what is the value of x in the following figure?

A: 128 degrees

B: 142 degrees

D: 52 degrees

C: 38 degrees

Show work

Answer:

I believe the answer is b??

The equation used in writing a partial fraction decomposition is given as:

Negative 15 x + 10 / (5 x - 2) = a / (5 x - 2) + b / (5 x - 2).

To determine the values of a and b, we can use a system of equations. This system of equations consists of two equations, one for a and one for b. The equation for a is: Negative 15 x + 10 = a * (5 x - 2). The equation for b is: 0 = b * (5 x - 2). We can solve these equations simultaneously to get the values of a and b.

For example, if x = 1, then the equation for a becomes: Negative 15 + 10 = a * (5 - 2), which simplifies to -5 = a * 9. Therefore, a = -5/9. The equation for b becomes: 0 = b * (5 - 2), which simplifies to 0 = b * 3. Therefore, b = 0.

In summary, the system of equations used to determine the values of a and b is:

Negative 15 x + 10 = a * (5 x - 2) and 0 = b * (5 x - 2). By solving these equations simultaneously, we can get the values of a and b.

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Answer:

B!!!

Right on Edge

Step-by-step explanation:

The demand curve graph demonstrates that when prices rise, fewer goods are demanded overall.

The link between price and quantity desired is graphically depicted by the demand curve. It demonstrates how a change in pricing affects how much of an item or service is wanted. The quantity demanded reduces when a good or service's price rises, and vice versa. The quantity demanded falls as the price rises because the demand curve is typically downward sloping. This is due to the fact that when prices are reduced, consumers are more likely to buy products and services. As the price rises, the amount demanded declines, as shown by the hypothetical demand curve that fits this pattern in the diagram to the right. This is a typical pattern observed in the actual world, which is used to guide business and economic decision-making regarding price and output.

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B(0) = 0 Inches of depth are present 0 minutes after filling started, or at time = 0; depth = 0.

B(1) denotes the function one minute into the filling process.

B(9) = 11 shows that 11 inches of water are present in the container 9 minutes after the filling started.

7 minutes after the filling process began, the feature displays the water depth in inches.

A.) B(0)=0

B(0) = 0 indicates that the depth in inches at time = 0 and depth = 0 is 0 minutes after filling started.

B.) B(1) (1) B(1) denotes the function one minute into the filling process.

C.B(9)=11

B(9) = 11 shows that 11 inches of water are present in the container 9 minutes after the filling started.

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The volume of the trapezoidal prism can be calculated using the formula V = (1/2)(h)(b1 + b2)h, where h is the height, b1 is the length of the top base, and b2 is the length of the bottom base.

In this case, the height is 7 cm, the length of the top base is 10 cm, and the length of the bottom base is 12 cm. Therefore, the volume of the trapezoidal prism is V = (1/2)(7)(10 + 12)7 = 630 cm3.

In addition to calculating the volume of a trapezoidal prism, you can also calculate the surface area of a trapezoidal prism using the formula A = 2h(b1 + b2) + 2(l1 + l2), where h is the height, b1 and b2 are the lengths of the top and bottom bases, and l1 and l2 are the lengths of the lateral faces. The surface area of a trapezoidal prism is the total area of all of the faces of the prism.

Additionally, the lateral surface area of a trapezoidal prism can be calculated by using the formula A = 2h(b1 + b2), where h is the height, b1 and b2 are the lengths of the top and bottom bases. The lateral surface area of a trapezoidal prism is the total area of all of the lateral faces of the prism.

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The equation for Chloe's growth rate would be y = ax + b, where a is the rate of growth in cm/month and b is the height at age 0.

To predict Chloe's height at two years old, we can plug in x = 24 (representing two years, or 24 months) into the equation.

We would then get y = 24a + b,

Which is Chloe's predicted height at age two. This equation gives us a simple way to predict Chloe's height at any age, as long as we know her rate of growth and her height at age 0.

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Running Bear ended up 29.204 miles from the village.

Running Bear left the village and traveled 30 miles in a direction of 30°. Then he went 50 miles in a direction of 220°. To find out how far he ended up from the village, we need to add up the distances he traveled in both directions.

Think of it like putting two arrows end to end on a piece of paper. The first arrow represents the 30 miles he traveled at 30°, and the second arrow represents the 50 miles he traveled at 220°. The total distance from the village to the final point is equal to the length of the combined arrow.

We can represent the two displacements as vectors in a rectangular coordinate system, with the x-axis as the East-West direction and the y-axis as the North-South direction.

