Prove the following question
​

To Prove :

[tex] \sf \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} = \tan54\degree \\ \\ [/tex]

[tex] \sf LHS = \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} \\ \\ [/tex]

[tex] \sf RHS = \tan54\degree \\ \\ [/tex]

Solving for LHS :

Divide numerator and denominator by cos9°

[tex]\longrightarrow \: \: \sf\dfrac { \dfrac{ \cos9\degree}{ \cos9\degree} + { \dfrac{\sin9}{ \cos9} }}{ \dfrac{ \cos9\degree }{ \cos9\degree} - { \dfrac{ \sin9\degree}{ \cos9\degree}}} \\ \\ [/tex]

[tex] \longrightarrow \: \: \sf\dfrac{1 + { \dfrac {\sin9\degree}{ \cos9\degree}} }{1 - { \dfrac{ \sin9\degree}{ \cos9\degree} }} \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf \dfrac{1 + \tan9\degree}{1 - \tan9\degree} \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf{ \dfrac{ \tan45 \degree + \tan9\degree}{1 - \tan45 \degree \tan9 \degree}} \: \: \: \: \: \: \: \sf \red{\bigg( \tan(A + B) = \dfrac{ \tan A + \tan B}{1 - \tan A \tan B} \bigg)} \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf \tan(45\degree + 9\degree) \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf \tan54 \degree[/tex]

LHS = RHS

Answer:

a. Runner A ran at a constant rate throughout the race.

b. Runner B stopped running between 20 and 30 seconds.

c. Runner C started off slow and gradually increased speed until reaching their maximum speed, then gradually slowed down towards the end of the race.

d. Runner A won the race because they crossed the finish line first, at 40 seconds, which is before runners B and C.

Answer:

12 and 78

Step-by-step explanation:

x + 2x+54 = 90 2x+54=2(12)+54

24+54

78

3x + 54 = 90

3x = 36

x=12

12 and 78

Answer:

Step-by-step explanation:

1)  $5 + (8 min - 3 min)($1/min) = $5 + $5 = $10

2) $7.50 + (30 km - 4 km)($1.25/km) = $7.50 + $32.50 = $40

3) $100 + (24 hr - 3 hr)($35/hr) = $100 + $735 = $835

The probability of three or more goals being scored in an EPL match is approximately 0.522, or 52.2%.

To find the probability that three or more goals will be scored in a game, we need to calculate the cumulative probability of the Poisson distribution for x = 3, 4, 5, and so on, up to infinity. This can be written as:

P(X ≥ 3) = 1 - P(X < 3)

where X is the random variable representing the number of goals scored in a match.

To calculate P(X < 3), we can use the Poisson distribution formula:

[tex]P(X = x) = (e^{(-\lambda)} \times \lambda^x) / x![/tex]

where e is the mathematical constant approximately equal to 2.71828, and x! represents the factorial of x.

Using this formula, we can calculate the probabilities of scoring 0, 1, and 2 goals:

[tex]P(X = 0) = (e^{(-2.768)} \times 2.768^0) / 0! = 0.063\\\\P(X = 1) = (e^{(-2.768)} \times 2.768^1) / 1! = 0.174\\\\P(X = 2) = (e^{(-2.768)} \times 2.768^2) / 2! = 0.241[/tex]

To find P(X < 3), we add these probabilities:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.063 + 0.174 + 0.241 = 0.478

Finally, we can calculate the probability of scoring three or more goals using the formula we derived earlier:

P(X ≥ 3) = 1 - P(X < 3) = 1 - 0.478 = 0.522 or 52.2%

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The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store, with both stores having the same price.

The difference between the two terms is that "difference" refers to the way in which two or more things are not the same, whereas "difference" is more of a comparison between two or more things.

The difference between the lowest price in store 1 and the lowest price in store 2 is the difference between the first digit of each store's key. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1.

The difference between the highest prices in store 1 and store 2 is the difference between the last digit of each store's key. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0.

The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1. This difference is reflected in the lowest prices of each store, with store 1 having a lower price than store 2.

The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0. This difference is reflected in the highest prices of each store, with both stores having the same price.

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A pyramid with a base having n sides will have n + 1 faces, excluding the base. So, the pyramid that shares the same base as the prism will have 16 + 1 = 17 faces.

