Which of the following number lines shows the solution to the inequality given below? 2x − 3 < -9 OR 2x − 3 > 3 A. -10-8-6-4-202468101214 B. -10-8-6-4-202468101214 C. -10-8-6-4-202468101214 D. -10-8-6-4-202468101214

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Part A:

To find the linear form of vector u=ST, we subtract the coordinates of the initial point S from the coordinates of the terminal point T:

u = T - S

u = (5, 19) - (14, 23)

u = (-9, -4)

Therefore, the linear form of vector u is u = -9i - 4j.

Part B:

To find 4u - 5v, we first need to find the linear forms of vectors u and v.

u = -9i - 4j

v = B - A

v = (32, 9) - (7, 17)

v = (25, -8)

Now we can calculate 4u - 5v:

4u - 5v = 4(-9i - 4j) - 5(25i - 8j)

4u - 5v = (-36i - 16j) - (125i - 40j)

4u - 5v = -36i - 16j - 125i + 40j

4u - 5v = (-36i - 125i) + (-16j + 40j)

4u - 5v = -161i + 24j

Therefore, 4u - 5v is equal to -161i + 24j.

Part C:

To determine if vectors t and u are parallel, orthogonal, or neither, we can use the dot product. The dot product of two vectors is given by the formula:

t · u = t1u1 + t2u2

Given vector 1 = -161 + 36j and vector u = -9i - 4j, we can calculate the dot product:

t · u = (-161)(-9) + (36)(-4)

t · u = 1449 - 144

t · u = 1305

Since the dot product is not equal to zero, vectors t and u are not orthogonal.

Part D:

To find another vector w that has the same relationship to vector t as vector u, we can use the concept of scalar multiplication. If we multiply vector t by a scalar value, we can obtain vector w.

Let's choose a scalar value of 3. We can calculate w as:

w = 3t

w = 3(-161i + 36j)

w = -483i + 108j

Therefore, vector w = -483i + 108j has the same relationship to vector t as vector u.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

If you have the coordinates of two points, you can use the distance formula to find the length of the line segment between them. The distance formula is:

[tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

where:

And to find a perimeter add all the sides as the perimeter is the sum of all sides of the shape or object.

Perimeter: Sum of all sides

Area : Length * breadth or base*height for rectangle

The costs for each item in this problem are given as follows:

The costs are obtained solving a system of equations, for which the variables are given as follows:

Seven hot dog(s) and four hamburger(s) cost $16.00, hence:

7x + 4y = 16

1.75x + y = 4

y = 4 - 1.75x.

Four hot dog(s) and seven hamburger(s) cost $19.75, hence:

4x + 7y = 19.75

x + 1.75y = 4.9375.

Replacing the first equation into the second, the value of x is given as follows:

x + 1.75(4 - 1.75x) = 4.9375

2.0625x = 2.0625

x = 1.

The value of y is given as follows:

y = 4 - 1.75

y = 2.25.

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The angle opposite the hypotenuse is always 90 degrees, as a result, angle C in the given triangle is a right angle.

In the triangle given below, angle C is a right angle: To prove that this triangle is a right-angled triangle,

we must first confirm that it meets the Pythagorean Theorem's requirements, which states that the sum of the squares of the legs equals the square of the hypotenuse.

In other words, if the Pythagorean Theorem holds for the given triangle, it is a right-angled triangle, and if not, it is not a right-angled triangle.

Given the triangle's lengths: Leg AB measures 15 units. Leg BC measures 20 units.

Therefore, AC's length can be determined as follows: AC2 = AB2 + BC2AC2 = 15^2 + 20^2AC2 = 225 + 400AC2 = 625AC = √625AC = 25We can now confirm that the Pythagorean Theorem holds for this triangle

since AC2 = AB2 + BC2AC2 = 15^2 + 20^2AC2 = 225 + 400AC2 = 625AC = √625AC = 25

Since the Pythagorean Theorem holds for the given triangle, we can conclude that it is a right-angled triangle.

The angle opposite the hypotenuse is always 90 degrees, as a result, angle C in the given triangle is a right angle.

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The percentage of the annual income spent on food by the family is 19.98 %.

