the keyword "friend" inside the class. One of the advantages of using friend functions is that they can directly modify or access the private data members of a class, bypassing the normal access restrictions.

Friend functions are able to do this because they are granted special privileges by the class they are declared in. This means that they can access private data members and even modify them without using the usual public member functions of the class.

This feature can be useful in certain scenarios. For example, if we have a class that represents a complex number, we may want to provide a friend function to calculate the magnitude of the complex number directly using its private data members, instead of going through a getter function..

In conclusion, friend functions in C++ can indeed directly modify or access private data members. While this can be a powerful tool in certain cases, it should be used with caution to maintain the integrity of the class's encapsulation.

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What is the solution to 5(x-1)+3x=7(x+1)

Answers

Answer: x = 12

Step-by-step explanation:

5(x-1)+3x=7(x+1)

5x - 5 + 3x = 7x + 7

8x - 5 = 7x + 7

x - 5 = 7

x = 12

Find the area of the sector to the nearest whole number.
____mm2

Find the area of the triangle to the nearest whole number.
____mm2

Find the area of the segment to the nearest whole number using the area of the sector and triangle.
___mm2

Find the area of the sector to the nearest whole number. ____mm2Find the area of the triangle to the

Answers

The area of the of the triangle to the nearest whole number is 140mm²

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The formula for the area of a triangle is: A = (1/2)bh

where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.

The area of the triangle given in the figure will be 1/2 * b*h

A = 1/2*14*20

A = 140mm²

Hence the area of the triangle to the nearest whole number is 140mm².

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Please help!!
Question below!!

Please help!!Question below!!

Answers

The side angle side property is what is used here to make the prove that ΔWXZ ≅ ΔYZX

How to prove this

The statements are

1. WX II YZ

2. ∠ WXY ≅ ∠YZX

3. WX ≅ YZ

4. ZX ≅ XZ

5. ΔWXZ ≅ ΔYZX

The reasons are

1. Given

2. Alternate interior angles are congruent ≅

3. Given

4. Reflexive property

5. Side angle side SAS property

The SAS property states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

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Is it a, b, c, d, plz answer this

Is it a, b, c, d, plz answer this

Answers

Answer:

d 4x^2 + 24x - 8

Step-by-step explanation:

Perimeter of the rectangle = 2x² - 5 + 12x + 1 + 2x² - 5 + 12x + 1

                                            = (2x²+ 2x²) + (12x+ 12x) + (- 5 + 1 - 5 + 1)

                                            = 4x² + 24x - 8

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 7500 and estimated standard deviation σ = 1750. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. (a) What is the probability that, on a single test, x is less than 3500? (b) Suppose a doctor uses the average x(sample mean) for two tests taken about a week apart. What can we say about the probability distribution of x(sample mean)? What is the probability distribution of x(sample mean) < 3500? (c) Repeat part (b) for n = 3 tests taken a week apart. (d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? The probabilities increased as n increased. If a person had x ( sample mean)< 3500 based on three tests, what conclusion would draw as a doctor or nurse?

Answers

The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

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what is 1 and 2/5 as an improper fraction

Answers

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

There are 12 elephants and 11 lions at the zoo . What is the ratio of elephants to lions?

Answers

for ever 12 elephants there is 11 lions

so it would be 12:11

when procedures are "mandated" by third party payers, what modifier would you use?

Answers

When procedures are mandated by third party payers, the modifier -32 (mandated services) is used. This modifier is used to indicate that a service or procedure is mandated by a third party payer, such as Medicare or Medicaid.

It is used to ensure that the service or procedure is reimbursed appropriately and to avoid denials. The use of the -32 modifier is important to accurately reflect the requirements of the payer and to avoid any potential billing or coding errors. It is important to check with the specific payer to determine if the use of this modifier is required for a particular service or procedure.


When procedures are "mandated" by third-party payers, you would use the modifier -32. This modifier indicates that a service or procedure is being performed due to specific requirements from a third-party payer. It helps to provide the necessary information for reimbursement and ensures that the claim is processed correctly by the payer. Remember to attach the modifier -32 to the appropriate procedure code on the claim form when submitting it to the third-party payer. This will help avoid any potential delays or denials in payment due to insufficient documentation.

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Match each equation to an equivalent equation with a perfect square on one side.

Match each equation to an equivalent equation with a perfect square on one side.

Answers

The equations to an equivalent equation with a perfect square on one side are below: x² + 8x = 2 ⇒ (x + 4)² = 18, x² + 10x = -13 ⇒  (x + 5)² = 12, x² - 14x = 5  ⇒ (x - 7)² = 54, x² + 2x = 0  ⇒ (x + 1)² = 1, x² + 4x -5 = 0  ⇒ (x + 2)² = 9 and x² -20x = -9  ⇒ (x - 10)² = 91.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

According to the given question, the required solution would be as:

x² + 8x = 2

x² + 2 × 4 × x = 2

Add both sides 16 in the above equation,

x² + 2 × 4 × x + 16 = 2 + 16

x² + 2 × 4 × x + 4² = 2 + 16

As per the formula : (a + b)² = a² + 2 × a × b + b²

(x + 4)² = 18

x² + 8x = 2 ⇒ (x + 4)² = 18

Evaluation each equation similarly, then we get

x² + 10x = -13 ⇒  (x + 5)² = 12

x² - 14x = 5  ⇒ (x - 7)² = 54

x² + 2x = 0  ⇒ (x + 1)² = 1

x² + 4x -5 = 0  ⇒ (x + 2)² = 9

x² -20x = -9  ⇒ (x - 10)² = 91

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The third term in an arithmetic sequence is 20 and the 5th term is 26. If the first term is a1, what is the equation for the nth term?

Answers

Answer:

.

Step-by-step explanation:

a number increased by 5 then divided by 2

Answers

Answer:

(x + 5) /2

Step-by-step explanation:

"a number" (this will represent as "x")

"increased" another way to say add or "+"

then divided by 2

If you wrote it out like this "x+5/2"it would be wrong because of PEMDAS making you want to divide first instead of after.

Factor the expression completely 18x2 - 32​

Answers

Answer:

4

Step-by-step explanation:

18x2=36

36-32=4

-4(y+3)+35>4(6-y) please find the answer to this. It can also be ARN or No solution

Answers

-4y-12+35>24-4y
-12+35>24
23>24
False= no solution


Can I get Brainly

Step-by-step explanation:

just like with every equation. we move things around by applying the same operations to both sides.

-4(y + 3) + 35 > 4(6 - y)

-4y - 12 + 35 > 24 - 4y

23 > 24

that is always false (23 is never larger than 24).

so, there is no solution.

Morgan has 5 blue t-shirts , 3 green t-shirts and 2 red t-shirts . She randomly picks a shirt. What is the probability of choosing each color?

Answers

Answer:

Confusing question but I think it's 10:10

Step-by-step explanation:

Total outcome = 5:3:2

= 5+3+2

=10.

Probability = number of success

Total outcome

= 10/10

Therefore the probability of Morgan choosing each colour is 10:10.

Please answer, no links please.

Answers

Answer:

what you need help with? there is no picture or question

Step-by-step explanation:

Answer:

Solution given:

area of semi circle h=½πr²=½×π×5²=39.27in²

area of rectangle EFHI=l×b=6×3=18in²

area of rectangle CDFG=l×b=17×2=34in²

Total area: 39.27+18+34=91.27 square inches

Please answer, no links please.

Need Help ASAP

What is the sum of interior angles of a triangle?Degrees

Given ABC, find the value of X.

What is the measure of angle A??

Need Help ASAP What is the sum of interior angles of a triangle?DegreesGiven ABC, find the value of X.What

Answers

The sum of the interior angles of a triangle is 180 degrees

2x-9+3x+x+3=180
6x-6=180
6x=186
x=31

A=2(31)-9
A=62-9
A=53

1. Formulate and write mathematically the four Maxwell's equations in integral form. 2. Explain the relation between electric and magnetic fields. Why electromagnetic waves do propagate in space? 3. How has Maxwell introduced the concept of a ""displacement current""?

Answers

1) The four Maxwell's Equations in the integral form are as follows:

a) Gauss's law for electric fields: ∮E⋅dA = Q/ε₀, where E is the electric field, dA is an infinitesimal area element, Q is the total charge enclosed by the surface, and ε₀ is the permittivity of free space.

b) Gauss's law for magnetic fields: ∮B⋅dA = 0, where B is the magnetic field and dA is an infinitesimal area element.

c) Faraday's law of electromagnetic induction: ∮E⋅dl = -dΦ/dt, where dl is an infinitesimal length element, Φ is the magnetic flux through a surface bounded by the closed loop, and t is time.

d) Ampere's law with Maxwell's correction: ∮B⋅dl = μ₀(I + ε₀(dΦ_E/dt)), where B is the magnetic field, dl is an infinitesimal length element, I is the total current passing through the surface bounded by the closed loop, μ₀ is the permeability of free space, ε₀ is the permittivity of free space, and dΦ_E/dt is the time rate of change of electric flux through the surface bounded by the closed loop.

2) The relationship between Electric and Magnetic Fields:

Electric fields are created by charged particles and exert a force on other charged particles within their vicinity. Magnetic fields, on the other hand, are created by moving charged particles and exert a force on other moving charged particles.

The two fields are related in that a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. This relationship is described by Maxwell's equations, which predict the existence of electromagnetic waves.

Propagation of Electromagnetic Waves:

Electromagnetic waves propagate in space because they are self-sustaining disturbances that do not require a medium to travel through.

They consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. These waves can be generated by accelerating charges or by changing magnetic fields, and they travel at the speed of light.

3) The Maxwell introduced the concept of a Displacement Current:

Maxwell introduced the concept of a displacement current to explain how changing electric fields can produce magnetic fields. He realized that a time-varying electric field could create a changing electric flux, which in turn could produce a magnetic field.

This changing electric flux is equivalent to a current, even though no charges are actually moving. Maxwell called this current the displacement current, and he added it to Ampere's law to obtain a more complete description of electromagnetic phenomena.

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Raj reads 7/12 of his book before dinner and another 2/12 of his book after dinner.


How much of his book did Raj read in total?


Enter your answer as a fraction in simplest form by filling in the boxes.

Answers

Raj read a total of 9/12 of his book.

To find out how much of the book Raj read in total, we need to add the fractions representing the portions he read before dinner and after dinner. Raj read 7/12 of his book before dinner, and then an additional 2/12 of his book after dinner. Adding these fractions together gives us:

7/12 + 2/12 = 9/12.

Since the fractions have the same denominator (12), we can simply add the numerators to get the numerator of the total fraction. The denominator remains the same. So, Raj read a total of 9/12 of his book.

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3 in this case:

9/12 ÷ 3/3 = 3/4.

Therefore, Raj read 3/4 of his book in total.

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Answer:

Step-by-step explanation:

hi me need help me 10

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b) find sin (θ+y)

Answers

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

\(\sin (\theta)=\frac{3}{5}\)

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

\(x^2+3^2=5^2\)

Solving for x, we have

\(\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}\)

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

\(\tan (y)=\frac{12}{5}\)

Describes the following triangle

Using the Pythagorean Theorem again, we have

\(5^2+12^2=h^2\)

Solving for h, we have

\(\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}\)

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

\(\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}\)

To calculate the sine and cosine of the sum

\(\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}\)

We can use the following identities

\(\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}\)

Using those identities in our problem, we're going to have

\(\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}\)

let sin() =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side
let sin() =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side
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