Select the correct location on the number line,
Plot on the number line.

Answer: 28282

Step-by-step explanation:

I think

Answer:

4

Step-by-step explanation:

\(\sqrt{4} *\sqrt{4}\\=2*2\\=4\)

Answer:

4

Step-by-step explanation:

√4 × √4 = 2 × 2 = 4

The degree of the sum or difference of two polynomial functions is equal to the maximum degree among the individual functions.

When adding or subtracting polynomial functions, the degree of the resulting polynomial function is determined by the highest degree term in the sum or difference.

Consider two polynomial functions f(x) and g(x) with degrees n and m, respectively. The general form of these functions can be written as:

f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀

g(x) = bₘxᵐ + bₘ₋₁xᵐ⁻¹ + ... + b₁x + b₀

When we add or subtract these functions, the resulting polynomial function (f + g)(x) or (f - g)(x) will have terms of the form (aₖ + bₖ)xᵏ, where k is the degree of the resulting polynomial.

Since each term in (f + g)(x) or (f - g)(x) is the sum or difference of terms from f(x) and g(x), the highest degree term will be obtained when the terms with the highest degrees in f(x) and g(x) are combined.

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Answer:

A. tan(2π/3) = \(-\sqrt{3}\)

The image of the square S under the given transformation is a parallelogram in the (x, y) plane, defined by the points (0, 0), (1, 0), (0, 1), and (1, 1).

To find the image of the set S under the given transformation, we substitute the coordinates of the points in S into the transformation equations. The set S is a square bounded by the lines u = 0, u = 1, v = 0, and v = 1.

Let's consider the four corners of the square:
Corner 1: (u, v) = (0, 0)
Corner 2: (u, v) = (0, 1)
Corner 3: (u, v) = (1, 0)
Corner 4: (u, v) = (1, 1)

For each corner, we apply the transformation:
Corner 1: (x, y) = (v, u(1 - v^2)) = (0, 0)
Corner 2: (x, y) = (v, u(1 - v^2)) = (1, 0)
Corner 3: (x, y) = (v, u(1 - v^2)) = (0, 1)
Corner 4: (x, y) = (v, u(1 - v^2)) = (1, 1)

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1/3 of the volunteers can complete the 8-hour workday

Total number of volunteers = 10

If it takes 1 volunteer = 24 hours = 1 day

It would take x number of volunteers = 8 hours

To find 'x' , cross multiply

We have,
x * 24 hours = 8 hours * 1

24x = 8

Make 'x' the subject of formula

x = 8/ 24

x = 1/3

Therefore, 1/3 of the volunteers can complete the 8-hour workday

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The teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

In order to help the students understand that the triangle is equivalent to half a square, the teacher can adopt different methods, including the following:

1. Drawing diagrams of the triangle and the square to show the comparison. The teacher can draw diagrams of a triangle and a square on the board and label the different parts.

They can then show the students that a triangle can be created by halving the square diagonally. This way, the students will be able to visualize the comparison and understand it better.

2. Demonstrating the concept practically. The teacher can also demonstrate the concept by using physical objects such as paper or cardboard.

They can show the students how to create a triangle by folding a square diagonally and cutting it along the fold. This way, the students will be able to see the practical application of the concept.

3. Using real-world examples. The teacher can also use real-world examples to help the students understand the concept better.

For example, they can show the students pictures of tents or rooftops that are shaped like triangles and explain how they are related to squares.

4. Conducting group discussions. The teacher can conduct group discussions where the students can share their understanding of the concept and ask questions.

This way, the students will be able to learn from each other and clarify any doubts they may have.

Overall, the teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

The key is to use different approaches that cater to different learning styles and to encourage the students to participate actively in the learning process.

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The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The total return on the 3 percent preferred stock for last year is $2.00.

To calculate the total return on the preferred stock, we need to consider two components: capital appreciation and dividends received.