The percentage of the annual income spent on food by the family is calculated as follows;

The given parameters include;

yearly income of the family = $29,850.00.

amount spent on food = $5963.00

The percentage of the annual income spent on food by the family is calculated as;

percentage of the annual amount on food = ( amount spent on food / total annual income) x 100%

percentage of the annual amount on food = ( $5963.00 /  $29,850.00) x 100%

percentage of the annual amount on food = 19.98 %

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The value of x is 18

To determine the value, we have that;

From the information given, we have that;

m/E = (8x - 16)°

m/F = (x+8)°, and

m/G = (2x - 10)°

Add the values, we get;

8x - 16 + x + 8 + 2x - 10 = 180

collect the like terms, we have;

8x + x + 2x = 180 + 18

add the values

11x = 198

x = 18

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To analyze the data, Sabastian should follow the following steps:Define the research question,Collect the data,Organize the data,Analyze the data,Interpret the results and Communicate the results

1. Define the research question: He needs to clarify the research question, and identify the variables he is investigating.

2. Collect the data: He should obtain the data he needs through a survey, experiment, observation, or any other appropriate method.

3. Organize the data: He needs to sort and arrange the data in a meaningful way, such as using tables, graphs, or charts.

4. Analyze the data: He should use statistical techniques to explore the data and identify patterns, trends, and relationships among the variables.

5. Interpret the results: He should draw conclusions based on the data analysis, and assess the implications of the findings for the research question.

6. Communicate the results: He should present the findings in a clear and concise manner, using appropriate visuals and language, to effectively communicate the results to others.

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One role of plants in the carbon cycle is the process of carbon dioxide (CO2) absorption during photosynthesis. Plants are able to take in atmospheric CO2 and convert it into organic carbon compounds through the process of photosynthesis.

During photosynthesis, plants utilize sunlight, water, and CO2 to produce carbohydrates and release oxygen as a byproduct.This absorption of CO2 by plants helps in reducing the concentration of greenhouse gases in the atmosphere, thus playing a crucial role in mitigating climate change.

By capturing carbon from the atmosphere, plants act as natural carbon sinks, storing carbon in their tissues, including leaves, stems, roots, and woody structures. Some carbon is stored temporarily, such as in leaves or as plant biomass, while other carbon can be stored for longer periods when plants die and decay, leading to the formation of fossil fuels over millions of years.

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Domain of the function represented by the graph of a quadratic function y = [tex]x^2[/tex] – 4 with a minimum value at the point (0,-4) is all real numbers.

The correct answer is option D.

To determine the domain of the quadratic function y = [tex]x^2[/tex] - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."

Let's analyze the given function and its graph to understand why the domain is "all real numbers."

The function y =  [tex]x^2[/tex] - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.

Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.

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According to the information, there are a total of 630 Roman coins in the museum's collection.

To calculate the total number of coins in the museum's collection, we need to determine the area under the histogram curve for the given range of 8 g to 17 g with the following steps:

Now, to calculate the frequency, we multiply the frequency density by the width of the interval:

So, there are 25 coins in the interval between 8 g and 17 g.

Additionally, to find the total number of coins in the museum's collection, we sum up the frequencies for all intervals in the histogram:

According to the above, the museum's collection has a total of 196 Roman coins.

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a) The function is vertically stretched and shifted parabola with translated horizontally to the right by 5 units, and vertically shifted upward by 2 units.

b) The function is vertically compressed and shifted parabola with translated horizontally to the left by 6 units, and vertically shifted downward by 4 units.

Given data,

a)

For the function g(x) = 3(x - 5)² + 2, the transformations of the graph of the parent function f(x) = x² can be described as follows:

Vertical Stretch: The coefficient 3 in front of the parent function causes a vertical stretch by a factor of 3. This means the graph of g(x) will be three times taller than the graph of f(x).

Horizontal Translation: The expression (x - 5) inside the square term indicates a horizontal translation to the right by 5 units. This means the graph of g(x) will be shifted horizontally to the right by 5 units compared to the graph of f(x).

Vertical Translation: The constant term 2 outside the square term causes a vertical translation upward by 2 units. This means the graph of g(x) will be shifted vertically upward by 2 units compared to the graph of f(x).

Therefore, the graph of g(x) = 3(x - 5)² + 2 will be a vertically stretched and shifted parabola, compared to the graph of the parent function f(x) = x². It will be taller, translated horizontally to the right by 5 units, and vertically shifted upward by 2 units.

b)

For the function g(x) = (1/3)(x + 6)² - 4, the transformations of the graph of the parent function f(x) = x² can be described as follows:

Vertical Compression: The coefficient 1/3 in front of the parent function causes a vertical compression by a factor of 1/3. This means the graph of g(x) will be one-third as tall as the graph of f(x).

Horizontal Translation: The expression (x + 6) inside the square term indicates a horizontal translation to the left by 6 units. This means the graph of g(x) will be shifted horizontally to the left by 6 units compared to the graph of f(x).

