Draw two line segments that are parallel to each other, and 2 rays that are perpendicular to both of the line segments.

To solve the right triangle and find the length of the side adjacent to the given angle, follow these steps:

1. Identify the angle given in the problem. This angle is often labeled with a Greek letter, such as θ.

2. Determine which side of the triangle is adjacent to the given angle. The side adjacent to an angle is the side that is directly connected to that angle and not the hypotenuse.

3. Use the trigonometric function that involves the angle and the adjacent side. In this case, since we are finding the length of the side adjacent to the angle, we will use the cosine function.

4. Write down the cosine function and plug in the value of the given angle. The cosine function is defined as the ratio of the adjacent side to the hypotenuse. Let's call the length of the adjacent side "a" and the hypotenuse "h". The cosine function can be written as cos(θ) = a/h.

5. Rearrange the equation to solve for the length of the adjacent side (a). Multiply both sides of the equation by h to isolate "a". The equation becomes a = h * cos(θ).

6. Determine the value of the hypotenuse (h) if it is not given in the problem. If the hypotenuse is given, simply use that value.

7. Substitute the values of the hypotenuse (h) and the given angle (θ) into the equation. Multiply the hypotenuse by the cosine of the given angle to find the length of the adjacent side.

8. Round your answer to two decimal places as specified in the problem.

By following these steps, you will be able to find the length of the side adjacent to the given angle in the right triangle.

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Answer:

3.5 min

Step-by-step explanation:

let'sAnswer:

P ≈ 102.83 cm

Step-by-step explanation:

The window is practically a semi-circle. The formula for the perimeter of a semi-circle is πr + d.

*Remember that d (diameter) = 2 · r (radius)

Let's plug in everything that we know into the formula!

r = 20

d = 2(20) → 40

π(20) + 40 = 102.8318531

Now lets round the answer to the hundredths place.

102.8318531 → 102.83

Answer:

62.83 (estimate)

Step-by-step explanation:

The equation for the perimeter of a circle (also called circumference) is 2 times pi times the radius, or pi times the diameter. Since the window is a semi-circle, you divide the result by two.

\(2\pi r\\2(20)\pi = 40 \pi\\40\pi= 125.6\\125.663706144/2=62.83\)

Answer:

210 balloons divided by 70 (the percent) = 3 (1% = 3 balloons)

3 times 100 = 300 Balloons

The total number of balloons purchased is

300 balloons

Step-by-step explanation:

up above  

Answer:

karma

Step-by-step explanation:

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Using basic mathematical operations such as addition, there was a total of 17,243 people who went to the NEC on Sunday.

Basic mathematical operations include addition, subtraction, multiplication, and division.

Addition is combining two or more values to come up with a total or sum.

If there were two exhibitions at the NEC on Sunday, and 3816 people went to one of the exhibitions and 13427 people went to the other exhibition, then the sum of these numbers are the total number of people who went to the NEC on Sunday.

total number of people = 3816 + 13427

total number of people = 17,243

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The correct option is b. 9.7 meters/second².

The magnitude of the acceleration of the falling ball is 9.7 meters/second².

Acceleration is the rate for which velocity changes over time, both in terms of speed and direction. A point or object travelling in a straight path gets accelerated if it accelerates or decelerates.

The final velocity of a falling ball, v = 33 m/s

The ball's initial velocity, u= 0 m/s

The time it required for the ball to arrive at the ground, t = 3.4 seconds

The ball's acceleration during the fall Equals 'a'.

The formula for acceleration is;

acceleration = (final velocity - initial velocity)/time

Substituting the values in the formula;

a = (33 - 0)/3.4

a = 9.7

Therefore, the rate of acceleration of the falling ball is 9.7 m/s².

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Answer:

Step-by-step explanation:

DF is the hypotenuse.

Find DF:

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

The answer looks like C.

Step-by-step explanation:

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent. That is how you find which expression is equivalent.

Answer:

C. p^16/q^12

Step-by-step explanation:

The reason why the answer would be p^16/q^12 would be because, that if it is exponents. You always. Always. Subtract or Add depending if its multiplication or subtraction. So p^24-p^8 would be p^16. q^4-q^12 would be q^12.

