Which equation is true?

The proof of cot²(x) - tan²(x) = csc²(x) - sec²(x) is the help of trigonometry

identity and Pythagorean identity .

A trigonometric identity is an equation that is true for all values of the variables in the equation, where the variables are trigonometric functions such as sine, cosine, tangent, cotangent, secant, or cosecant.

The Pythagorean identity is a fundamental trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent, in terms of the unit circle or right triangle.

The identity you provided, cot²(x) - tan²(x) = csc²(x) - sec²(x), is a trigonometric identity that can be derived from the Pythagorean identity and the reciprocal identities. Here's one way to prove it:

Start with the Pythagorean identity:

sin²(x) + cos²(x) = 1

Divide both sides by sin²(x):

1 + cos²(x)/sin²(x) = 1/sin²(x)

Recall that cot(x) = cos(x)/sin(x) and tan(x) = sin(x)/cos(x):

1 + cot²(x) = csc²(x)

Subtracting sec²(x) from both sides:

cot²(x) - tan²(x) = csc²(x) - sec²(x)

Therefore, cot²(x) - tan²(x) = csc²(x) - sec²(x) is a valid trigonometric identity.

To know more about trigonometry Visit:

https://brainly.com/question/20972755

#SPJ1

the correct answers are E(-4, 5) and F(3, 2). According to given probabilities  condition

How to solve the question?

To find the coordinates of Checkpoints E and F, we need to first understand what is meant by "located at CD's location in a 180° rotation of the course."

A 180° rotation means that we flip the course upside down, with the line segment connecting Checkpoints C and D acting as the axis of rotation. This means that Checkpoints E and F will be on the same line as CD, with E being the reflection of C and F being the reflection of D across the line CD.

To find the coordinates of E, we reflect C across the line CD. To do this, we first find the slope of the line CD:

slope = (2 - 5) / (-3 - (-4)) = -3

The midpoint of CD is:

midpoint = ((-3 + (-4))/2 , (2 + 5)/2) = (-3.5, 3.5)

The line perpendicular to CD passing through the midpoint has slope -1/(-3) = 1/3. Using point-slope form, we can find the equation of this line:

y - 3.5 = (1/3)(x + 3.5)

Simplifying, we get:

y = (1/3)x + 4

To reflect C across CD, we can find the intersection point of this line with the line passing through C and CD. This line has slope -3 and passes through (-4, 5). Using point-slope form, we can find its equation:

y - 5 = (-3)(x + 4)

Simplifying, we get:

y = -3x - 7

Setting these two equations equal to each other, we get:

(1/3)x + 4 = -3x - 7

Solving for x, we get:

x = -4

Substituting this value back into either equation, we get:

y = 5

Therefore, the coordinates of Checkpoint E are (-4, 5).

To find the coordinates of F, we reflect D across CD. We can use a similar method as above to find the line passing through D and CD:

slope = (2 - 5) / (-3 - (-4)) = -3

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

Simplifying, we get:

y = -3x - 7

To reflect D, we find the intersection point of this line with the line perpendicular to CD passing through the midpoint:

y - 3.5 = (1/3)(x - (-3.5))

Simplifying, we get:

y = (1/3)x + 4

Setting these two equations equal to each other, we get:

(1/3)x + 4 = -3x - 7

Solving for x, we get:

x = 3

Substituting this value back into either equation, we get:

y = 2

Therefore, the coordinates of Checkpoint F are (3, 2).

So the correct answers are E(-4, 5) and F(3, 2).

To know more about probability visit :-

https://brainly.com/question/13604758

#SPJ1

The angles of △ABC are approximately:

A ≈ 36.1 degrees

B ≈ 55.9 degrees

C ≈ 101.3 degrees

To find the angles of △ABC, we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(C)

where C is the angle opposite the side c.

Using the given values, we can substitute and solve for cos(C):

18^2 = 11^2 + 20^2 - 2(11)(20)cos(C)

324 = 441 + 400 - 440cos(C)

cos(C) = -17/440

C ≈ 101.3 degrees

We can now use the Law of Sines to find the other angles:

sin(A)/a = sin(C)/c

sin(A)/11 = sin(101.3)/18

sin(A) ≈ 0.593

A ≈ 36.1 degrees

sin(B)/b = sin(C)/c

sin(B)/20 = sin(101.3)/18

sin(B) ≈ 0.820

B ≈ 55.9 degrees

Therefore, the angles of △ABC are approximately:

A ≈ 36.1 degrees

B ≈ 55.9 degrees

C ≈ 101.3 degrees

Learn more about angles of triangle below.

https://brainly.com/question/25215131

#SPJ1

The hanger in the illustration will have the value x = 6, and it will remain balanced.

Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It demonstrates the equality of the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in each mathematical equation. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.

Here's the query,

Considering the graph,

The hanger's equation is as follows:

4x= 24

There are 4 numbers here that represent the value of the hanger.

So, x+x+x+x will be 24.

The equation is thus:

4x = 24.

Now, by resolving the equation, we can determine the value of x that balances the hanger:

4x = 24.

When you divide 4 on both sides:

x = 24/4

x = 6.

As a result, the hanger will remain in equilibrium for x = 6.

To know more about equations, visit:

brainly.com/question/29657983

#SPJ1

The probability that the mean tariff rate of 400 randomly selected​ railroad-car shipments of ethanol will be within ​$80 of the mean tariff rate of all​ railroad-car shipments of ethanol is: 0.305.

The interpretation of the statement that the probability of the sample mean being within $80 of the population mean is 0.305 is that if we take multiple samples of 400 ethanol railroad-car shipments, about 30.5% of the time, the sample mean tariff rate will be within $80 of the population mean tariff rate.

To arrive at the propability, we will first list the data as follows:

Standard deviation of tariff rates, σ = $1200

Sample size, n = 400

Margin of error, E = $80

Standard deviation of sample mean = σ/√n = 1200/√400 = 60

To find the probability, we need to calculate the z-score for the margin of error.

z = E / standard deviation of sample mean = 80 / 60 = 4/3.

When we use the standard normal distribution table, we will arrive at  the probability of a z-score between -1.33 and 1.33. This probability is approximately 0.305.

Learn more about the probability of a z-score here:

https://brainly.com/question/25638875

#SPJ1

Answer:

Hello... im exhausted but ill solve it i guess

To solve for x in the equation 2/5 + x = 1, we can follow these steps:

Subtract 2/5 from both sides of the equation to isolate the x term:

2/5 + x - 2/5 = 1 - 2/5

This simplifies to:

x = 1 - 2/5

Find a common denominator for 1 and 2/5, which is 5:

x = 5/5 - 2/5

Subtract 2/5 from 5/5:

x = 3/5

So, the solution for x in the given equation is x = 3/5.

To determine if (2, 6) is a solution to the system of equations:

y = 3/2x + 3 ... (equation 1)

y = -9x + 1 ... (equation 2)

We need to substitute x = 2 and y = 6 into both equations and check if they are true.

Substituting x = 2 and y = 6 into equation 1, we get:

6 = 3/2(2) + 3

6 = 3 + 3

6 = 6

This equation is true.

Substituting x = 2 and y = 6 into equation 2, we get:

6 = -9(2) + 1

6 = -18 + 1

6 = -17

This equation is false.

Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.

The result of adding -3 (row 1) to row 2 is determined as (0  10) |-14.

The result of the row multiplication in the matrix is calculated by applying the following method;

row 1 in the given matrix = [1  -4] | 8

To multiply row1 by -3, we will multiply each entity by -3 as shown below;

= -3(1  -4) | 8

= (-3  12) | -24

To add the result to 3;

(-3  12) | -24  +  (3   -2)|10

= (0  10) |-14

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.

Learn more about row multiplication here: brainly.com/question/31531585

#SPJ1

92 grams of recycled plastic were used to make Chanasia's bucket

Chanasia buys a plastic bucket

The bucket weighs 460 grams

The label on the bucket says it was made with 20% recycled plastic

The number of grams of recycled plastic that was used to make the bucket can be calculated as follows

= 460/100

= 4.6

= 4.6 × 20

= 92

Hence 92 grams of recycled plastic was used to make the bucket

Read more on grams here
https://brainly.com/question/23768528

#SPJ1

The complete table for the pie chart is;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            198

Comedy                         5                            90

From the given table used to form the pie chart, we see that;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            

Comedy                         5

We know that the angles in a circle is equal to 360 degrees. Thus;