The capital appreciation represents the increase in the stock's price over time. In this case, the stock was purchased for $97.06 and its current market price is $99.06. To calculate the capital appreciation, we subtract the initial purchase price from the current market price:

Capital Appreciation = Current Market Price - Purchase Price

= $99.06 - $97.06

= $2.00

Therefore, the capital appreciation of the stock is $2.00.

Preferred stocks typically pay fixed dividends at regular intervals. Since the question does not provide any information about dividends received, we assume that no dividends were paid during the last year. Hence, the dividend component of the total return is zero.

To calculate the total return, we sum up the capital appreciation and dividend components:

Total Return = Capital Appreciation + Dividends

= $2.00 + $0.00

= $2.00

Therefore, the total return for the last year on the 3 percent preferred stock is $2.00.

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13 is the value of z from the given figure.

The properties of the triangle are:

From the given figure,

∠ABE + ∠EBC =. 180

∠EBC = 180- ∠ABE

∠EBC = 180 - 9z -----(1)

∠ECB + 115 = 180

∠ECB = 65-----(2)

IN ∆EBC

∠BEC + ∠ECB + ∠EBC = 180

4Z + 180- 9Z + 65 = 180 ---------(from eq i & ii)

-5Z = -65

Z = -65/-5y

Z = 13

The value of z from the given figure is 13.

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Complete question:

Using function concepts, it is found that the correct option is given by:

D. The function is negative when x<0

In this problem, the graph of the function is the red line, and:

Thus, option D is correct.

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Answer:

A. 1/cos(2x)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

on edge

Samuel's family took a road trip to Mount Rushmore. Samuel fell asleep after they had traveled 990 miles. If the total length of the trip was 1000 miles, then 99% of the total trip they had completed together and only 10 miles Samuel fell asleep.

We can use the following formula to calculate the percentage of the overall trip that Samuel had completed when he fell asleep:

(Part/Whole) * 100 = Percentage

In this instance, the portion is the distance traveled when Samuel fell asleep, which is 990 miles, and the total trip length is 1000 miles. Substituting the values in the formula Percentage equals (990/1000) multiplied by 100 = 99%

As a result, when Samuel fell asleep, the family had completed 99% of the entire journey. This meant that they were almost there, with only 10 miles remaining.

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To give your daughter $50,000 towards her college education in 15 years, you must set aside approximately $14,803.42 today.

To calculate the amount of money you need to set aside today, we can use the concept of future value of a lump sum. The future value is the amount of money an investment will grow to in the future, given a certain interest rate and time period.

In this case, we want to determine the present value (the amount you need to set aside today) to achieve a future value of $50,000 in 15 years, assuming an annual interest rate of 9 percent. The formula to calculate present value is:

Present Value = \(Future Value / (1 + Interest Rate)^T^i^m^e\)

Plugging in the values, we have:

Present Value = \($50,000 / (1 + 0.09)^1^5\)

Present Value ≈ $14,803.42

Therefore, you would need to set aside approximately $14,803.42 today in order to accumulate $50,000 for your daughter's college education in 15 years, assuming an annual interest rate of 9 percent.

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Answer:

Vertical asymptote x= 1

Horizontal asymptote y= -1

Step-by-step explanation:

Answer:

no asymptotes

Step-by-step explanation:

since y=-3x-1-1 is not a ratinal expression there are no asymptotes.

Answer:

the 1/2w +22 one is a binomial

Step-by-step explanation:

a binomial is a equation with one two separate numbers AFTER simplifcation. so "1+1" is not a binomial because its equal to just 2, but "1 + x" is a binomial because its simplifed

Part 1 The turning point for the function y = 3x² - 5x is (5/6, -1/12). The given function is y = 3x² - 5x. the maxima and minima values for the function y = x³ - 4x + 6 are 5.0796 and 8.9204 respectively.

Now we need to locate the co-ordinates of the turning point and determine whether it is a maxima or minima by examining the sign of the slope either side of the turning point. We need to take the derivative of the given function

y = 3x² - 5x using power rule of derivative.

dy/dx = 6x - 5

Now to find the critical point we equate the above derivative equation to zero.

