What kind of sequence is this? –41, –51, –61, –71

Answer:

y= - 13/15x + 6/5

Step-by-step explanation:

The solutions on the interval [0, 2π) are: x = π/4, 3π/4, 5π/4, 7π/4.The circle answer is 4

The given equation is 1 - cos x = sin x.

The required task is to solve the equation on the interval [0, 2π).

Solution:

1 - cos x = sin x

Rearranging the terms, we get1 - sin x = cos x

Squaring both sides, we get1 - 2 sin x + sin² x = cos² x + sin² x - 2 cos x + 1

Simplifying the above equation, we get2 sin² x - 2 cos x = 0

We know that sin² x + cos² x = 1

Dividing the above equation by cos² x,

we get2 tan² x - 2 = 0⇒ tan² x = 1⇒ tan x = ±1If tan x = 1, then x = π/4 and 5π/4

satisfy the equation on the interval [0, 2π).

If tan x = -1, then x = 3π/4 and 7π/4

satisfy the equation on the interval [0, 2π).

Therefore, the solutions on the interval [0, 2π) are: x = π/4, 3π/4, 5π/4, 7π/4.The circle answer is 4.

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Sample Response: Positive fractions are to the right of zero, and negative fractions are to the left. Fractions increase as you go from left to right. They decrease as you go from right to left.

Check all that you included in your response.

I learned to locate and plot fractional distances on a number line.

Positive fractions are to the right of zero.

Negative fractions are to the left of zero.

From left to right, fractions increase.

From right to left, fractions decrease.

Negative fractions are to the left of zero, whereas positive fractions are to the right. Fractions get larger as you move from left to right. They get smaller as you move from right to left.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.

|____|____|____|____|____|____|____|____|____|____|

-1/4   -1/5   -1/6   -1/7   -1/8       0       1/8    1/7     1/6     1/5    1/4

Negative fractions are to the left of zero, whereas positive fractions are to the right. Fractions get larger as you move from left to right. They get smaller as you move from right to left.

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Answer: 3.6 ft

Step-by-step explanation:

Since the weight is 1500 lb, we can substitute P = 1500.

This means we have 1500 = 5400/D.

1500D = 5400

D = 5400/1500

D = 3.6

The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is \(f(x,y,z) =xyz^{2} + e^{\pi }\)   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = \((yz^{2} )i + (xz^{2} )j + (2xyz)k\) ,

So , we can write the partial derivatives function of potential function as :

\(\frac{\partial f}{\partial x} = yz^{2}\) ; \(\frac{\partial f}{\partial y} = xz^{2}\) ; \(\frac{\partial f}{\partial z} = 2xyz\),

On Antidifferentiating any of the above three partial derivatives ,

we get ; \(f=xyz^{2} + C\) , here the constant C can take any value ,

so , we take C as \(e^{\pi }\) .

Therefore , the potential Function is \(f(x,y,z) =xyz^{2} + e^{\pi }\) .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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Answer:

each chicken cost 3.65

Step-by-step explanation:

divide 18.25 by 5 and you'll get 3.65

The two buses are initially 515 miles apart and are moving toward each other. They will pass each other around 2:30 P.M.

To solve this problem, we can use the concept of relative speed. The combined speed of the two buses is the sum of their individual speeds, which is 48 + 55 = 103 miles per hour.

We can calculate the time it takes for the buses to meet by dividing the initial distance between them (515 miles) by their combined speed (103 miles per hour):

Time = Distance / Speed

Time = 515 miles / 103 miles per hour

Time ≈ 5 hours

Therefore, the two buses will pass each other approximately 5 hours after they start traveling toward each other. To determine the exact time, we need to consider the starting time (9:30 A.M.) and add 5 hours to it. So, they will pass each other around 2:30 P.M.