Let's say the base of the pyramid is a polygon with n sides. There are n faces in the pyramid (excluding the base), each of which is a triangle. Since there is just one base, the number of faces in the pyramid is n + 1.A prism is a polyhedron that is formed when two congruent polygons are joined by parallelograms. As a result, a prism with a polygon base has two polygons as bases and a number of rectangular faces equal to the number of sides of the polygon, which in this scenario is n.There are 2 bases and n rectangular faces in total for the prism. Since the number of edges in the prism is 99, we may express this as:Edges in prism = (Number of edges in each rectangular face × Number of rectangular faces) + (Number of edges in each base × Number of bases)= [tex]4n + 2n = 6n = 99n = 16.5[/tex] faces are in the pyramid = 16 + 1 = 17 faces.

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The height of the partially finished brick wall was 2.9 meters.

Let's denote the height of the partially finished brick wall as x meters. Mark stacked 1.2 meters of bricks onto the wall, which made the final height of the wall 4.1 meters.

Here's the equation to represent the situation:

x + 1.2 = 4.1

To solve this equation, subtract 1.2 from both sides:

x = 4.1 - 1.2

x = 2.9

So, the height of the partially finished brick wall was 2.9 meters.

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The optimal solution would be to use $240 worth of professional grade material for each frame.

An optimal solution is a solution that provides the best possible outcome for a problem or situation, given a set of constraints or requirements. In mathematical optimization, an optimal solution is the solution that maximizes or minimizes an objective function while satisfying a set of constraints.

In other words, an optimal solution is the solution that is most efficient, effective, or desirable according to a certain set of criteria. It is the solution that achieves the best possible outcome, given the available resources and limitations.

To find the optimal solution, we need more information about the specific weight specification and the cost of different types of materials.

However, if we assume that there is only one type of material available, and that it costs $x per yard, we can set up an equation to find the optimal solution:

30x = cost per frame

If the professional grade material costs $8 per yard, then the equation becomes:

30(8) = $240 per frame

So, the optimal solution would be to use $240 worth of professional grade material for each frame, assuming that it meets the weight specification. If the weight specification requires a different amount of material, or if there are other materials available at different prices, the optimal solution would be different.

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False to say that "cos(0) = 0." Cos(0) is equal to 1, as the input yields the x-coordinate of the spot on the circle for each arc in right spot, where first side coincides positive x-axis or final side spins clockwise first side.

What does it mean to coincide?

occupying the same location in time or space; coinciding; taking up the same spots on a scale. 3. Exactly concur.

Nevertheless, if the query is changed to ask for the angle that measures between 0 & 2 radians for which cos(x) = 0, the response is:

When x is equal to 2 or 3, cos(x) equals 0. The unit circle's corresponding points at these angles are, respectively, (0, 1) and (0, -1).

b. The sin(x) values for these angle measurements are:

As the equivalent point is at (0, 1) just on unit circle, sin(/2) equals 1.Due to (0, -1) being the corresponding point on the unit circle, sin(3/2) = -1.

therefore, False to say that "cos(0) = 0." Cos(0) is equal to 1, as the input yields the x-coordinate of the spot on the circle for each arc in right spot, where first side coincides positive x-axis or final side spins clockwise first side.

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The aquarium tank that holds 190 liters of water equals to 50.15 gallons. Therefore, the answer to the given problem is 50.15 gallons.

Conversion factors are the ratios that describe the numerical relationship between two units of measurement.

The conversion factor of liters to gallons is 1 gallon is 3.8 liters.

Therefore, by multiplying the given value of liters by the conversion factor of liters to gallons, we can convert liters to gallons.

190 liters x 1 gallon/3.8 liters = 50.15 gallons

Thus, the aquarium tank that holds 190 liters of water equals to 50.15 gallons.

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Answer:

Point I and Point II may not need to be main points.

Ann's main points are not balanced.

Parallel structure will not work with Ann's speech topic.

Step-by-step explanation:

This division indicates that Ann prioritized Point III above Points I and II. Point III was allocated the most of Ann's time (75%), while Point I and II were each given 10% and 15%, respectively. This is a sign that Ann placed a higher priority on Point III.

In terms of the actual percentages, this could indicate a variety of things. It could mean that Ann felt Point III was more important than the other two points, or that Point III took more time to complete than the other two points. It could also mean that Ann was trying to achieve a specific ratio of her time dedicated to each point.
Regardless of the reasoning, this division of Ann's time shows that she placed a higher priority on Point III. This could mean that Point III was more important to her overall goal than the other two points, or that Point III required a larger amount of her time.