The first displacement, 30 miles at 30°, can be written as a vector in the x and y directions using trigonometry:

x1 = 30 cos 30° = 15

y1 = 30 sin 30° = 15

The second displacement, 50 miles at 220°, can be written as a vector in the x and y directions using trigonometry:

x2 = 50 cos 220° = -25

y2 = 50 sin 220° = -43.301

The total displacement from the village to the final point is found by adding the components of the two vectors:

x = x1 + x2 = 15 - 25 = -10

y = y1 + y2 = 15 - 43.301 = -28.301

Finally, we can use the Pythagorean theorem to find the magnitude (distance) of the total displacement:

d = √(-10)^2 + (-28.301)^2 = √851.121 = 29.204 miles

So, Running Bear ended up 29.204 miles from the village.

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Answer:200%

Step-by-step explanation: A different way of saying that a number has doubled is by saying it has increased by 200%.

Answer:

x = 70 , x = 24

Step-by-step explanation:

the measure of a secant- tangent and a tangent- tangent angle is half the difference of the measures of the intercepted arcs.

9

24 = [tex]\frac{1}{2}[/tex] (118 - x) ← multiply both sides by 2 to clear the fraction

48 = 118 - x ( subtract 118 from both sides )

- 70 = - x ( multiply both sides by - 1 ) , then

x = 70

10

61 = [tex]\frac{1}{2}[/tex] (10x + 1 - (5x - 1) ) ← multiply both sides by 2 to clear the fraction

122 = 10x + 1 - 5x + 1

122 = 5x + 2 ( subtract 2 from both sides )

120 = 5x ( divide both sides by 5 )

24 = x

Answer:

475

Step-by-step explanation:

475

(50%)%×950= 475.

have a nice day

The three statements that represent a unit rate are:

a. Carrots cost $2 per pound

d. A recipe calls for 2 cups of sugar for every gallon of water.

e. A teacher divides her class so there are 11 students per group.

The formula for calculating the overall score is:

overall value = number of units x value per unit.

For example, Budi buys a dozen pencils. The price of one pencil is IDR 2000. What is the total value or purchase price to be paid by Budi?

One dozen equals 12 pieces.

So, the purchase price = 12 x 2000 = 24,000

So, the total purchase price is IDR 24,000.

"The overall value is obtained from the product of the number of units with the value per unit."

The formula for calculating the unit rate is:

value per unit = total value : number of units.

For example, Aan bought ten candies for Rp. 2,500. How much does one candy cost?

To calculate it, we must use the value per unit formula.

The price of one candy = 2,500 : 10 = 250.

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The statement is referring to a market economy, where supply and demand forces affect the production and consumption decisions and there is little to no government control in such a system.

In a market economy, individuals and businesses make the decisions regarding production and consumption, and prices are determined by the interaction of supply and demand. The market is seen as the most efficient allocation mechanism, as prices communicate information about relative scarcities and help to direct resources to their most valuable uses. However, market economies may result in income inequality and market failures, where the market fails to allocate resources efficiently. Government intervention in a market economy is limited to correcting market failures and ensuring a level playing field.

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Answer:

17.6lbs

Step-by-step explanation:

If 1kg equals 2.2 lbs, therefore multiply the number of pounds per kg by 8:

2.2lbs * 8 = [17.6lbs]

Answer: 63.125

Step-by-step explanation: I got it correct ;)

The simplest form of the sum of the mixed fraction  [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex] is [tex]12\frac{11}{15}[/tex]

A fraction represented with its quotient and remainder is a mixed fraction.

Given is a sum of two mixed fractions, [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex]

Converting into the simplest forms,

[tex]3\frac{2}{6} + 9\frac{4}{10}\\\\= \frac{20}{6} + \frac{94}{10} \\\\= \frac{10}{3} + \frac{47}{5} \\\\= \frac{50+141}{15} \\\\= \frac{191}{15} \\\\= 12\frac{11}{15}[/tex]

Hence, the simplest form of the sum of the mixed fraction  [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex] is [tex]12\frac{11}{15}[/tex]

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Answer:60

Step-by-step explanation:

10+5=15

15x4=60

The probability that exactly two couples are dancing together in a party of 5 male-female couples is 1/126, which is a very low probability.