Therefore, your answer would be p^16/q^12

Answer:

x=13 x=7

Step-by-step explanation:

distribute 2(3x-6) = 6x-12

Plug in x:  6 x 2 -12>5 x 2-10?  

Plug in x for all the other values (x=13,x=0,x=-5,x=-1,x=7)

x>2 so all values of x have to be greater than 2 (no negatives)

Hope this helps :D

The value of 6 divided by 396 is 0.1515.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The primary purpose of division is to determine how many equal groups are formed or how many people are in each group when equitably sharing.

The steps include:

Step 1: Take the first digit of the dividend from the left.

Step 2: Divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and then write the difference below.

Step 4: Bring down the next digit of the dividend.

In this case, 6/396 will give the value illustrated above.

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The only factors of the given expression are: 8, xy, 4x³

A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. Now we can also use what's called prime factorization for numbers which actually consist of using factor trees.

The expression that needs to be factored is given as;

2^(5) × x⁴ × y

This can also be written as;

32 × x⁴ × y

Now, looking at the options, it is clear that the only factors are;

8, xy, 4x³

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Answer:

5 mph

Step-by-step explanation:

10/2 is 5 miles in one hour.

Answer:

5mph

Step-by-step explanation:

10/2

Using the fundamental theorem of arithmetic, we have proven that (a, 6) [a, b] = ab for positive integers a and b.

To prove that (a, 6) [a, b] = ab for positive integers a and b using the fundamental theorem of arithmetic, we'll proceed as follows:

Step 1: Prime factorization of a and 6:

Using the fundamental theorem of arithmetic, we can write a and 6 as products of their prime factors:

a = p1^k1 * p2^k2 * ... * pn^kn,

6 = 2^1 * 3^1.

Step 2: Finding the greatest common divisor (a, 6):

To find the greatest common divisor (a, 6), we consider the common prime factors between a and 6 and take the minimum exponent for each prime factor. In this case, the common prime factor is 2 with an exponent of 1. Therefore, (a, 6) = 2^1.

Step 3: Prime factorization of [a, b]:

Using the fundamental theorem of arithmetic, we can write [a, b] as a product of its prime factors:

[a, b] = p1^m1 * p2^m2 * ... * pn^mn.

Step 4: Finding the least common multiple [a, b]:

To find the least common multiple [a, b], we consider the prime factors between a and b and take the maximum exponent for each prime factor. In this case, we have already determined that the common prime factor is 2 with an exponent of 1. Therefore, [a, b] = 2^1.

Step 5: (a, 6) [a, b] = ab:

Substituting the values we found, we have:

(a, 6) [a, b] = 2^1 * 2^1 = 2^2 = 4.

Since ab = 4, we have proven that (a, 6) [a, b] = ab for positive integers a and b using the fundamental theorem of arithmetic.

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The range of the function f(x) = 3x + 9 option is B: {y | y > 9}.

The range is the set of all values which the given function can output.

we have the function as

f(x) = 3x +9

The linear function has a range of all real numbers that is (-∞, ∞).

f(x) can take any real value.

x = -3

The correct option is B: {y | y > 9}.

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On solving the provided question, we can say that, A 4 cm Cube has a 96 cm2 total surface area.

Total surface area is the total area, which includes the curved portion and any bases. It refers to the entire surface area of the thing. The total area will be the sum of the two areas if the shape has a curved base and surface.

The cube's surface area is calculated as six times the square of its side lengths. 6a2, where an is the cube's side length, serves as its representation. Basically, it refers to the overall surface area.

total surface area of a cube of 4 cm is 96 cm2

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The probability that a test taker chosen at random takes 9 minutes or more to read the article is 0.38. Rounded to four decimal places, this is 0.3800.

To find the probability that a test taker chosen at random takes 9 minutes or more to read the article, we need to calculate the integral of the probability density function f(t) from 9 to 10 (since t is between 0 and 10).
∫(9 to 10) 0.012t^2 − 0.0012t^3 dt
Using the power rule of integration, we get:
[0.004t^3 - 0.0003t^4] from 9 to 10
Substituting the limits, we get:
[0.004(10)^3 - 0.0003(10)^4] - [0.004(9)^3 - 0.0003(9)^4]
Simplifying, we get:
0.38

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4 times as likely is Phillip to get exactly three heads than exactly two heads

A chance that something might exist, happen, or be true : the state or fact of being possible is called possibilities.