Angle composed of horror and comedy = 360 - 72 = 288°

Thus;

Angle for horror film = (11/(4 + 11 + 5)) * 360°

= (11/20) * 360°

= 198°

Thus;

Angle for comedy = 288° - 198° = 90°

Read more about Pie Chart at;

brainly.com/question/26851221

#SPJ1

Step-by-step explanation:

At low tide   depth =  (3)(-1) + 7  = 4

at HIGH tide  depth = (3) (+1)  + 7 =   10 feet

Answer:

We can use the cosine double angle formula to find cos(2π/3):

cos(2θ) = cos^2(θ) - sin^2(θ)

Letting θ = π/3, we get:

cos(2π/3) = cos^2(π/3) - sin^2(π/3)

Using the values of cosine and sine of π/3 (which are known), we have:

cos(2π/3) = (1/2)^2 - (√3/2)^2

Simplifying, we get:

cos(2π/3) = 1/4 - 3/4

cos(2π/3) = -1/2

Therefore, cos(2π/3) is equal to -1/2.

Answer:

cos(2π/3) = cos(π/3 + π/3)

= cos²(π/3) - sin²(π/3)

= (1/2)² - (√3/2)²

= 1/4 - 3/4

= -2/4

= -1/2

Step-by-step explanation:

here are the steps:

Therefore, cos(2π/3) = -1/2

4[tex]\pi[/tex]/9 radians equals 80 degrees.

To convert a radian angle to a degree angle, multiply it by 180°/[tex]\pi[/tex]. To convert a degree angle to a radian angle, multiply it by [tex]\pi[/tex]/180°.

We utilize the conversion factor that 1 radian = 180/[tex]\pi[/tex] degrees to convert radians to degrees.

So we multiply 4[tex]\pi[/tex]/9 radians by the conversion factor to get degrees:

[tex]\\\frac{4\pi }{9} * \frac{180}{\pi } \\\frac{720}{9}[/tex]

On simplifying we get,

720 / 9 = 80 degrees

As a result, 4[tex]\pi[/tex]/9 radians equals 80 degrees.

Learn more about radians here:

https://brainly.com/question/7721249

#SPJ1

Complete question:

attach in the image form

The probability that Frank gets a head and a tail in any order is 2/5.

We have,

The sample space of tossing two coins.

= {HT} x {HT}

= {HH, HT, TH, TT}

So,

The table is filled as:

First coin   Second coin

  Head         Head

  Head         Tail

  Tail             Head

   Tail             Tail

Now,

The probability that Frank gets a head and a tail in any order.

= Number of required outcomes / Total outcomes

{HT, TH} = 2

{HH, HT, TH, TT} = 5

So,

= 2/5

Thus,

The probability that Frank gets a head and a tail in any order is 2/5.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

The correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.

It also goes by the name cuboid.

Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.

It is referred to as a prism because of the length of its cross-section.

There are 6 faces, 8 vertices, and 12 edges on a rectangular prism.

A rectangular prism's volume can be determined by packing unit cubes into it without any gaps or overlaps, then counting the number of unit cubes.

A rectangular prism's surface area is equal to the sum of the areas of each of its faces.

It can be calculated using the formula 2(lw+ wh+ hl).

Therefore, the correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.

Know more about the rectangular prism here:

https://brainly.com/question/128724

#SPJ1

Therefore, we estimate that there are 2250 Art majors in the total population.

In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two quantities expressed as a fraction or a decimal. Since both sides of the equation are equal, the proportion is true. Proportions are used in many mathematical and real-world contexts, such as in geometry, finance, and statistics. They are useful for comparing and scaling quantities, and for solving problems involving unknown quantities or variables.

Here,

We can use proportions to estimate the total number of Art majors in the population based on the proportion of Art majors in the sample.

The proportion of Art majors in the sample is:

75/250 = 0.3

We can assume that this proportion is representative of the proportion of Art majors in the population.

So, if x is the total number of Art majors in the population, then we can set up the following proportion:

0.3 = x/7500

To solve for x, we can cross-multiply and simplify:

0.3 * 7500 = x

x = 2250

To know more about proportion,

https://brainly.com/question/31010676

#SPJ1

Answer:

Step-by-step explanation:

You want the union and the intersection of the given sets D and E.