6x - 5 = 0 (or) x = 5/6

Now let us examine the sign of the slope on either side of x = 5/6

When x < 5/6 , dy/dx < 0.

which implies that the slope of the curve is negative to the left of x = 5/6

When x > 5/6 , dy/dx > 0.

which implies that the slope of the curve is positive to the right of

x = 5/6.

Hence, we can conclude that the turning point for the function

y = 3x² - 5x is (5/6, -1/12).

Since the sign of the slope changes from negative to positive, we can infer that it is a minimum point.

Part 2The given function is

y = x³ - 4x + 6.

Now we need to find the maxima and minima values for the function.

First, we need to take the derivative of the given function

y = x³ - 4x + 6 using power rule of derivative.

dy/dx = 3x² - 4

Now to find the critical points we equate the above derivative equation to zero.

3x² - 4 = 0 (or)

x = ±sqrt(4/3)

When x = -sqrt(4/3).

dy/dx is negative which implies that it is a maxima.

When x = +sqrt(4/3),

dy/dx is positive which implies that it is a minima.

Now we need to substitute these critical points in the original function to get the maxima and minima values for the function.

When x = -sqrt(4/3),

y = (-sqrt(4/3))³ - 4(-sqrt(4/3)) + 6

= 5.0796 (approx)

When x = +sqrt(4/3),

y = (+sqrt(4/3))³ - 4(+sqrt(4/3)) + 6

= 8.9204 (approx).

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Answer:

x=3

Step-by-step explanation:

When you substitute x = 3 to both equations, you get y = -4 for both so that is a solution

Step-by-step explanation:

The wavelength of x rays are between 1 and 10 nanometers.

1 nm = 10⁻⁹ m

The greatest wavelength is 10 nm.

10 nm = 10 × 10⁻⁹ m

= 10⁻⁸ m

Here, (-8) is the exponent of 10.

Hence, the wavelength of the greatest wavelength of x-ray is 10⁻⁸ m.

A set of transformations that have been performed on the graph of f(x) = ∛x to obtain the graph of g(x) = 1/4(∛(x + 3) + 6 include the following:

A. Translate the graph up

B. Stretch the graph away from x-axis

E. Translate the graph to the left

In Mathematics, the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

In conclusion, we can logically deduce that the graph of the parent function was stretched away from x-axis.

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Step-by-step explanation:

9 metres = 900cm

Scale = Object length :image length

= 900:12

= 75:1

This means that every 75cm length of the court is represented by 1cm on the drawing paper.

Answer:

9.6 ounces of butter, 8 ounces of sugar, 12 ounces of flour, 4 eggs

Explanation: 20 / 16 = 4/5. 16 is four-fifths of 20. So multiply 4/5 with everything.

12 * 4/5 = 9.6 ounces

10 * 4/5 = 8 ounces

15 * 4/5 =  12 ounces

5 * 4/5 = 4 eggs

We have defined the criteria for SAS congruency of triangles.

What is SAS?

The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."

According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.

Hence, we have defined the criteria for SAS congruency of triangles.

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Answer:

F. p \(\leq\) -4/3

Step-by-step explanation:

3p + 6 \(\leq\) 2

Subtract 6 from both sides.

3p \(\leq\) -4

Divide by 3 on both sides.

p \(\leq\) -4/3

Step-by-step explanation:

3 p + 6 <=  2       subtract 6 from both sides of the equation

3 p <=  -4               divide through by 3

p  ≤ - 4/3        Done.

When a cone with a volume of 5000 m³ is dilated by a scale factor of 15, the volume of the resulting cone is 3375000 m³.

The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. Since the scale factor of 15 applies to all dimensions of the cone, the new radius and height will be 15 times the original values. Let's assume the original cone has radius r and height h.

After dilation, the new cone will have a radius of 15r and a height of 15h. Plugging these values into the volume formula, we get

V' = (1/3)π(15r)²(15h) = (1/3)π(15²)(r²)(h) = 3375V.

