trig worksheet questions
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Answer: Thats a Trapezoid

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

The calculated value of the period of the function is 6

From the question, we have the following parameters that can be used in our computation:

The equation, f(x) = 2cos(2π/6(x + 4)) +3

A sinusoidal function is represented as

f(x) = acos(2π/b(x + c)) + d

Where the period is B

When the equations are compared, we have

2π/b = 2π/6

This gives

b = 6

Hence, the period of the function is 6

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Complete question

Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?

Answer:

D=2, 3, 5, 6, 7, 8, 9,

Step-by-step explanation:

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{2,3,5,6,7,8,9}

The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.

The value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc TV = 2(m∠TUV)

54x - 2 = 2(80)

54x - 2 = 160

54x = 160 + 2 {collect like terms}

54x = 162

x = 162/54 {divide through by 3}

x = 3

Therefore, the value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3.

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Answer:

Dependent and Independent could be used like a ride on a bike, or even traveling to a friend's house. The dependent variable depends on the independent variable, so let's say I biked at a speed of 7 min per hour and I traveled 42 miles. The independent variable is minutes, because distance depends on time.

Step-by-step explanation:

Answer:

By substituting the values of A, C, and D the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

Step-by-step explanation:

From the given information, we have;The vertical stretch of the sine function = 3 × The parent function∴ A = 3Given that the horizontal shift left = π/2 units, (from an online source with similar question)The vertical shift down = 4 unitsThe given function, g is g(x) = A·sin(x + C) + DWhere;A = The amplitude = The maximum displacement from the rest or equilibrium position = 3C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)Therefore, the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

[tex]|\Omega|=6^2=36\\A=\{(1,1),(1,4),(4,1),(2,3),(3,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]

Answer:

2a+15b+11

Step-by-step explanation:

2*a + 2*4b + 5 + 7b + 6

2a + 8b + 5 + 7b + 6

2a + 8b + 7b + 5 + 6

2a + 15b + 11

Answer:

The answer is 49

Step-by-step explanation:

We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.

We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:

14/42 = 0.3333

We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:

0.3333 * 147 = 49

Therefore, the best estimate for the number of dogs that suffer from the disease is 49.

After considering the given data we conclude that the value generated after performing divison of the given expression is 18x, under the condition that we follow the principles of divison.

Let us proceed by evaluating the given expression by applying division
4x(3+6) divided by 2
= 4x9/2
= 36x/2
= 18x
Division is considered one of the four basic mathematical operations, then the other three are addition, subtraction, and multiplication.
In short , division is referring to the breaking down of a given bigger number or expression into simpler yet smaller forms to meet the criteria of performing a function.
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Factoring in the dimensions , Design 1 would be the best recommendation because it requires less material and can hold a slightly larger volume of sand in comparison to Design 2.  

For Design 1:

Dimensions: 3 m x 3 m x 30 cm

We find the total area:

Two faces measures 3 m x 3 m = 9 m² each for the bottom and top

Two faces measures 3 m x 30 cm = 0.9 m² each for back and front

Two faces measures 3 m x 30 cm = 0.9 m² each

Therefore the total area of materials needed for Design 1 is found as

= 9 m² + 9 m² + 0.9 m² + 0.9 m² + 0.9 m² + 0.9 m² = 21.6 m²

Design 2:

Dimensions: 3.25 m x 3.25 m x 25 cm

In the same way, we find  the area of materials needed for Design 2:

Total area of materials needed for Design 2 = 10.5625 m² + 10.5625 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² = 24.375 m²

Design 1 volume is :

Volume = Length x Width x Height

Volume of sand for Design 1 = 3 m x 3 m x 0.3 m = 2.7 m³

Design 2 volume is :

Volume of sand for Design 2 = 3.25 m x 3.25 m x 0.25 m = 2.40625 m³

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The sentence given in the question does not include a participial phrase. Hence, correct option is False

The sentence "The picture frame held a picture of our family on vacation" does not include a participial phrase.

A participial phrase is a phrase that acts as an adjective. In this sentence, the phrase "on vacation" is an adjective phrase that describes the noun "family." However, it is not a participial phrase because it is not formed from a verb.

A participle is a verb form that can be used as an adjective. In this sentence, the verb "hold" is not used as an adjective.

Therefore, the phrase "on vacation" is not a participial phrase.

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Rounding to the nearest tenth of a degree, the direction angle of w = 8j is 90.0 degrees.

To find the direction angle of a vector, we can use the formula:

θ = arctan(y/x)

In this case, the vector w is given as w = 0 + 8j, which means its x-component is 0 and its y-component is 8.

Plugging the values into the formula, we get:

θ = arctan(8/0)

However, the division by zero is undefined, indicating that the x-component of the vector is zero, and thus the vector lies along the y-axis.

When a vector lies along the y-axis, its direction angle is either 90 degrees or -90 degrees.

In this case, since the vector is pointing upwards (in the positive y-direction), the direction angle is 90 degrees.

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It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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The Triangle is Equilateral and Equiangular.

We will use theses property of Equilateral Triangle as

We have a Triangle.

The Triangle all three angles measured 60 degree each.

and, We know the equilateral Triangle all angles measures 60 degree.

Now, from the figure all the three sides of triangle are equal.

and, we know Equilateral triangle have the three sides equal

Thus, the Triangle is Equilateral and Equiangular.

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Answer:

  302 m²

Step-by-step explanation:

You want the area of the figure composed of a triangle and rectangle.