The problem of finding the probability that exactly two couples are dancing together can be solved using the combination formula. The number of ways to choose two couples from the five available couples is given by the binomial coefficient "C(5,2) = 10". The number of ways to arrange the chosen two couples is given by 2! (two factorial), since the order of the couples doesn't matter. The total number of ways to randomly pair the males and females is given by 10!. To find the number of ways in which exactly two couples are dancing together, we need to find the number of arrangements where two couples are dancing together and the remaining three couples are not dancing together.

Therefore, the probability that exactly two couples are dancing together is given by:

(C(5,2) * 2!) / 10! = 1/126

This shows that it is unlikely that exactly two couples will be dancing together in a random pairing of the males and females.

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The value of k is 90.

The other factor of g(x) is, (x + 5)(x - 3)(x + 3)

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given the function,

g(x) = x⁴ + 3x³ - 19x² - 27x + k

and  (x - 2) a factor of g(x)

so g(2) = 0

g(x) = x⁴ + 3x³ - 19x² - 27x + k

g(2) = 2⁴ + 3(2)³ - 19(2)² - 27(2) + k

2⁴ + 3(2)³ - 19(2)² - 27(2) + k = 0

16 + 24 - 76 - 54 + k = 0

k = 90

the function is g(x) = x⁴ + 3x³ - 19x² - 27x + 90

B: -5 is a zero of the function,

f(-5) = 0, or x = -5

so factor is (x + 5)

the two factors are (x + 5)(x - 2)

(x + 5)(x - 2) = x² + 5x - 2x -10

(x + 5)(x - 2) = x² + 3x - 10

to find the other two factors we need to divide the function by

x² + 3x - 10

=>  (x⁴ + 3x³ - 19x² - 27x + 90) ÷ (x² + 3x - 10)

quotient after division is

x² - 9 = (x - 3)(x + 3)

The factors of the function are (x - 2)(x + 5)(x - 3)(x + 3)

Hence k = 90, and

the three other factors of g(x) are (x + 5)(x - 3)(x + 3)

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16 ounces is equivalent to 1 pound. In other words, 16 ounces per pound.

What is one pound?

A weight measurement unit: The weight of one pound is roughly equal to 454 grams. A kilogram is equivalent to about 2.2 pounds. One pound contains 16 ounces.

One pound is equal to 0.4535 kilograms and is referred to as an imperial unit of mass or weight measurement.

16 ounces = 1 pound

1 pound (lb) equals 16 ounces (oz)

Pounds To Ounces Conversion Table

1 pound = 16 ounces

2 pounds = 32 ounces

3 pounds = 48 ounces

5 pounds = 80 ounces

6 pounds = 96 ounces

7 pounds = 112 ounces

8 pounds = 128 ounces

9 pounds = 144 ounces

10 pounds = 160 ounces

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The solution to the system of equations is x = 7/8 and y = 71/8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equations be represented as A and B

Now , substituting the values in the equation , we get

y = 9x + 1   be equation (1)

y = x + 8   be equation (2)

On simplifying the equations , we get

x + 8 = 9x + 1

Subtracting x on both sides of the equation , we get

8x + 1 = 8

Subtracting 1 on both sides of the equation , we get

8x = 7

Divide by 8 on both sides of the equation , we get

x = 7/8

Substitute the value of x in the equation (2) , we get

y = 7/8 + 8

y = 71/8

Hence , the equations are solved and the solution is ( 7/8 , 71/8 )

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The true statements bout Gretchen's adjusted data set are (1), (4), and (5).

Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.

It is given that:

Which statements are true about Gretchen's adjusted data set:

The options are:

The data set is approximately symmetric.

The center moved farther from the center of Manuel's data set.

The center moved closer to the center of Manuel's data set.

The spread values are closer to the spread values of Manuel's data set.

The data set is skewed left.

The spread values are farther from the spread values of Manuel's data set.

As we know,

The spread values are more similar to Manuel's data set's spread values, and the data set is roughly symmetric and tilted to the left.

The true statements are:

The data set is approximately symmetric.

The spread values are closer to the spread values of Manuel's data set.

The data set is skewed left.

Thus, the true statements bout Gretchen's adjusted data set are (1), (4), and (5).

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The amount of interest earned in 6 years will be $15.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.

Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.

Given that Ellie has $50 in a savings account that earns 5% annually.  The simple interest is calculated as:-

Simple interest = ( P x R x T ) / 100

Simple interest = ( 50 x 5 x 6 ) / 100

Simple interest = $15

Hence, the value of the simple interest after 15 years will be $15.