Given that the original cone has a volume of 5000 m³, we can calculate the volume of the resulting cone by multiplying 5000 by 3375:

V' = 5000× 3375 = 3375000 m³.

Therefore, the volume of the resulting cone, after being dilated by a scale factor of 15, is 3375000 m³.

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To find the surface area of the smaller pyramid, we can use the concept of similarity. The ratio of the base areas of the two pyramids is equal to the square of the ratio of their heights.

Let's call the height of the larger pyramid h1 and the height of the smaller pyramid h2. The ratio of their heights is h1/h2 = √(base area of larger pyramid/base area of smaller pyramid) = \(√(16 cm^2/12.2 cm^2).\)

Given that the surface area of the larger pyramid is 56 cm^2, we can find the surface area of the smaller pyramid by using the formula: surface area of smaller pyramid = (base area of smaller pyramid) * (height of smaller pyramid + (base perimeter of smaller pyramid * (h1/h2)) / 2.

Plugging in the values, we get: surface area of smaller pyramid =\(12.2 cm^2 * (h2 + (4 * h1/h2)) / 2.\)

We can simplify this equation to: surface area of smaller pyramid = \(12.2 cm^2 * (h2 + 2h1/h2).\)

To find the surface area of the smaller pyramid, we need to substitute the value of h1 and the given surface area of the larger pyramid into this equation. Unfortunately, the information given does not include the height of the larger pyramid. Therefore, we cannot determine the surface area of the smaller pyramid.

Regarding the second part of your question, without any information about the dimensions or properties of the other triangular prisms, it is impossible to determine which prism is similar to the described prism.

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The correct answer is the first Option i.e., 40.1 cm². The surface area of the smaller pyramid is approximately 40.1 cm². The surface area of a pyramid is found by adding the area of the base to the sum of the areas of the lateral faces. Since the two pyramids are similar, the ratio of their surface areas will be the square of the ratio of their corresponding side lengths.

Let's find the ratio of the side lengths first. The ratio of the base areas is given as 12.2 cm² : 16 cm². To find the ratio of the side lengths, we take the square root of this ratio.

    \(\sqrt {\frac{12.2}{16} } = \sqrt {0.7625} \approx 0.873\)

Now, we can find the surface area of the smaller pyramid using the ratio of the side lengths. We know the surface area of the larger pyramid is 56 cm², so we can set up the equation:

    (0.873)² × surface area of the smaller pyramid = 56 cm²

Solving for the surface area of the smaller pyramid:

    (0.873)² × surface area of the smaller pyramid = 56 cm²
=> Surface area of the smaller pyramid = 56 cm² / (0.873)²

Calculating this value:

    Surface area of the smaller pyramid ≈ 40.1 cm²

Therefore, the surface area of the smaller pyramid is approximately 40.1 cm².

In conclusion, the surface area of the smaller pyramid is approximately 40.1 cm².

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the volume of the rectangular prism is 1,080 cubic inches.

Why is it?

The volume V of a rectangular prism is given by the formula:

V = length x width x height

Substituting the given values, we get:

V = 10 inches x 18 inches x 6 inches

Simplifying, we get:

V = 1,080 cubic inches

Therefore, the volume of the rectangular prism is 1,080 cubic inches.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces, where each pair of opposite faces are congruent and parallel to each other. It is also known as a rectangular parallelepiped.

A rectangular prism is characterized by its length, width, and height or depth. The length is the measurement of the longest side of the prism, the width is the measurement of the shorter side, and the height or depth is the measurement of the perpendicular distance between the two faces that are parallel to each other.

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Answer:

C)

Step-by-step explanation:

The highest point on the graph for c) is in the first quadrant (where x=2 would be).

If you had an equation, you would be able to find critical points on the function by setting the numerator and denominator equal of f'(x)=0 and solve. You'd have to evaluate f(x) at these critical points and end points to figure that out. This is, if you're in calculus and you would ever need assistance otherwise!

Answer:

$10.26

Step-by-step explanation:

....................

Answer:

712.5

Step-by-step explanation: