Help I dont understand how to do this

The exact value of side lengths of triangle are d= \(\frac{8}{\sqrt{3} }\) and h=\(\frac{5\sqrt{2} }{2}\)

A triangle is a closed, two-dimensional shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry and is often used in various mathematical and scientific contexts.

The three sides of a triangle are usually named using lowercase letters a, b, and c, and the three angles are named using uppercase letters A, B, and C, with the opposite angles and sides having the same letter. The sum of the angles in a triangle is always 180 degrees, and this property is known as the Angle Sum Theorem.

Triangles can be classified based on their side lengths and angles. Based on the side lengths, triangles can be classified as:

Scalene triangle: A triangle in which all three sides have different lengths.

Isosceles triangle: A triangle in which two sides have the same length, and the third side has a different length.

Equilateral triangle: A triangle in which all three sides have the same length.

Let's start with the first triangle. We can use the trigonometric ratios for a 30-60-90 triangle:

sin(60) = opposite / hypotenuse = d / (2d) = \(\frac{1}{2}\)

cos(60) = adjacent / hypotenuse = 4 / (2d) = \(\frac{1}{2\sqrt{3} }\)

Solving for d:

d = 2 * sin(60) = 2 *\(\frac{1}{2}\)  = 1

2d = 4 / cos(60) = \(\frac{4}{\frac{1}{2\sqrt{3} }}\) = \(\frac{8}{\sqrt{3} }\)

So d = 1 and 2d = \(\frac{8}{\sqrt{3} }\) in the first triangle.

For the second triangle, we can use the trigonometric ratios for a 45-45-90 triangle:

sin(45) = opposite / hypotenuse = \(\frac{h}{5}\)

cos(45) = adjacent / hypotenuse = \(\frac{h}{5}\)

Since sin(45) = cos(45) = \(\frac{1}{\sqrt{2} }\), we can solve for h:

h = 5 * sin(45) = 5 * \(\frac{1}{\sqrt{2} }\) = \(\frac{5\sqrt{2} }{2}\)

So h =  \(\frac{5\sqrt{2} }{2}\) in the second triangle.

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To make NH3 from N2, you need to balance the chemical equation first. The balanced equation is:

4N2 + 6H2 -> 2NH3

To find the number of moles of NH3 that can be produced from 4. 2021 g of N2, you can divide the mass of N2 by its molar mass. The molar mass of N2 is 28 g/mol, so the number of moles of N2 is:

4.2021 g N2 / 28 g/mol = 0.1507 mol N2

Since the ratio of N2 to NH3 in the balanced equation is 2:1, the number of moles of NH3 produced is half the number of moles of N2, or 0.1507 mol / 2 = 0.0753 mol NH3.

To find the number of moles of Cl2 needed to react with 34.485 g of Na, you can divide the mass of Na by its molar mass. The molar mass of Na is 22.99 g/mol, so the number of moles of Na is:

34.485 g Na / 22.99 g/mol = 1.50 mol Na

Since the ratio of Na to Cl2 in the balanced equation is 1:1, the number of moles of Cl2 needed is the same as the number of moles of Na, or 1.50 mol Cl2.

To find the mass of NaNO2 needed to make 24.14714 g of Na2SO4, you can first balance the chemical equation:

2H2SO4 + 4NaNO2 -> 4HNO2 + 2Na2SO4

Then, you can convert the mass of the desired product, Na2SO4, to moles by dividing it by the compound's molar mass (142.04 g/mol). This gives you the number of moles of Na2SO4 you need to produce:

24.14714 g Na2SO4 / 142.04 g/mol = 0.169 mol Na2SO4

Since the ratio of NaNO2 to Na2SO4 in the balanced equation is 2:1, the number of moles of NaNO2 needed is twice the number of moles of Na2SO4, or 2 * 0.169 mol = 0.338 mol NaNO2. To convert this to mass, multiply the number of moles by the compound's molar mass:

0.338 mol NaNO2 * 85.01 g/mol = 28.82 g NaNO2

To find the mass of NaOH that can be made with 8.0465 g of Na, you can first balance the chemical equation:

2Na + 2H2O -> 2NaOH + H2

Then, you can convert the mass of the starting material, Na, to moles by dividing it by the compound's molar mass (22.99 g/mol). This gives you the number of moles of Na available:

8.0465 g Na / 22.99 g/mol = 0.35 mol Na

Since the ratio of Na to NaOH in the balanced equation is 1:1, the number of moles of NaOH produced is the same as the number of moles of Na, or 0.35 mol NaOH. To convert this to mass, multiply the number of moles by the compound's molar mass:

0.35 mol NaOH * 40.00 g/mol = 14.00 g NaOH

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To find f(x)-g(x), we need to subtract the two given functions.

f(x) = x^(2)-6x-40

g(x) = x+4

f(x)-g(x) = (x^(2)-6x-40) - (x+4)

Next, we need to distribute the negative sign to the terms inside the parentheses:

f(x)-g(x) = x^(2)-6x-40 - x - 4

Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44

Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.

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Answer:

linear

Step-by-step explanation:

We can write this  in the form

y = mx+b

where m is the .75 per mile and b is the 39 dollars

y = .75x + 39

Answer:

The answer is "\(\bold{\frac{2 \pi}{3}}\)"

Step-by-step explanation:

Please find the complete question in the attached file.

Using formula:

\(\to \bold{\theta = \frac{S}{r}}\)

Where,

\(\theta =central \ angle \\\\{S} = arc \ length\\\\{r} = radius \ length\)

\(\to \theta = \frac{PQ }{OQ}\)

       \(=\frac{6 \pi}{9} \\\\ = \frac{2 \pi}{3}\)

The radian measure of central angle POQ is 3π/4 radians. Option b) is the correct option.

Line segments PO and QO are radii.

We need to find the radian measure of central angle POQ.

\(2\pi^c = 360^\circ = \text{Full circumference}\)

The superscript 'c' shows angle measured is in radians.

If the radius of the circle is of r units, then:

\(1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}\)

We know that

π radians = 180°

Therefore,

180° = π radians

135° = x

180° × x = 135° × π radians

x = 135° × π radians/180

x = 3π/4 radians

Hence, the radian measure of central angle POQ is 3π/4 radians. Option b) is the correct option.

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Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

The function f(x) is:

We have to find the functions that perform the following transformations:

a) Stretches f(x) by a factor of 4 away from the x-axis.

This is a vertical stretching, meaning that the values of y=f(x) are scaled by the factor.

This can be represented as:

Answer: g(x) = 8x - 24

b) Shifts f(x) 4 units right

This is a translation in the x-axis, in the direction of the positive values.

Then:

Answer: g(x) = 2x - 14

c) Compresses f(x) by a factor of 1/4 towards the y-acis.

In this case is an horizontal stretching, and the input x is divided by the factor of compression.

Then:

Answer: g(x) = 8x - 6

d) Shifts f(x) 4 units down.

This is a vertical translation and can be written as:

Answer: g(x) = 2x - 10

Answer:

5 and 5

Step-by-step explanation:

5 divided by 5 is 1

5 plus 5 is 10

Answer:

2. ☑ A \(\displaystyle f(x) = tan\:\frac{1}{2}x\)

☐ B \(\displaystyle f(x) = tan\:2x\)

☐ C x = \(\displaystyle 2tan\:x\)

1. ☐ A \(\displaystyle \frac{\pi}{2}\)

☐ B \(\displaystyle \pi\)

☑ C \(\displaystyle 2\pi\)

Explanation:

\(\displaystyle \boxed{f(x) = -cot\:(\frac{1}{2}x - \frac{\pi}{2})} \\ \\ y = Acot(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A\)

OR

\(\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A\)

Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS the tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = cot\:\frac{1}{2}x,\) in which you need to replase "tangent" with "cotangent", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cotangent graph [photograph on the right] is shifted \(\displaystyle \pi\:units\) to the left, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph FORWARD \(\displaystyle \pi\:units,\) which means the C-term will be positive, and perfourming your calculations, you will arrive at \(\displaystyle \boxed{\pi} = \frac{\frac{\pi}{2}}{\frac{1}{2}},\) but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is \(\displaystyle y = -cot\:(\frac{1}{2}x - \frac{\pi}{2}).\) Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are \(\displaystyle -\pi = x\:and\:\pi = x.\) From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you \(\displaystyle \boxed{2\pi} = \pi + \pi.\) So, the period of this function is \(\displaystyle 2\pi.\) Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at \(\displaystyle y = 0.\)

Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.