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Answer:

-1 degrees

Step-by-step explanation:

The average = sum of all values/# of values = sum of all temperatures/# of days=

(-3+0+2-1-3)/5=  -1

Right ascension (RA) and declination (Dec) are coordinates used in astronomy to precisely describe the location of an object in the sky is  total of 62.3358° for the Dec.

RA is measured eastward along the celestial equator from the vernal equinox, which is the point in the sky where the Sun crosses the celestial equator from south to north at the beginning of spring. Dec measures the angle of an object above or below the celestial equator.

In this example, the right ascension is 15 06 53.62 and the declination is 62 20 10.0. This is expressed in terms of hours, minutes, seconds for the RA and degrees, minutes, seconds for the Dec. The RA can be converted to a decimal value by taking the 15 hours and multiplying it by 15 (1 hour = 15°) to get 225°. Then add 6 minutes (6/60 of an hour) which is equal to 10°, and add 53.62 seconds (53.62/3600 of an hour) which is equal to 0.1489°. This gives us a total of 225.1489° for the RA. For the Dec, we take the 62° and add 20 minutes (20/60 of a degree) which is equal to 0.333°, and add 10 seconds (10/3600 of a degree) which is equal to 0.0028°. This gives us a total of 62.3358° for the Dec.

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The correct option is C) [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]

Vectors, in Math's, are objects which have both, magnitude and direction. Magnitude defines the size of the vector.

It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.

According to the given conditions,

[tex]c1^{2}+c2^{2} +c3^{2} = 1, a.c =0, b.c=0[/tex]

and [tex]cos\frac{π}{6} = \frac{\sqrt{3} }{2} =\frac{a1b1+a2b2+a3c3}{\sqrt{a1^{2} +a2^{2} +a3^{2} } \sqrt{x=b1^{2} +b2^{2} +b3^{2} } }[/tex]

thus, a1c1+a2c2+a3c3=0 , b1c1+b2c2=b3c3=0

and [tex]\frac{\sqrt{3} (a1^{2}+a2^{2} +a3^{2} )^{1/2} (b1^{2}+b2^{2} +b3^{2} )^{1/2} }{2}[/tex] = a1b1+a2b2+a3b3

Now,

[tex]\left[\begin{array}{ccc}a1&b1&c1\\a2&b2&c2\\a3&b3&c3\end{array}\right]^{2}[/tex]

= [tex]\left[\begin{array}{ccc}a1&a2&a3\\b1&b2&b3\\c1&c2&c3\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}a1&b1&c1\\a2&b2&c2\\a3&b3&c3\end{array}\right][/tex]

= [tex](a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} ) - (a1b1+a2b2+a3b3)^{2}[/tex]

= [tex](a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} ) -\frac{3}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]

= [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]

Therefore, The correct option is C) [tex]\frac{1}{4} (a1^{2} +a2^{2} +a3^{2} )(b1^{2} +b2^{2} +b3^{2} )[/tex]

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The initial population of city A is 175,000 while its growth rate is 10%. The function that models the population of city B is B(t) = 350,000(0.97)^t, which is a case of exponential decay.

Here since nothing else is mentioned we will assume the Initial population of city A to be that of 2018, which is 175,000.

The growth rate of any city will be the percentage increase in its population every year. Here it is mentioned that the population of city A increases by 10% every year. Hence, the growth rate of city A is 10%.

Here we are already given that the function of the population of city B in a year is B(t) = 350,000(0.97)^t.

In model B(t) with every successive increase in time, the value of (0,97)^t will keep on reducing. Due to this, the product of 350,000(0.97)^t will reduce. Hence this is a case of exponential decay.

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In case of (a) Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.

a. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who use social media in their job search, we need to set up the null and alternative hypotheses:

H0: p = 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is equal to the proportion of the population that use social media in their job search)

Ha: p > 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is greater than the proportion of the population that use social media in their job search)

Where p is the true proportion of 22- to 30-year-old job seekers who use social media.

We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as: z = (p1 - p) / sqrt(p * (1 - p) / n)

where p1 = 310/370 = 0.838 and n = 370.

Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.

If the calculated z-value is greater than the critical value, we reject the null hypothesis.

z = (0.838 - 0.79) / sqrt(0.79 * (1 - 0.79) / 370) = 3.41

Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search.

b. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume, we need to set up the null and alternative hypotheses:

H0: p = 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is equal to 70%)

Ha: p > 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is greater than 70%)

Where p is the true proportion of 22- to 30-year-old job seekers who have electronically submitted a resume.

