What is the domain of the function shown on the graph?

Answer:

19π/6 radians and 31π/6 radians

Step-by-step explanation:

To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:

The angle of point B = angle of point A + 7π/6 radians

= 0 radians + 7π/6 radians

= 7π/6 radians

Angle of point B in degrees = (7π/6) * (180/π) degrees

= 210 degrees

To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:

angle of rotation 1 = angle of point B + 2π radians

= 7π/6 radians + 2π radians

= 19π/6 radians

angle of rotation 1 in degrees = (19π/6) * (180/π) degrees

= 285 degrees

angle of rotation 2 = angle of point B + 4π radians

= 7π/6 radians + 4π radians

= 31π/6 radians

angle of rotation 2 in degrees = (31π/6) * (180/π) degrees

= 465 degrees

So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.

Note:

To convert the angles from radians to degrees, we can use the conversion factor:

1 radian = 180/π degrees

Answer:

To solve for C in the formula V = CLS, we need to isolate C on one side of the equation.

Starting with the given formula:

V = CLS

Divide both sides of the equation by LS:

V/LS = C

Therefore, the formula for C is:

C = V/LS

Answer:

Step-by-step explanation:

25%

80%

60%

100%

25%

The coordinates of the fourth vortex of the rectangular piece of material drawn by Freddy would be  (4. 6, - 3 ).

Rectangles are quadrilaterals which have two sets of parallel lines. This means that two sets of sides are equal which are the opposite ones. This means that when plotted on a coordinate plane, of the four points, the x - values should repeat twice and the y - values should repeat twice as well.

They would do so by alternating with each other. This means that in a rectangle with (-2, -3), (- 2 . 3, 1 . 6), ( 4 . 6 , 1. 6 ), the fourth vertex would be the two x and y values that are yet to repeat which would be:

( 4. 6, - 3 ).

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Answer: The Correct answer is E (2,pie/6)

Step-by-step explanation:

To find the polar coordinates of a point given its Cartesian coordinates (x, y), we can use the following formulas:

r = √(x^2 + y^2)

θ = atan2(y, x)

where r is the radial distance from the origin to the point, and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin and the point.

Given the Cartesian coordinates (x, y) = (√3, 1), we can plug these values into the formulas to find the polar coordinates:

r = √(√3^2 + 1^2) = √(3 + 1) = 2

θ = atan2(1, √3)

Using a calculator, we can find that θ is approximately 0.5236 radians.

So, the polar coordinates of the point (√3, 1) are (r, θ) = (2, 0.5236 radians).

Answer: -161

Step-by-step explanation: you solve by plugging 9 in for x so you get f(9) = -2(9)^2 +9-8 you solve using PEMDAS and you get -161

The graph that represents the function f(x) = -2sin(x) +37 is graph D

The graph of the function f(x) = -2sin(x) +37 is a sinusoidal wave with an amplitude of 2 and a vertical shift of 37. The negative sign in front of the sine function indicates that the wave is inverted or reflected about the x-axis.

In this graph, the maximum value of the function is 39 (when x = 0) and the minimum value is 35 (when x = π).

In conclusion, the graph that represents the function f(x) = -2sin(x) +37 is graph D

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The solutions are x = 0 and x = 3π/4, written as 0, 2.35619 (in radians).

We can factor out 6 tan(x) from the left-hand side of the equation:

6 tan(x) (tan(x) + 1) = 0

This equation is satisfied if either 6 tan(x) = 0 or tan(x) + 1 = 0.

If 6 tan(x) = 0, then tan(x) = 0. This occurs when x = 0, π, 2π, etc. However, we need to restrict our attention to the interval [0, 27), so the only solution in this case is x = 0.

If tan(x) + 1 = 0, then tan(x) = -1. This occurs when x = 3π/4 + nπ, where n is an integer. However, we need to restrict our attention to the interval [0, 27), so the only solution in this case is x = 3π/4.

Therefore, the solutions of the equation 6 tan²(x) + 6 tan(x) = 0 in the interval [0, 27) are x = 0 and x = 3π/4, which can be written as the comma-separated list: 0, 2.35619.

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It looks like there are five data points in the box plot, representing Juan's total sales during each shift. The third data point is $200, which is the median value. Since there are an odd number of data points, we know that the median is exactly in the middle of the data set. This means that two of the data points are less than $200, and two of the data points are greater than $200.