I am delighted to assist you at any time.

The statement is true. If the two nonadjacent angles are formed by two intersecting lines, then the  angles are congruent

When two non-adjacent angles are formed with two intersecting lines then they are called​ opposite angles.

There are some properties of nonadjacent angles:

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Answer:

x = 2

Step-by-step explanation:

6 : 4 = 3 : x

x = 4 * 3 / 6

x = 4/2

x = 2

The value of x in the given figure is 2

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

Given that, Triangle ABC is dilated into A'B'C'

We know that dilated triangles are similar

Hence, their corresponding sides are in equal ratio,

BC : B'C' = AC : A'C'

6 : 4 = 3 : x

x = 4 × 3 / 6

x = 4/2

x = 2

Hence, The value of x in the given figure is 2

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The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

Here, 6k + 10.5 = 3k + 12

         6k - 3k = 12 - 10.5

         3k = 1.5

          k = 1.5/3

          k = 1/2

Thus, The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

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The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

We have,

Two functions:

f(x) = b^x

g(x) = log_b(x)

Now,

From the table,

f(0.699) = b^0.699 = 5

Taking the logarithm of both sides with base b.

log_b(5) = 0.699

b = 5^(1/0.699)

b = 8.343

Now, we can find the value of f(1.477).

f(1.477) = b^1.477 = 8.343^1.477 = 32.857

Similarly, we can find the value of g(20).

g(20) = log_b(20) = log_8.343(20) = 1.729

Thus,

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

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Answer:

Step-by-step explanation:

\(a_n=a_1\cdot r^{n-1}\\\\a_{12}=30\cdot 4^{12-1}\\\\a_{12}=30\cdot 4^{11}=15\cdot2\cdot2^{22}=15\cdot2^{23}\)

The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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the probability that in a randomly selected office hour, the number of student arrivals is 7 is approximately 0.0857 or 8.57%.

To find the probability that the number of student arrivals is 7, we need to determine the probability of a specific count of arrivals in a Poisson distribution.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

In this case, the average rate of student arrivals in an office hour is given as 1.9 students.

The probability mass function of the Poisson distribution is given by the formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

P(x; λ) represents the probability of x events occurring,

λ is the average rate of occurrence,

e is the base of the natural logarithm (approximately 2.71828), and

x! represents the factorial of x.

Plugging in the values, we have:

P(7; 1.9) = (e^(-1.9) * 1.9^7) / 7!

Using a calculator or software, we can calculate this probability:

P(7; 1.9) ≈ 0.0857

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The domain of this function is that: C. the domain is all real numbers 0 through 30.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By critically observing this graph of a function shown, we can reasonably infer and logically deduce the following:

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The seismograph reading of the earthquake is approximately 1.99526.To determine the seismograph reading of the earthquake with a magnitude of 3.3 on the Richter scale, we can use the formula M(I) = log(I/0.001), where M(I) represents the magnitude and I represents the intensity of the earthquake.

In this case, we are given the magnitude of 3.3. Let's substitute this value into the formula and solve for I:

3.3 = log(I/0.001)

To isolate I, we need to convert the equation into exponential form:

10^(3.3) = I/0.001

Simplifying the equation, we have:

I = 10^(3.3) * 0.001

Using a calculator, we find that 10^(3.3) is approximately 1995.26.

So, the seismograph reading of the earthquake is:

I = 1995.26 * 0.001

≈ 1.99526.

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Answer:

26.563, 1.977

Step-by-step explanation:

I will be honest I'm not 100% sure but i believe that the total distance all together is 26.563. I simply added all the distances.

Jada ran 1.977 miles further than Noah.

I'm so sorry if im wrong hope this helps though <3

The length of the curve is 3.12π units.  where r = 4, z = -12, and 1.14π < ∅ < 1.92π, can be calculated using line integrals.