By understanding this division of Ann's time, we can gain insight into what she felt was important, and how she chose to prioritize her time. This can be used to better understand Ann's thought process and her overall goal.

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Answer: 1250 miles

Step-by-step explanation:

50 miles in 1/5 of an hour = 250 miles in 1 hour = 1250 miles in 5 hours

Answer:

1,250

Step-by-step explanation:

50 divided by 1/5 equals 250.

Multiply 250 by 5.

250*5= 1,250

The given equation is 7(x+4) = -21 . Therefore, the value of x is 7

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation is made up of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Many times the right side of the equation is assumed to be zero. Assuming this does not reduce generality, this can be achieved by subtracting the right side from both sides.

According to the Question:

The given equation is:

   7(x+4)= -21

⇒ 7x + 28 = -21

⇒ 7x = -49

⇒ x = 7

Complete Question:

Solve the Equation : 7(x+4)= -21

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The simplified expression is −5x³y − 2x²y + 12y.

The given expression is (4x³y − 5x²y + 6y) − (9x³y − 3x²y − 6y). To simplify this expression, we need to distribute the negative sign inside the second set of parentheses and then combine like terms.

Distributing the negative sign inside the second set of parentheses, we get:

(4x³y − 5x²y + 6y) − 9x³y + 3x²y + 6y

Next, we can group the terms that have the same variables and exponents:

4x³y − 9x³y = −5x³y −5x²y + 3x²y = −2x²y 6y + 6y = 12y

Finally, we can combine the like terms to obtain the simplified expression:

−5x³y − 2x²y + 12y

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Answer:

B:−5x3y − 2x2y + 12y

Step-by-step explanation:

i took the test and got it right

Answer: 9 cm

Step-by-step explanation: 4+5=9

The two solutions to the equation (2x - 3)(3x + 5) = 0 when solved are x = 3/2 and x = -5/3

Given that, we have the following equation

(2x - 3)(3x + 5) = 0

The above equation means that

2x - 3 = 0 and 3x + 5 = 0

When the equations are evaluated, the equations becoms

2x = 3 and 3x = -5

Lastly, we divide both sides of the equation by the coefficent of x i.e 2 and 3

So, we have

x = 3/2 and x = -5/3

So, the values of the solutions to the equation are x = 3/2 and x = -5/3

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Answer: k898

iiii

Step-by-step explanation:

k8ni7mrvnyrt

Answer:

Step-by-step explanation:

Not sure.

According to the information, the distance between Daytona beach and Orlando would be 52 miles.

To calculate the distance from Daytona beach to Orlando we must perform the following rule of three mathematical procedure:

1. In this case, we must consider the procedure like this:

If one unit is equal to 26 miles, how many miles are 2 units equal to?

So, we can conclude that the distance between Orlando and Baytona beach is 52 miles.

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Answer:

If you want to decrease 144 in the ratio of 4:3, you can do so by first finding the difference between the two parts of the ratio (4-3=1) and then dividing 144 by this difference (144/1=144). This gives you the value of one part of the ratio. You can then multiply this value by 3 to find how much you need to decrease 144 by: 144 * 3 = 432. So if you decrease 144 by 432, it will be in the ratio of 4:3.

Step-by-step explanation:

The method of documentation that describes the setting up of squares of known dimension over the entire pattern is known as grid method.

Grid method is a method of documentation that involves the setting up of squares of known dimensions over the entire pattern to document a site. This method is commonly used in archaeological surveys and historical preservation.

Therefore, grid method is a simple and effective way of recording data, and it is still widely used in the field of archaeology today.

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Therefore, the average velocity of the person over the interval 0 ≤ t ≤ 12 can be calculated as follows:Average Velocity = Total distance travelled / Total time taken= 6.6 / 12= 0.55 m/s.

In the given question, we need to find the average velocity of a person running in a straight line across a field, given differentiable function v(t) on the interval [0,12]. Therefore, to calculate the average velocity of a person, we use the following formula:Average Velocity = Total distance travelled / Total time takenWe have a graph with the velocity of the person, which is a differentiable function v(t) given above on the interval 0 ≤ t ≤ 12.

We need to find the distance travelled by the person. Therefore, we use the following formula:Distance travelled = ∫v(t)dt From the given graph, the velocity of the person is zero when t = 0 and when t = 5. Similarly, the velocity of the person is 0 when t = 10 and when t = 12.So, we have to calculate the distance travelled from 0 to 5, from 5 to 10, and from 10 to 12 to determine the total distance travelled by the person over the given interval .Distance travelled from 0 to 5 can be calculated as follows :

Distance travelled from 0 to 5 = ∫v(t)dt from [tex]0 to 5= 5 x 0.6 = 3[/tex]Distance travelled from 5 to 10 can be calculated as follows :Distance travelled from 5 to 10 = [tex]∫v(t)dt[/tex] from [tex]5 to 10= 5 x 0.4 = 2[/tex]

Distance travelled from 10 to 12 can be calculated as follows: Distance travelled from 10 to 12 = ∫v(t)dt from 10 to 12= 2 x 0.8 = 1.6Total distance travelled = Distance travelled from 0 to 5 + Distance travelled from 5 to 10 + Distance travelled from 10 to [tex]12= 3 + 2 + 1.6= 6.6[/tex]

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Answer:

6.3cm

Step-by-step explanation:

73/5 = 92/x

cross multiply to get: 73x=460

divide both sides by 73

x=6.3

The answer is yes, we have all the information needed to solve for how many licenses each central office department will get.

If this very individual acquired about 250 program licenses and 50 licenses are taken or conveyed to departments in the satellite office of same organization, then, number of licenses which will be moved to the central office is:

= 250 - 50

= 200 licenses.

This conclude that 200 licenses will be moved to the central office while 50 licenses will be kept or used at the satellite office.

Then, as given if there are 10 company's departments in central office of this organization and all that 250 licenses will be evenly or equally distributed among the departments, each department will get:

200/10

= 20 licenses.

Since dividing 200 by 10 does give a perfect integer, then there's no further information we are yet to be furnished with. One department will  get 10 license.

Therefore, we have all the information we need to solve for how many licenses each central office department will get.

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Answer:

x < 2

Step-by-step explanation:

57x - 32 < 72

57x < 104

x < 2

Answer:

C and E

Step-by-step explanation: C represents a nonlinear relationship because a nonlinear relationship is a relationship that does not have a straight line. E is a nonlinear relationship because it does not have a straight line. Hope this helps!! :))

Also, please mark me brainliest!! :))

Answer:

We can begin by simplifying each equation:

A. 52 = 8n + 4 can be rewritten as 48 = 8n or 6 = n

B. 4(2n + 1) = 52 can be simplified to 8n + 4 = 52 or 8n = 48 or 6 = n

C. 4=52-8n can be rewritten as 8n = 48 or 6 = n

D. 4n = 48 can be simplified to n = 12

Therefore, equations A, B, and C are equivalent, and equation D is not equivalent to the others.

So, the correct answers are A, B, and C.

Answer:

Step-by-step explanation:first you have to multiply then divide then add then subtract and then substitute and then you will get the answer.

Answer: To find the mean of this data set, we need to add up all the amounts of rainfall and divide by the number of weeks. From the line graph, we can estimate the following amounts of rainfall:

Week 1: 2 inches

Week 2: 3 inches

Week 3: 1 inch

Week 4: 3 inches

Week 5: 5 inches

Week 6: 4 inches

To calculate the mean, we need to add up these amounts and divide by 6 (the number of weeks):

(2 + 3 + 1 + 3 + 5 + 4) / 6

= 18 / 6

= 3

Therefore, the mean amount of rainfall in this data set is 3 inches. The answer is (B) 3.

Step-by-step explanation:

Answer:

(5,2)

Step-by-step explanation:

Let's solve your system by substitution.

[tex]x+y=7{\text{ ; }}x=y+3[/tex]

Step 2: let Solve [tex]$x+y=7$[/tex] for[tex]$x$[/tex]

[tex]x+y=7[/tex]

[tex]x+y +(-x)=7+(-x)[/tex] (Add (-x) on both sides)

[tex]y=-x+7[/tex]

0+(x)=7-x-y+(x)   (Add (x) on both sides)

x = -y + 7

x/1 = -y+7/1  (divide through by 1)

x = -y + 7

Substitute -y+7 for x in x = y + 3, then solve for u

(-y + 7) = y + 3

-y + 7 = y + 3 (simplify)

-y+7+(-7) = y + 3 + (-7)    (Add (-7) on both sides)

-y=y-4

-y = y-4 (simplify)

-y+(-y)=y-4+(-y)  (Add (-y) on both sides)

-2y-=-4

-2y/-2 = -4/-2  (Divide through by -2)

y = 2

Substitute in 2 for y in x = -y + 7

x =  -y+7

x = -2+7

x = 5

Answer:

x = 5 and y = 2