The last data point is $300, which is the maximum value. So we know that only one of the data points is between $200 and $300. Therefore, the fraction of Juan's shifts that had total sales of $225 or more is 1/5, or 20%.

Answer:

Step-by-step explanation:

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

[tex](3 + 2x)(2 + 2x) = 7[/tex]

[tex]6 + 10x + 4{x}^{2} = 7[/tex]

[tex]4 {x}^{2} + 10x - 1 = 0[/tex]

Answer:

4x2 + 10x − 1 = 0

Step-by-step explanation:

Answer:

To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The expression is:

1234 - 4566 / 45.44 + 67 * 755.34

First, we need to perform the division operation since it comes before addition and multiplication.

4566 / 45.44 = 100.50

Now, we can substitute that into the expression:

1234 - 100.50 + 67 * 755.34

Next, we need to perform the multiplication operation:

67 * 755.34 = 50,548.78

Now, we can substitute that into the expression:

1234 - 100.50 + 50,548.78

Next, we can perform the addition and subtraction operations:

1234 + 50,448.28 = 51,682.28

Therefore, the result of the expression is 51,682.28.

The sinusoidal function of the form y = A·sin(k·x) + C that matches the function in the graph is; y = 4·sin((π/5)·x) - 1

A sinusoidal function is a periodic function based on the sine or cosine functions.

The form of the function is y = A·sin(k·x)

The peak and trough of the graph are; (-7.5, 3), (-2.5, -5)

The amplitude of the function is therefore; A = (3 - (-5))/2 = 4

The vertical shift of the function is; C = (3 + (-5))/2 = -1

The period of the graph (Number of input x-values required to complete a cycle) = 2.5 - (-7.5) = 10 = 2·π/k

Therefore; k = 2·π/10 = π/5

The horizontal shift can be found as follows;

When x = 0, y = -1, therefore;

-1 = 4 × sin(π/5 × (0 - θ)) - 1

arcsin(0/4) = π/5 × (- θ)

θ = 0

The sinusoidal function is therefore;

y = 4·sin((π/5)·x) - 1

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The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:522

Step-by-step explanation:

cut the shape on top to make a triangle and rectangle so then it would be 25x18=450 then for the triangle it would be 18x8=72 450+72=522

2401/16 square inches

Step-by-step explanation:

Given:

The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is  in long.

To find: the area of the whole quilt

Solution:

Side of each quilt =

Quilt is in the form of a square such that area of square is given by

Therefore, area of quilt =   square inches

The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.

The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:

Sₙ = a(1 - rⁿ)/(1 - r),

where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:

S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))

Simplifying the expression, we get:

S₈ = 761/2

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Answer:

SA = 48 cm²

Step-by-step explanation:

the surface area (SA) is the sum of the areas of the 5 faces.

1 square and 4 congruent triangles form the pyramid

area of square = 4 × 4 = 16 cm²

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

here b = 4 and h = 4

area = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²

area of 4 triangles = 4 × 8 = 32 cm²

SA = 16 + 32 = 48 cm²

From the graph, Jerimiah walks along 44 city blocks.

Hence the correct option is (D).

It is given that each unit on the grid represents 1 city block.

From the given graph we can see that

Number of city block between Restaurant and Museum = 7

Number of city blocks between Museum and Hotel = 4

Number of city blocks between Hotel and Arena = 7

Number of city blocks between Arena and Restaurant = 4

Total number of city blocks along the rectangular path = (7 + 4 + 7 + 4) = 22 city blocks.

Jerimiah walks twice around the rectangular path.

So Jerimiah walks through = 2*22 = 44 city blocks.

Hence the correct option will be (D).

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The question is incomplete. The complete question will be -

USD 438

Step-by-step explanation:If we add 20% to the gross amount of USD 365, the total amount would be:USD 365 + 20% of USD 365 = USD 365 + (0.20 * USD 365) = USD 365 + USD 73 = USD 438

If the gross amount is USD 365, then the net amount after adding 20 percent is USD 438.

Net amount refers to the final total after deductions or additions have been made whereas gross amount refers to the total amount before any deductions or additions have been made.