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Answer:

A' = (-4, 4)

B' = (0, 0)

C' = (2, 5)

Step-by-step explanation:

When a point is reflected across the line y = -x, the x-coordinate becomes -y, and the y-coordinate becomes -x. Therefore, the mapping rule is:

Given vertices of triangle ABC:

Therefore, if we reflect the given points across the line y = -x, the coordinates of the reflected points are:

\(\begin{aligned}& \sf A = (-4, 4)& \implies\;\; \sf A'& =\sf (-4,-(-4))=(-4,4)\\& \sf B = (0, 0) &\implies\;\; \sf B' &= \sf (-0, -0)=(0,0)\\& \sf C = (-5, -2)& \implies\;\; \sf C' &= \sf (-(-2),-(-5))=(2,5)\end{aligned}\)

Answer:

1/3 is less than 2/3

7/9 is greater than 2/3

4/10 is less than 2/3

4/6 is equal to 2/3

Answer:

30

Step-by-step explanation:

rise over run = slope (m)

(4,120) and (2,60)

m=(y2-y1)/(x2-x1)

m=(60 - 120)/(2-4)

m= ( -60)/( -2)

m=30

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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Step-by-step explanation:

1. set of even numbers

3. set of months that start with J

4. set of vowel sounds

5. set of days that start with T

6. set of perfect squares

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Answer:

The thickness of the new dirt cover is 0.144 yards.

Step-by-step explanation:

Dimension of garden = 25 feet by 25 feet.

Volume of soil bought = 10 cubic yards

Volume = length x width x height

But,

1 foot = 0.333333 yard

So that,

25 feet = 25 x 0.333333

            = 8.33333 yards

The new dimension of the garden = 8.33333 yards by 8.33333  yards.

Let the thickness of the new dirt cover be represented by h.

Thus,

Volume = 8.33333 x 8.33333 x h

10 = 69.44439 x h

h = \(\frac{10}{69.44439}\)

  = 0.144

h = 0.144 yards

The thickness of the new dirt cover is 0.144 yards.

From the concepts and properties of triangles, m∠BDC is 26°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is equal to 180°.

In the given ΔABD, line segment AD and BD are equal and hence it is an isosceles triangle.

Therefore,

x° + x° + 70° = 180°.

2x° = 110°.

x = 55°.

So, m∠DAB = m∠DBA = 55°.

We know the sum of linear pair of angles is 180°.

Therefore, m∠ABD + m∠DBC = 180°.

55° + m∠DBC = 180°.

m∠DBC = 125°.

Now,

m∠BDC + m∠DCB + m∠CBD = 180.

m∠BDC + 29° + 125° = 180°.

m∠BDC = 26°.

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Answer:

1/2

Step-by-step explanation:

1/2 x 1/2 = 1/4

3/4 x 1/2 = 3/8

1/1 x 1/2 = 1/2

5/4 x 1/2 = 5/8

(5/4 = 1 1/4)

The graph of y = f(x) will have a downward concave shape for x < 0, and an upward concave shape for x > 0. The curve will have a local maximum at x = 0.

To determine this :

A curve with these properties is called a "saddle shape" or "saddle point." To sketch such a curve, imagine the graph of y = f(x) as a surface in 3D space, where the height at any point (x, y) is given by f(x). The curve y = f(x) is the intersection of this surface with the xy-plane.

The condition f"(x) < 0 for x < 0 means that the surface is "curving downward" in the negative x direction, while f"(x) > 0 for x > 0 means that the surface is "curving upward" in the positive x direction.

Therefore, the graph of y = f(x) will have a downward concave shape for x < 0, and an upward concave shape for x > 0. The curve will have a local maximum at x = 0.

The resulting graph will resemble a horse saddle, with the "saddle point" at the origin.

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Answer:

$618.24

Step-by-step explanation:

The area of the room is 224. Then for each square feet is 2.76 do multiplying that you get the answer.

Answer:

Last one.

Step-by-step explanation:

To enhance your chances of being accepted into an elite university with a high SAT score (1600/1600) but a lower cumulative GPA (3.4), it's crucial to focus on several key strategies.

The first paragraph provides a concise summary of the answer, while the second paragraph explains the solution in more detail.