Possibility is the universal set whereas probability is the subset. Possibility is surer to occur than probability. Possibility has its opposite in the word impossibility whereas probability has its opposite in the word improbability.

We can find;

P (three heads) =  C(8,3)(2/3)^3(1/3)^5  = 448 / 6561

P (two heads) = C(8,2)(2/3)^2(1/3)^6  = 112 / 6561

So......     448 / 112   =  4 times more likely to get 3 heads than 2 heads

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The rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall is approximately 1.57 feet per second.

1. Let's start by drawing a diagram to visualize the situation. We have a rotating light located 18 feet from a wall, and we're interested in finding the rate at which the light projected onto the wall is moving along the wall.

2. Since the light completes one rotation every 4 seconds, we can determine the angular speed of the light. Angular speed is given by the formula ω = θ/t, where ω is the angular speed, θ is the angle (in radians), and t is the time. In this case, the angular speed is 2π/4 = π/2 radians per second.

3. To find the rate at which the light projected onto the wall is moving along the wall, we need to consider the component of the light's velocity that is parallel to the wall. This component is given by v = rω, where v is the velocity, r is the distance from the light to the wall, and ω is the angular speed. In this case, v = 18 * (π/2) = 9π feet per second.

4. Now we have the velocity of the light projected onto the wall, but we're interested in the rate of change of this velocity when the light's angle is 5 degrees from perpendicular to the wall.

5. To find the rate of change of the velocity, we need to differentiate the velocity function with respect to time. In this case, since the velocity is constant (9π feet per second), the rate of change of the velocity is zero.

6. Therefore, when the light's angle is 5 degrees from perpendicular to the wall, the rate at which the light projected onto the wall is moving along the wall is approximately 1.57 feet per second.

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I hope this helps! :)

Answer: 45 combined

25 angelfish 20 eels

Step-by-step explanation:

25 angelfish

20 eels

Cyber safety is the use of information and communication technologies in a responsible and safe manner. It involves protecting information and keeping it secure, but it also entails handling information responsibly, showing consideration for others online, and following proper internet etiquette.

The Essential Eight are a collection of eight mitigation techniques: application control, application patching, configuring Microsoft Office macro settings, user application hardening, limiting administrative rights, operating system patching, multi-factor authentication, and regular backups.

Best Cybersecurity Advice for 2023:

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The mathematical relationship between Celsius and Fahrenheit scale is:

C = (F - 32) * 5 / 9

We know that ice melts at 32◦F and water boils at 212◦F. In Celsius, these temperatures are 0◦C and 100◦C, respectively. We can use these two points to find the slope and y-intercept of the linear relationship between Celsius and Fahrenheit.

The slope is calculated by dividing the change in Celsius by the change in Fahrenheit. In this case, the change in Celsius is 100◦C and the change in Fahrenheit is 212◦F - 32◦F = 180◦F. Therefore, the slope is 100◦C / 180◦F = 5/9.

The y-intercept is calculated by finding the Celsius value when Fahrenheit is 0◦F. In this case, the Celsius value is 0◦C. Therefore, the y-intercept is 0.

Substituting the slope and y-intercept into the standard form of a linear equation, we get the equation:

```

C = (F - 32) * 5 / 9

```

This equation can be used to convert between Celsius and Fahrenheit temperatures.

Here is a table showing some conversions between Celsius and Fahrenheit:

| Celsius | Fahrenheit |

|---|---|

| 0◦C | 32◦F |

| 100◦C | 212◦F |

| -10◦C | 14°F |

| 50◦C | 122◦F |

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Diagonal of rectangle is changing by the rate of 4.373 in. /sec.

Rate of change (ROC) is the rate at which a variable changes over a particular period of time

To find the average rate of change, divide the change in the y-values ​​by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values ​​such as average speed or average velocity.

A ratio is a special ratio in which the two terms have different units.

the calculation part is shown in the below picture attached .

so after seeing the solution we come to an answer of = 4.373 in./sec

therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec

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Answer:

(-4,-2)

Step-by-step explanation:

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