Us the formula:

Net Amount = Gross Amount + (Gross Amount x Percentage)

Given that,

Gross amount = $365

The given percentage = 20%

We can write 20% = 20/100

So, 20% = 0.2

Now put the values into the formula

Net amount  = 365 + (365 x 0.2)

Net amount  = 365 + 73

Net amount  = 438

Hence,

The net amount is USD 438.

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The sum of the geometric series is -12,276.

So, the correct answer is C. -12,276.

To find the sum of the geometric series, we can use the formula:

[tex]S = a \times (1 - r^n) / (1 - r),[/tex]

where S is the sum of the series,

a is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the first term (a) is 6(2) = 12, the common ratio (r) is 2, and the number of terms (n) is 10.

Plugging these values into the formula, we get:

[tex]S = 12 \times (1 - 2^{10} ) / (1 - 2).[/tex]

Calculating further:

[tex]S = 12 \times (1 - 1024) / (-1) = 12 \times 1023 = 12276.[/tex]

Therefore, the sum of the geometric series is -12,276.

So, the correct answer is C. -12,276.

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The graph of the function f(x) with vertex (1, 2) and another point (0, 2) is shown below.

Consider a function f(x) = 3x² - 6x + 2

We know that the graph of quadratic function is a parabola.

We graph the function f(x)

The graph of function f(x) is shown below.

From the graph of f(x), we can observe that the vertex of parabola is (1, 2)

For x = 0 the value of the function f(x) would be,

f(x) = 3x² - 6x + 2

f(0) = 3(0)² - 6(0) + 2

f(0) = 0 - 0 + 2

f(0) = 2

This means that the y-intercept of f(x) is (0, 2)

Therefore, the reuired graph of the function f(x) is shown below.

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Answer:

  $9.34 per square foot

Step-by-step explanation:

You want the cost per square foot of a 36 foot square building that costs $12,099.

The cost per square foot is found by dividing the cost by the number of square feet. That area is found as the square of the side length:

  A = s²

  A = (36 ft)² = 1296 ft²

Then the cost is ...

  cost per square foot = ($12099)/(1296 ft²) ≈ $9.34/ft²

The cost of the building is about $9.34 per square foot.

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Answer:

When n is greater than 1/2 or always true

n > 1/2

Step-by-step explanation:

Rewrite.

0+0+6(n−1)=2(n+1)

Simplify by adding zeros.

6(n−1)=2(n+1)

Apply the distributive property.

6n+6⋅−1=2(n+1)

Multiply 6 by −1.6n−6=2(n+1)

Simplify 2(n+1).

6n−6=2n+2

Move all terms containing n to the left side of the equation.

4n−6=2

Move all terms not containing n to the right side of the equation.

4n=8

Divide each term in 4n=8 by 4 and simplify.

n=2

The surface area of the cube of side x-4 in terms of x is 6x² - 48x + 96.

Given length of a side of a cube (a) = x-4

The formula for finding the surface area of a cube = 6a²

By, substituting the 'a' value in the above formula we can obtain the surface area of the cube.

6a² = 6 * (x-4)²                           [a = x-4]

      = 6 * (x² - 8x + 16)

      = 6x² - 48x + 96

From the above analysis, we can conclude that the surface area of the given cube in terms of 'x' is 6x² - 48x + 96.

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Basd on the information about the triangle, DF is approximately 5.68 units long.

First, let's find the length of EF using the sine function:

sin 20° = EF / DE

cos 20° = 6 / DE

DE = 6 / cos 20°

Now that we know DE, we can solve for EF:

sin 20° = EF / DE

EF = DE * sin 20°

EF = (6 / cos 20°) * sin 20°

EF ≈ 1.95

DF^2 = DE^2 - EF^2

DF^2 = (6 / cos 20°)^2 - (1.95)^2

DF ≈ 5.68

DF is approximately 5.68 units long.

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Answer: The answer is 171.2 Miles

Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.

Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.

An expression that represents the amount of Huang's change include the following: A. 100 – (12(3x)).

In this scenario and exercise, you are required to write and determine an expression that represents the amount of change which Huang should receive from the seller.

This ultimately implies that, an expression that models or represents the amount of Huang's change would have the form;

Huang's change = Money presented - Total cost of 3 shirts

Huang's change = 100 - (12(3x))

By simplifying further, we have the following expressions;

Huang's change = 100 - 36x

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