Although a lower cumulative GPA may present a challenge, there are steps you can take to improve your chances of being accepted into an elite university. Firstly, focus on excelling in your junior and senior years to demonstrate an upward trend in your academic performance. Take challenging courses and aim for strong grades.

Secondly, highlight your unique strengths and accomplishments in your application, such as impressive extracurricular activities, leadership positions, and impactful community involvement.

Additionally, write a compelling personal statement that explains any extenuating circumstances during your freshman and sophomore years and emphasizes personal growth and resilience. Lastly, consider showcasing your talents through outstanding recommendation letters and performing well on any additional standardized tests or subject-specific exams.

Present a well-rounded application that showcases your potential and highlights your dedication and growth since your earlier academic struggles

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To find the surface area , first calculate the height of the triangle.

We can divide it into 2 right triangle and apply the pythagorean theorem:

c^2 = a^2+b^2

Where:

c= hypotenuse = 14

a = 14/2 = 7

b= height

Replacing:

14^2 = 7^2 + b^2

Solve for b

196= 49+b^2

196-49=b^2

147 = b^2

√147= b

b= 12.1 ft

Now, calculate the area of each rectangular face and each triangular face:

Area of a triangle = 1/2 x base x height = 1/2 x 14 x 12.1 = 84.8 ft2

Area of a rectangle = length x width = 14 x 10 = 140 ft2

Since it has 2 triangular faces and 3 rectangular faces

SA = 2 (84.7) + 3 (140) = 169.4+420= 589.7 ft2

Answer:

7g^2 - 13g

Step-by-step explanation:

2g(4g+3)= 8g^2 + 6g

g(g-7)+ g^2 - 7g

8g^2 + 6g = g^2 - 7g

7g^2 = -13g

The following numbers are rounded up as follows:

8.6134

5.5218

Rounding up a number means to round a number to the smallest integer that is not less than it, or to some other greater value.

Thousandth, hundredth and tenth are used after the decimal point.

8.6134

5.5218

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The probability that the artist chosen will be a painter or a photographer is 3/4

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

To solve this exercise the formula and the procedure that we have to use for probability is:

probability= (achieving success / possible outcomes)

Achieving success = 7 painters + 5 photographer = 12

Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16

Applying the formula to calculate the probability we get:

probability= (achieving success / possible outcomes)

probability= 12/16

Simplifying:

probability= 3/4

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Answer: B, C, and E

Step-by-step explanation:

The values must add up to 180 for it to be a triangle. X and Y especially need to add up to 120.

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

A rational number

Step-by-step explanation:

A rational number is a number that can be made by dividing two integers (an integer is a number with no fractional part). The word comes from "ratio". A fraction can be divided and when it is it is a rational number.

The problem in standard LP form can be represented as:

Minimize:

\(f = 5x_1 + 4x_2 - x_3\)

Subject to:

\(x_1 + 2x_2 + x_3 + s_1 = 21\\2x_1 + x_2 + x_3 + s_2 = 24\\x_1, x_2, x_3, s_1, s_2 \geq 0\)

To convert the given problem to the standard LP (Linear Programming) form, we need to rewrite the objective function and the constraints as linear expressions.

Objective function:

Minimize \(f = 5x_1 + 4x_2 - x_3\)

Constraints:

\(x_1 + 2x_2 + x_3 \geq 21\\2x_1 + x_2 + x_3 \geq 24\\x_1, x_2 \geq 0\)

\(x_{3}\) is unrestricted in sign (can be positive or negative)

To convert the constraints into standard LP form, we introduce slack variables and convert the inequalities into equalities:

Since \(x_{3}\) is unrestricted in sign, we don't need to introduce any additional variables or constraints for it.

Finally, we ensure that all variables are non-negative:

\(x_1, x_2, x_3, s_1, s_2 \geq 0\)

The problem in standard LP form can be represented as:

Minimize:

\(f = 5x_1 + 4x_2 - x_3\)

Subject to:

\(x_1 + 2x_2 + x_3 + s_1 = 21\\2x_1 + x_2 + x_3 + s_2 = 24\\x_1, x_2, x_3, s_1, s_2 \geq 0\)

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