We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as:

z = (p1 - p) / sqrt(p * (1 - p) / n)

where p1 = 275/370 = 0.743 and n = 370.

Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.

If the calculated z-value is greater than the critical value, we reject the null hypothesis.

z = (0.743 - 0.70) / sqrt(0.70 * (1 - 0.70) / 370) = 2.01

Since 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.

Therefore, In case of (a) Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.

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In case of (a) Since 3.41 > 1.64485,  job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search. And in (b) 2.01 > 1.64485,  the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.

a. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who use social media in their job search, we need to set up the null and alternative hypotheses:

H0: p = 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is equal to the proportion of the population that use social media in their job search)

Ha: p > 0.79 (the proportion of 22- to 30-year-old job seekers who use social media is greater than the proportion of the population that use social media in their job search)

Where p is the true proportion of 22- to 30-year-old job seekers who use social media.

We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as: z = (p1 - p) / sqrt(p * (1 - p) / n)

where p1 = 310/370 = 0.838 and n = 370.

Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.

If the calculated z-value is greater than the critical value, we reject the null hypothesis.

z = (0.838 - 0.79) / sqrt(0.79 * (1 - 0.79) / 370) = 3.41

Since 3.41 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that uses social media in their job search.

b. To conduct the hypothesis test for the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume, we need to set up the null and alternative hypotheses:

H0: p = 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is equal to 70%)

Ha: p > 0.70 (the proportion of 22- to 30-year-old job seekers who have electronically submitted a resume is greater than 70%)

Where p is the true proportion of 22- to 30-year-old job seekers who have electronically submitted a resume.

We can use a one-sided z-test for proportions to test the hypothesis. The test statistic is calculated as:

z = (p1 - p) / sqrt(p * (1 - p) / n)

where p1 = 275/370 = 0.743 and n = 370.

Using a significance level of 0.05, we can find the critical value from the standard normal distribution table to be 1.64485.

If the calculated z-value is greater than the critical value, we reject the null hypothesis.

z = (0.743 - 0.70) / sqrt(0.70 * (1 - 0.70) / 370) = 2.01

Since 2.01 > 1.64485, we reject the null hypothesis and conclude that the results of the survey justify concluding that more than 70% of 22- to 30-year-old job seekers have electronically submitted a resume to an employer.

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The equation has been verified and the solution has been obtained by using trigonometric identities.

What are trigonometric identities?

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

We are given cotθ/1-tanθ + tanθ/1-cotθ = 1 + tanθ + cotθ

Solving the LHS, we get

⇒ [(cosθ/sinθ)/1-(sinθ/cosθ)] + [(sinθ/cosθ)/1-(cosθ/sinθ)]

⇒ [(cosθ/sinθ)/[(cosθ-sinθ)/cosθ]] + [(sinθ/cosθ)/[(sinθ-cosθ)/sinθ)]]

⇒ [cos²θ/(cosθ-sinθ)sinθ] + [sin²θ/(sinθ-cosθ)cosθ]

⇒-[cos²θ/(sinθ-cosθ)sinθ] + [sin²θ/(sinθ-cosθ)cosθ]

⇒[sin²θ/(sinθ-cosθ)cosθ] - [cos²θ/(sinθ-cosθ)sinθ]

⇒(sin³θ - cos³θ)/(sinθ-cosθ)sinθcosθ

⇒(sinθ - cosθ)(sin²θ + sinθcosθ + cos²θ)/(sinθ-cosθ)sinθcosθ

⇒(sin²θ + sinθcosθ + cos²θ)/sinθcosθ

⇒sin²θ/sinθcosθ + sinθcosθ/sinθcosθ + cos²θ/sinθcosθ

⇒tanθ + 1 + cotθ

⇒1 + tanθ + cotθ = RHS

Hence, the expression is verified.

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The admission fee for one person is 9.

The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).

Intercept Form of Equation of a Line: x/a + y/b = 1.

Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.

Total cost = 4x +36

It means we have a linear function where 4 is the slope ( the cost per person) and 36( the y-intercept).

The admission fee for four people= 36

So, the admission fee for one person = 36/4 = 9

Thus,  the admission fee for one person is 9.

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The admission fee for one person is 9.

The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).

Intercept Form of Equation of a Line: x/a + y/b = 1.

Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.

Total cost = 4x +36

It means we have a linear function where 4 is the slope ( the cost per person) and 36( the y-intercept).

The admission fee for four people= 36

So, the admission fee for one person = 36/4 = 9

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