[tex]x-\frac{1}{2} =\sqrt\frac{1}{4} x[/tex]

Answer:

  see below

Step-by-step explanation:

You want to show that csc²(θ) -cot²(θ) -sin²(θ) = cos²(θ).

It often works well to express the trig functions in terms of sine and cosine. The identity sin²(θ) +cos²(θ) = 1 is also useful.

  [tex]\csc^2\theta-\cot^2\theta-\sin^2\theta=\cos^2\theta\\\\\dfrac{1}{\sin^2\theta}-\dfrac{\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{1-\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{\sin^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\1-\sin^2\theta=\cos^2\theta\\\\\cos^2\theta=\cos^2\theta\qquad\text{Q.E.D.}[/tex]

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Answer: 484cm

Step-by-step explanation:

Every side of a square has equal lengths.

88/4 = 22

A = LW

   = 22 x 22

   = 484cm

Answer:  42 inches

Step-by-step explanation: Simple Math.

Answer: 42 inches

Step-by-step explanation:

There is 12 inches per foot and 6 inches for every 1/2 a foot so 12 x 3 = 36 + 6 = 42 inches

The net signed area in the above graph can be written as

(x² + 10x - 2√2)dx.

The net signed area can be found by summing the areas of the three parts:

The three being

Hence the area

: 48 + 0 + 8 = 56

We now calculate values:

of c, d, a, and b:

c = 8 - (-2) = 10

d = 3 - 2 = 1

a = 2 + 8 = 10

b = -2√2

It is important to  note that since the area under the x-axis is negative hence the reason value of b is negative.

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The number of students who chose comedy movies more than drama movies were 60 students

First, find the number of students who chose comedy :

= 20 % x 1, 200 students

= 0. 20 x 1, 200

= 240 students

Then find the students who chose drama movies ;

= 15 % x 1, 200

= 0. 15 x 1, 200

= 180 students

The number who chose comedy more :

= 240 - 180 students

= 60 students

In conclusion, the number of students who chose comedy more than those who chose drama was 60 students.

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The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

[tex]x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\[/tex]

The difference between the two sides rule

[tex]29 - 16.5 < x \\ 12.5 < x[/tex]

Therefore, the value of x is 12.5

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(1) The triangles ABC and DEF are not similar

(2) The triangles JKL and JMN are similar by the SAS similarity statement

(3) The triangles ABC and XYZ are similar

(4) The triangles PQR and TSR are similar

(1) Triangle ABC and DEF

The triangles in this figure are

ABC and DEF

These triangles are not similar is because:

The triangles do not have similar corresponding sides i.e. Ratio = 30/24 ≠ Ratio = 24/18

Evaluate

Ratio = 1.25 ≠ Ratio = 1.33

(2) Triangle JKL and JMN

The triangles in this figure are

JKL and JMN

"If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar"

This means that they are similar by the SAS similarity statement

(3) Triangle ABC and XYZ

The triangles in this figure are

ABC and XYZ

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 33/22 = 45/30 = 42/28

Evaluate

Ratio = 1.5

(4) Triangle PQR and TSR

The triangles in this figure are

PQR and TSR

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 10/5 = 9/4.5

Evaluate

Ratio = 2

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The GPA of the student who earned a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology is 3.

To calculate the GPA, we need to assign point values to each grade and then calculate the weighted average.

Given:

Trigonometry (C) = 2 points

American History (B) = 3 points

Botany (A) = 4 points

Microbiology (B) = 3 points

To calculate the GPA, we'll sum the total points earned and divide by the total number of courses:

Total Points = 2 + 3 + 4 + 3 = 12

Total Courses = 4

GPA = Total Points / Total Courses = 12 / 4 = 3

Therefore, the GPA of the student who earned a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology is 3.

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The two areas where buckeyes and monarchs have the same proportion are areas A and B.

Based on the information given, we can determine the two areas where the number of buckeye butterflies and the number of monarch butterflies are in the same proportion.

Comparing the data in the table, we can see that the ratio of buckeye butterflies to monarch butterflies is consistent in areas A and B.

In area A, there are 15 buckeye butterflies and 27 monarch butterflies, which simplifies to a ratio of 5:9.

In area B, there are 27 buckeye butterflies and 48 monarch butterflies, which also simplifies to a ratio of 5:9.

Therefore, the two areas where buckeyes and monarchs have the same proportion are areas A and B.

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Answer:

The word or phrase that describes the probability that Ariana will win the raffle if she buys 50 tickets is "likely." Therefore, option (d) is the correct choice.

Since there are 100 tickets in total and Ariana buys 50 of them, her chance of winning the raffle is 50/100 or 1/2, which is equal to 0.5 or 50%. This means that it is more likely than not that she will win the raffle, but it is not guaranteed, as there is still a 50% chance that someone else will win the prize.

Answer:

three more couches are needed to increase the truckload to one ton.

Step-by-step explanation:

First, let's calculate the weight of the five couches:

5 couches * 250 pounds/couch = 1250 poundsSince one ton is equal to 2000 pounds, we can subtract the weight of the couches from one ton to find out how much additional weight is needed:

2000 pounds - 1250 pounds = 750 poundsEach couch weighs 250 pounds, so we can divide the additional weight needed by the weight of each couch to determine how many more couches are needed:

750 pounds / 250 pounds/couch = 3 couches Therefore, three more couches are needed to increase the truckload to one ton.

The expression 2log(5) can be rewritten as log(25) in the form log(c), representing the Logarithm to the base 10 that yields the value 25.

The expression 2log(5) in the form log(c), we can use the logarithmic property that states:

nlog(b) = log(b^n)

Applying this property, we can rewrite 2log(5) as:

2log(5) = log(5^2)

Simplifying further, we have:

2log(5) = log(25)

Therefore, the expression 2log(5) can be written in the form log(c) as log(25).

The logarithmic function log(c) represents the exponent to which a given base must be raised to obtain the value c. In this case, log(25) represents the exponent to which the base 10 must be raised to obtain the value 25.

In summary, the expression 2log(5) can be rewritten as log(25) in the form log(c), representing the logarithm to the base 10 that yields the value 25.

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Hello!

13/14 x 26/49

= 13x26/14x49

= 338/686

= 169/343

Benny (B) would win the election using the plurality method.

To determine the winner using the plurality method, we need to calculate the total number of first-place votes for each candidate and see which candidate receives the most votes.

According to the given preference schedule, the number of first-place votes for each candidate is as follows:

Abe (A): 1st - 20 votes, 3rd - 2 votes (from the 2nd preference of voter 1)

Benny (B): 1st - 19 votes, 2nd - 5 votes

Chloe (C): 1st - 5 votes, 2nd - 19 votes, 3rd - 3 votes (from the 1st and 2nd preferences of voter 1)

Now, let's calculate the total number of first-place votes for each candidate:

Abe (A): 20 + 2 = 22 votes

Benny (B): 19 + 5 = 24 votes

Chloe (C): 5 + 0 + 3 = 8 votes

Based on the plurality method, the candidate with the highest number of first-place votes wins.

In this case, Benny (B) received the most first-place votes with a total of 24 votes.

Therefore, Benny (B) would win the election using the plurality method.

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Answer:

To determine the length you're referring to, we need more information about the specific configuration or diagram you're referring to. Please provide additional details or clarify your question so that I can assist you more accurately.

Step-by-step explanation:

x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations.

To simplify this expression, we need to use the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). We can simplify the expression step-by-step, following the rules of PEMDAS.
First, we need to simplify the parentheses, which contain an addition operation. We have:
x - 3(9 + 7)x - (-3x)
= x - 3(16)x + 3x   (remember that -(-3x) is the same as +3x)
= x - 48x + 3x     (multiplying 3 by 16 gives us 48)
= -44x + x
= -43x

Therefore, the expression x - 3(9+7)x-(-3x) simplifies to -43x.
In summary, x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations. Remember to follow the rules of PEMDAS carefully, and take your time simplifying each part of the expression.

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Answer:

region I

Step-by-step explanation:

Based on the description given, the regions that represent A ∩ B' ∩ C' are:

Region I: Items only in group A, not in B or C. (A intersection not B intersection not C)

These regions fulfill the condition of being in group A (A) and not in group B (B') and not in group C (C') simultaneously.

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Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

Answer:21 cm.

Step-by-step explanation:

Para encontrar la longitud del lado de un cuadrado con un área de 441 cm², podemos usar la fórmula del área de un cuadrado.

El área de un cuadrado se calcula elevando al cuadrado la longitud de uno de sus lados, es decir, A = L², donde A es el área y L es la longitud del lado.

Dado que el área del cuadrado es 441 cm², podemos escribir la ecuación:

441 = L²

Para encontrar L, podemos tomar la raíz cuadrada de ambos lados de la ecuación:

√441 = √L²

21 = L

Por lo tanto, la longitud del lado de un cuadrado con un área de 441 cm² es de 21 cm.

Answer:

1. Group B

2. Group A

3. The median.

Answer:

1. Group B has the lowest age range out of both groups. Group B has at least 18 students under 16 and Group A has ages from 5 through 30.

2. Group A has more of a variability of ages because it is more scrambled than Group B. Group B had more students that had ages that were all close to each other.

3. I think it's best to use the median because it measures the age above which is found. If we use the mean, it will only be calculated by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Answer:

The cross product of v x u is (-6, 2, 6).

Step-by-step explanation:

so,

   v x u = ( 0 x 4 - 1 x 6 , 1  x 2 - 1 x 4, 1 x 6 - 0 x 2)

   v x u = ( 0 - 6, 2 -4, 6 - 0)

   v x u = ( -6, 2, 6)

Therefore the cross product of u, v is ( -6, 2, 6).

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The graph that represents the motion of Joe on his bike is: Graph D

A speed time graph is defined as a graph that shows the motion of an object against time. They can also be referred to as even a velocity-time graph.

In a speed-time graph, we note that the speed is always plotted on the vertical axis and time is always plotted on the horizontal

Now, since Joe started at a constant rate, then it means that the line will be horizontal.

When he picks up the pace, the graph line will ascend upwards and when he maintains the peak speed, it means that the graph line remains horizontal.

Thus, option D is the correct option.

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Here are the completed tables for each sequence:

Sequence 1 Sequence 2 Ordered Pair

5                    15                   (5, 15)

6                        14               (6, 14)

7                        13             (7, 13)

8                    12                 (8, 12)

9                   11                (9, 11)

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x.

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x. This means that the two sequences are increasing at the same rate.

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Answer:

what's that

Step-by-step explanation:

Hello !

student's number / total students

9)

288/360 = 0,8

⇒ it's C

10)

90/360 = 0,25

⇒ it's B

Have a good day!

The amount of cars you need to break even is 5.

To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.

Let's denote the number of cars as x.

Revenue = Number of cars × Price per wash

= x × $10

Total cost = Cost per car × Number of cars + One-time cost

= $3x + $35

To break even, the revenue should be equal to the total cost:

x × $10 = $3x + $35

Now, let's solve this equation to find the value of x:

10x = 3x + 35

Subtract 3x from both sides:

10x - 3x = 3x + 35 - 3x

7x = 35

Divide both sides by 7:

x = 35 / 7

x = 5

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Answer:

3.33 minutes

Step-by-step explanation:

h = rt - 4.9t^2

In this case, the rocket is launched upward, so the initial velocity (r) is positive 1960 m/s. The rocket will fall to the ground when the height (h) becomes zero.

0 = 1960t - 4.9t^2

To solve this quadratic equation, we can set it equal to zero and use the quadratic formula:

4.9t^2 - 1960t = 0

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 4.9, b = -1960, and c = 0. Plugging in these values:

t = (-(-1960) ± √((-1960)^2 - 4 * 4.9 * 0)) / (2 * 4.9)

Simplifying further:

t = (1960 ± √(3841600)) / 9.8

t = (1960 ± 1960) / 9.8

t = 1960 / 9.8 = 200

So, the rocket will fall to the ground after 200 seconds. To convert this to minutes, divide by 60:

200 seconds / 60 = 3.33 minutes (approximately)

Therefore, the rocket will fall to the ground after approximately 3.33 minutes.