The union of the two sets is the list of elements in either set. It will contain all of the elements of D along with all of the elements of E, with duplicate values removed so that each element is only listed once.

The intersection of the two sets is the list of elements that appear in both sets. Any element that only appears in one of the sets is not part of the union.

<95141404393>

A sampling distribution is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population.

To get the possible samples, use the formula "N choose n", where N is the population size, and n is the sample size to be taken. The total probability of the sample mean must be equal to 1.

Since the mean of all possible samples must be equal to the population mean. The sampling distribution is an important concept in statistics as it allows us to make inferences about the population based on the characteristics of the sample, and helps us estimate parameters and test hypotheses.

To learn more about frequency distribution here:

https://brainly.com/question/14926605

#SPJ1

Answer:

False

Step-by-step explanation:

(x+4)^2 =  x^2 + 8x + 16

The length of the guy wire should be option D √(25) ft. that is 25 ft.

Perpendicular means that two lines or objects intersect each other at a 90-degree angle, forming a right angle. This means that if you were to draw a line at the point of intersection, it would split the angles on either side of it into two equal parts. In simpler terms, if you imagine a horizontal line and a vertical line intersecting each other, they would be perpendicular to each other. The concept of perpendicularity is important in geometry and is used in many different applications, such as construction, engineering, and design.

We can use the Pythagorean theorem to find the length of the guy wire c. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore:

c² = a² + b²

Substituting the given values:

c² = (20 ft)² + (15 ft)²

c² = 400 ft² + 225 ft²

c² = 625 ft²

Taking the square root of both sides:

c = √(625) ft

c = 25 ft

Therefore, the length of the guy wire should be 25 feet.

To know more about perpendiculars visit:

brainly.com/question/18271653

#SPJ1

The equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

We can observe from the table that the number of books collected increases by 10 for each week.

Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:

b = mw + c

where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).

The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):

10 = 10 * 1 + c

c = 0

Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

Read more about data sets here:

https://brainly.com/question/28168026

#SPJ1

the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1 10

2 20

3 30

4 40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

Answer:

65

Step-by-step explanation:

cups per pizza- 13

for 5 pizza- 13×5= 65

think of it this way you eat 2 slices of pizza in an hour, how many will you eat in 6 hours? 2x6 = 12

Answer:

B

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 7 and h = 4 , then

A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 cm²

A quadratic equation with opposite solutions can be found by multiplying a variable by its negative value. Specifically, if we start with a quadratic equation of the form:

ax^2 + bx + c = 0

We can find an equation with opposite solutions by multiplying either a or c by -1. For example, if we multiply c by -1, we get:

ax^2 + bx - c = 0

This equation will have opposite solutions if the discriminant, b^2 - 4ac, is negative. This is because the solutions of a quadratic equation are given by the formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Thus, if the discriminant is negative, then the square root term will be imaginary, which means that the solutions will be complex conjugates of each other.

For more details regarding quadratic equation, visit:

https://brainly.com/question/30098550

#SPJ1

The probability that the bus will arrive early is 0.1, or 10%.

It is possible to calculate the likelihood that the bus will arrive early using the rule that the sum of all possible outcomes must equal 1.

P(on time) + P(late) + P(early) = 1 if P(E) is the likelihood that the bus will arrive early.

Using the probabilities as a replacement, we get:

0.6 + 0.3 + P(E) = 1.

For P(E), use the formula:

P(E) = 1 - 0.6 - 0.3 = 0.1.

Therefore, the probability that the bus will arrive early is 0.1.

Learn more about probability here : brainly.com/question/251701

#SPJ1

The values of b and c include the following:

c = 8

b = 4√3

In order to determine the length of b, we would apply the law of tangent because the given side lengths represent the adjacent side and opposite side of a right-angled triangle.

Tan(θ) = Opp/Adj

Where:

Therefore, we have the following tangent trigonometric function:

Tan(θ) = Opp/Adj

Tan(30°) = 4/b

√3/3 = 4/b.

b = 4√3

From Pythagorean Theorem, the length of c is given by;

c² = (4√3)² + 4²

c² = 48 + 16

c = √64

c = 8

Read more on right-angled triangle here: brainly.com/question/26733667

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A Map Scale.

Step-by-step explanation:

A Map Scale is the relationship with the ground.