What is the distance from the given point to the horizontal axis. (-7, -8)? The answer is in unit

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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Answer:

20 m

Step-by-step explanation:

First find the side length

A = s^2 for a square garden

200 = s^2

Take the square root of each side

sqrt(200) = sqrt(s^2)

sqrt(2) sqrt(100) = s

10 sqrt(2) = s

Now we can use the Pythagorean theorem to find the diagonal

a^2 + b^2 = c^2  where  a and b are the side lengths a c is the hypotenuse

s^2 + s^2 = c^2

200 + 200 =c^2

400 = c^2

Take the square root of each side

sqrt(400) = sqrt(c^2)

20 = c

First find the lenght of a side:

\(a=\sqrt{200}\implies a\approx 14.14\)

Then multiply the approximated side by \(\sqrt{2}\) and obtain the lenght of diagonal:

\(d\approx14.14\sqrt{2}=\boxed{20\mathrm{m}}\)

Hope this helps.

The value of the variables in the right triangle are as follows;

A right triangle is a triangle that has one of its angles as 90 degrees.

The side of a right triangle can be found by using trigonometric ratios.

Therefore, let's find the variable length of the right triangle as follows;

sin 30 = opposite / hypotenuse

sin 30 = v / 3√2

1 / 2 = v / 3√2

cross multiply

3√2 = 2v

divide both sides by 2

v = 3√2 / 2

Let's find the variable w.

cos 30 = adjacent  / hypotenuse

cos 30 = w  / 3√2

√3 / 2 = w  / 3√2

cross multiply

√3 × 3√2 = 2w

3√6 = 2w

divide both sides by 2

w = 3√6 / 2

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Answer:

X=10

Step-by-step explanation:

4.5x +55=100

Answer:

X=10

Step-by-step explanation:

4.5x +55=100

Answer:true

Step-by-step explanation:

Answer:

7 dollars

Explanation: subtract 28 from 35 to get your answer

Answer:

The measure of an arc is the size of the corresponding central angle, so angle 1 for AB,

Answer: B 30

Answer:

C and D

Step-by-step explanation:

\(\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}\)

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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A data set where the median is triple the mean is one that is heavily skewed to the right.

Median is a type of average, which is used to calculate the central value of a set of data. It is the middle value in an ordered list of numbers, which is determined by arranging the numbers in ascending or descending order.

This means that the majority of values in the data set are much larger than the mean. This could be due to a few outliers that are very large compared to the rest of the values in the data set. The median value is not affected by any outliers, so it remains at a much higher value than the mean. This type of data set is known as a right skewed data set because the majority of the values are concentrated on the right side of the graph. To get a better understanding of the data set it is important to look at the distribution of the data in order to identify any outliers.

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A data set where the median is triple the mean is one that is heavily skewed to the right.

Median is a type of average, which is used to calculate the central value of a set of data. It is the middle value in an ordered list of numbers, which is determined by arranging the numbers in ascending or descending order.

This means that the majority of values in the data set are much larger than the mean.

This could be due to a few outliers that are very large compared to the rest of the values in the data set.

The median value is not affected by any outliers, so it remains at a much higher value than the mean.

This type of data set is known as a right skewed data set because the majority of the values are concentrated on the right side of the graph.

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Question:

How is a graph for a data set where the median is triple the mean represented?

Answer:

C

Step-by-step explanation:

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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Answer:

Step-by-step explanation:

I think its b

Answer:

Step-by-step explanation:

Using point-slope intercept form:

The equation of line is given by:

             .....[1]

where,

m is the slope of the line and  is the point on the line.

As per the statement:

A line with slope 4/5 that contains the points (-2,1)

⇒m =  and

Substitute these values in [1] we have;

Therefore,   is the point slope form of a line with slope 4/5 that contains the points (-2,1).

Answer:

See Explanation

Step-by-step explanation:

Required

Prove that Dexter is wrong

To prove that Dexter is wrong, we use the following numbers.

\(Number = 4\)

The factors are:

\(Factor = 1,2\ and\ 4\)

3 factors

Using a greater number:

\(Number = 5\)

The factors are:

\(Factor = 1\ and\ 5\)

2 factors

From the above analysis:

4 has 3 factors and 5 has 2 factors; which shows that 5 has fewer factors

This shows that Dexter is wrong

Answer:

Hans Lipperhey made the telescope

Answer:

Hans lipperhey and Lyman Spitzer

Answer:

D stays for 1 and as B is -6

the length of BD should be 7

good luck <3!

Answer: Number 2

Step-by-step explanation: yes

Answer:

$21.15

Step-by-step explanation:

(235)(.045)(2)

The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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Answer:

19107

Step-by-step explanation:

First, we need to find the common difference (d), which we can find by subtracting two consecutive terms.  Thus, we can do d = 1 - (-3) = 4.

Now, we need to know how many terms are in the arithmetic series.  We can find the number using nth term formula, which is

\(a_{n}=a_{1}+(n-1)*d\), where a1 is the first term, n is the term position (e.g., 1st, 2nd).

Although we don't know the term position of 389, we can still plug it into the formula and solving for n will reveal it's term number and the total number of sums in the sequence:

\(389=-3+(n-1)*4\\392=(n-1)*4\\392=4n-4\\396=4n\\99=n\)

Now, we can find the sum using the sum formula, which is

\(S_{n}=n/2*(a_{1}+a_{n})\)

Sn can become S99 since there are 99 terms and we can let an = a99, which we know is 389.

Now, we must solve for S99:

\(S_{99}=\frac{99}{2}*(-3+389)\\ S_{99}=\frac{99}{2}*(386)\\ S_{99}=19107\)

The boxplot shows that the majority of the people who attended the lecture were age 53 or younger, which means at least 75 percentage of the people were in that range.

The table and boxplot provide information about the ages of the people who attended a lecture last week. The boxplot shows that the majority of the people who attended the lecture were age 53 or younger. This is supported by the table, which shows that the median age is 53 and the interquartile range is between 36 and 53. This indicates that at least 75% of the people who attended the lecture were age 53 years or younger. The range of the distribution is 20 years, with the minimum age being 18 and the maximum age being 38. This suggests that there were at least two people in each age range, from 18 to 38. This also indicates that there were at least 43 people who attended the lecture. The boxplot also shows that at least 25% of the people who attended the lecture were 33 years old. This is supported by the table, which shows the lower quartile is 33.

Interquartile range = Maximum - Minimum

Interquartile range = 53 - 36 = 17

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Answer:

\(d = 10\)

Step-by-step explanation:

Distance Formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in your 2 coordinates into the formula to find distance d:

\(d=\sqrt{(-3-5)^2+(-4-2)^2}\)

\(d=\sqrt{(-8)^2+(-6)^2}\)

\(d=\sqrt{64+36}\)

\(d=\sqrt{100}\)

\(d = 10\)

The number of bags of rice that would be needed to make 80 recipes is 48.664 bags.

1 recipe = 3.5 Cups of rice

If

1 cup of rice = 158 grams

1 bag of rice = 2 pounds

2.2 lbs. = 1 kg,

1kg = 1000 g

80 recipes = 3.5 cups 80

= 280 cups

1 cup of rice = 158 grams

280 cups = 158 × 280

= 44,240 grams

1kg = 1000 g

44,240 grams = 44.24 kg

2.2 lbs. = 1 kg; x lbs = 44.24

2.2/1 = x/44.24

x = 2.2 × 44.24

x = 97.328 pounds

1 bag of rice = 2 pounds ; x bags = 97.328 pounds

1/2 = x/97.328

97.328 = 2x

x = 48.664 bags

Hence, 48.664 bags of rice is needed for 80 recipes.

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Answer:

133

Step-by-step explanation:

Answer:

y = -2x+7

Step-by-step explanation:

2x+y=7

Subtract 2x from each side

2x+y -2x=-2x+7

y = -2x+7

Step-by-step explanation:

Total insects = 270

Days = 7

If 80 insects to 700 insects

Days = 700 ÷ 80 = 8.75

It will take 8.75 days