The formulas for the areas of the parts are given in the problem statement.

The base length of the triangle is (18 m - 5m - 5 m) = 8 m. Then its area is ...

  A = 1/2bh

  A = 1/2(8 m)(8 m) = 32 m²

The area of the rectangle is ...

  A = LW

  A = (18 m)(15 m) = 270 m²

The area of the figure is the sum of the areas of its parts:

  A = (triangle area) + (rectangle area)

  A = 32 m² +270 m² = 302 m²

The area of the figure is 302 m².

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The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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There are 10 possible results when Dan spins the wheel of destiny with the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 20.

Every possible result is represented by a different number, and Dan has an equal probability of choosing any of them.

The wheel serves as a tool for randomization, adding a degree of ambiguity and unpredictability to the experiment. There are 20 possible outcomes total, with increments of 2 between the lowest and highest numbers.

Thus, these results stand in for various values that Dan might get from spinning the wheel. We may analyse the likelihood and probable range of results for this particular experiment by taking into account all the conceivable possibilities.

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To answer these questions, I would need more information about the population being referred to. Specifically, I would need to know the number of residents who have only completed high school and are under age 50, as well as the total number of residents who have only completed high school. I would also need to know the number of residents aged 20-29 who have completed only high school or just some college, as well as the total number of residents aged 20-29.

Do you have this information available?

The interest Pedro will have to pay is $5200

From the question, we have the following parameters that can be used in our computation:

Principal = $32.500

Rate = 4% simple interest

Time = 4 years

The formula of simple iinterest is

I = Principal * Rate * Time

substitute the known values in the above equation, so, we have the following representation

I = 32500 * 4% * 4

Evaluate

I = 5200

Hence, Pedro have to pay $5200 as interest

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The given image is a parallelogram, because the two lines are Parallel to each other implying that they will never cross each other

Based on the question above,  the coordinates of the figure are:

O = (0,0)

P = (a, b)

S = (a + c, b)

T = (c,0)

Note that the vertices O and T and they can be seen on the same horizontal level, due to the fact that they have the same y-coordinate and can be used also for vertices P and S

The length of the sides by distance formula will be:

PS = c

OT = c

So this implies that the opposite sides are parallel and congruent. Therefore, the image is a parallelogram

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The solution is: the values of x and y is 32° and 51° respectively.

Using the triangle theorem, the values of x and y is 32° and 51° respectively

From △MNP

∠M + ∠N + ∠P = 180° (Sum of interior angles in a triangle)

N = 180 - (142 + 24)

N = 180 - 168

N = 14°

Equate the expression :

2x - 50 = 14

2x = 14 + 50

2x = 64

x = 64 / 2

x = 32°

From ; 2x - y = 13 _____(1)

Substitute x = 32 into the expression ;

2(32) - y = 13

64 - y = 13

64 - 13 = y

51° = y

Therefore, the values of x and y is 32° and 51° respectively.

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complete question:

Find the value of x and y. Triangle MNP = triangle TUS

Scale drawings are valuable tools in various fields such as architecture, engineering, and design, allowing professionals to visualize and communicate ideas accurately. By employing scale factors and maintaining proportions, these drawings provide a reliable representation of real-world objects and spaces.

A scale drawing is a representation of an object or space that is proportional to the actual size or dimensions of the original. It involves using a scale factor, which is a ratio that compares the measurements on the drawing to the measurements of the real object or space. The scale factor determines how much the drawing is enlarged or reduced in relation to the actual size.

When creating a scale drawing, it is important to maintain the same proportion as the original object. Proportion refers to the relationship between the different parts of an object or space, ensuring that the relative sizes are accurate. This ensures that the scaled drawing provides an accurate representation of the original, even if it is smaller or larger in size.

The scale factor is typically expressed as a ratio or a fraction, such as 1:100 or 1/4. This ratio indicates how many times larger or smaller the drawing is compared to the actual object. For example, if the scale factor is 1:10, every unit on the drawing would represent ten units in reality. This allows for accurate measurements of length, as well as area.

Length is an essential aspect of scale drawings. By using the scale factor, the length of lines or dimensions on the drawing can be determined to reflect the corresponding measurements in the real object. For instance, if a line on the scale drawing represents 5 centimeters, and the scale factor is 1:10, the actual length of the line would be 50 centimeters.

In addition to length, scale drawings can also accurately represent areas. The scale factor can be used to determine the relationship between the areas on the drawing and the actual areas of the object or space. By applying the scale factor to the dimensions, the areas can be scaled up or down accordingly, maintaining the proportionality of the original.

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The distance between point A (2, 4) and point B (-2, 1) is equal to 5 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-2 - 2)² + (1 - 4)²]

Distance = √[(-4)² + (-3)²]

Distance = √[16 + 9]

Distance = √25

Distance = 5 units.

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Complete Question:

3. Find the distance from point A to B.

A (2, 4) B (-2, 1) C(2, -1)​ D (0, 0)

Answer: Obtuse triangle? The line marked with O and E is more than 90 degrees

Step-by-step explanation:

Answer:

Median, because Sunny Town is symmetric.

Answer: 15/38 or 0.39473684210526315789473684210526

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)

The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C

Selection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.

In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.

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Answer:

Step-by-step explanation:

4x/3 + x/6 =6

get a common denominator first

8x/6 + x/6 =6

then add

9x/6 = 6

multiply by six

9x = 36

divide by 9

x= 4