To calculate the length of the given curve using line integrals, we need to parametrize the curve in terms of a parameter t. In cylindrical coordinates, the curve can be parametrized as follows:

r(t) = 4

z(t) = -12

θ(t) = t, where 1.14π < t < 1.92π

Now, we can calculate the length using the line integral formula for a curve in cylindrical coordinates:

L = ∫[a, b] √(\((r'(t))^2\) + \((z'(t))^2\) + (r(t)\((\theta'(t))^2\)) dt

In this case, a = 1.14π and b = 1.92π.

Let's find the derivatives:

r'(t) = 0 (since r is constant)

z'(t) = 0 (since z is constant)

θ'(t) = 1

Substituting these values into the formula, we get:

L = \(\int\limits^{(1.14\pi)} _{(1.92\pi)}\)√(\(0^2\) + \(0^2\) +\((4*1)^2\)) dt

= \(\int\limits^{(1.14\pi)} _{(1.92\pi)}\)√(16) dt

= \(\int\limits^{(1.14\pi)} _{(1.92\pi)}\)4 dt

= 4 \(\int\limits^{(1.14\pi)} _{(1.92\pi)} {1} \,\) dt

= 4[t] from 1.14π to 1.92π

= 4(1.92π - 1.14π)

= 4(0.78π)

= 3.12π

Therefore, the length of the curve is 3.12π units.

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Based on the weight and the model that is given, it should be noted that  W(t) in radians will be W(t) = 0.9cos(2πt/366) + 8.2.

From the information, W(t) = a cos(bt) + d. Firstly, calculate the phase shift, b. At t= 0, the dog is at maximum weight, so the cosine function is also at a maximum. The cosine function is not shifted, so b = 1.

Then calculate d. The dog's average weight is 8.2 kg, so the mid-line d = 8.2. W(t) = a cos t + 8.2. Then calculate a, the dog's maximum weight is 9.1 kg. The deviation from the average is 9.1 kg - 8.2 kg = 0.9 kg. W(t) = 0.9cost  + 8.2

Lastly, calculate t. The period p = 2π/b = 2π/1 = 2π. The conversion factor is 1 da =2π/365 rad. Therefore, the function with t in radians is W(t) = 0.9cos(2πt/365) + 8.2.

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Answer:

measure angle SRW = 95

Step-by-step explanation:

angleSRW & angle VRT are vertical angles and they are congruent or same.

If angle VRT is 95 then SRW is 95 degrees too.

Answer:

Function                         Not a function      

not a Function                   function

pg 2

B- explanation is that 2 inputs dont have the same output 8-1, 8-1,4-1,3-1

pg 3

1. yes; -5 is not in the set

2. yes; 2 is not in the set

3. no; .75 is 3/4

4. no; -4 is already in the set

it would be  2, 2 3 0

Answer:

They are zeroes when y=0

Step-by-step explanation:

For a function \(f(x)\), if \(f(x)=0\), the values of x that make the function true are known as roots, or x-intercepts, or zeroes.

Answer:

it might be 8%

Step-by-step explanation:

Answer:

8!!

Step-by-step explanation:

5+3

Answer:

2.68

Step-by-step explanation:

Answer: The bags cost about $2.68 each

Step-by-step explanation: All I did was simple Division: ($10.72 ÷ 4 = $2.68) If you need to double check to see if this is accurate, you can do ($2.68 x 4= 10.72)  Therefore, this equation has an accurate answer.~

Hope this helps, have a great day/night!

~IFoundJiminsLostJams~

option a is the answer you are which class same question is there for me

The mean of both the binomial distribution and the Poisson distribution used to approximate it is μ = np, where n is the number of trials and p is the probability of success in each trial.

The mean of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success in each trial. The mean represents the average number of successes.

When a binomial distribution is approximated by a Poisson distribution, the mean of the Poisson distribution is also μ, which is equal to the mean of the binomial distribution.

In conclusion, both the binomial and Poisson distributions have a mean of μ = np. The mean represents the average number of successes, and the Poisson distribution is used as an approximation when the binomial distribution has a large number of trials and a small probability of success.

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