Vertical Translation: The constant term -4 outside the square term causes a vertical translation downward by 4 units. This means the graph of g(x) will be shifted vertically downward by 4 units compared to the graph of f(x).

Hence , the graph of g(x) = (1/3)(x + 6)² - 4 will be a vertically compressed and shifted parabola, compared to the graph of the parent function f(x) = x². It will be one-third as tall, translated horizontally to the left by 6 units, and vertically shifted downward by 4 units.

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Answer:

Marshmallow weighs 10 kilograms.

Step-by-step explanation:

Let's use the variable "M" to represent Marshmallow's weight in kilograms.

Based on the information given, we know that Marshmallow weighs 1 kilogram less than Fluffy, whose weight is 11 kilograms. Therefore, we can write the equation:

M = 11 - 1

Simplifying the equation:

M = 10

So, Marshmallow weighs 10 kilograms.

The area of triangle BCD is 12 square centimeters.

To find the area of triangle BCD, we need to determine the height of the triangle. Since rectangle ABDE shares side BD with triangle BCD, the length of BD is equal to the width of the rectangle, which is given as 9 centimeters.

The area of a triangle is given by the formula: Area = (base × height) / 2.

In this case, the base of the triangle is CD, which is given as 6 centimeters.

To find the height of the triangle, we can use the fact that the area of rectangle ABDE is 36 square centimeters. The area of a rectangle is given by the formula: Area = length × width.

Since the area of the rectangle is 36 square centimeters and the length of DE is 9 centimeters, we can determine the width of the rectangle: width = Area / length = 36 / 9 = 4 centimeters.

Since the width of the rectangle is equal to the length of BD, we can conclude that the height of the triangle, which is perpendicular to the base CD, is also 4 centimeters.

Now we can calculate the area of triangle BCD using the formula mentioned earlier:

Area = (base × height) / 2 = (6 × 4) / 2 = 24 / 2 = 12 square centimeters.

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Answer:

Let h be the number of hamburgers sold on Friday.

We know that the number of cheeseburgers sold was three times the number of hamburgers sold.

c = 3h

where c is the number of cheeseburgers sold.

We also know that the combined total of hamburgers and cheeseburgers sold was 584, so we can write:

h + c = 584

Substituting c = 3h into the second equation, we get:

h + 3h = 584

Simplifying:

4h = 584

Dividing both sides by 4, we get:

h = 146

Therefore, 146 hamburgers were sold on Friday.

As per the given data, to enable the drain pipe to carry 60 liters per second, there needs to be a 66.67% increase in the diameter of the drain pipe.

We must comprehend the link between the carrying capacity and the area of the pipe's cross-section in order to calculate the percentage increase in the drain pipe's diameter required to make it capable of carrying 60 litres per second.

The cross-sectional area of the pipe directly relates to its carrying capacity. This implies that the carrying capacity will grow if the cross-section's area increases.

Q ∝ A

Q1/A1 = Q2/A2

A2 = (Q2/Q1) * A1

A2 = (60/36) * A1

A2 = (5/3) * A1

Percentage increase = (A2 - A1)/A1 * 100

Percentage increase = [(5/3) * A1 - A1]/A1 * 100

Percentage increase = (2/3) * 100

Percentage increase = 66.67%

Thus, the answer is 66.67%.

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The graph of the function y = 4 ÷ x is added as an attachment

The line of the symmetry is y = -x

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

y = 4 ÷ x

The above function is a rational function that has been transformed as follows

Vertically stretched by a factor of 4

Next, we plot the graph using a graphing tool by taking not of the above transformations rule

The graph of the function is added as an attachment

Also, from the graph the line of the symmetry is y = -x

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The area of the wildlife refuge on the map is 1 square inch : 25 square miles.

To find the area of the wildlife refuge on the map, we need to square the scale ratio of 1 inch : 5 miles.

Since the scale ratio is given as 1 inch : 5 miles, we can write it as 1 inch / 5 miles.

To square this ratio, we multiply it by itself:

(1 inch / 5 miles) x (1 inch / 5 miles)

Squaring the ratio gives us:

1 square inch / (5 miles x 5 miles)

Simplifying further:

1 square inch / 25 square miles

Therefore, the area of the wildlife refuge on the map is 1 square inch : 25 square miles.

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The graph for the circle equation (x-2)²+(y+1)²=9 is in option D.

The given circle equation is (x-2)²+(y+1)²=9.

The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r².

From the given equation, we have

Center: (2, -1)

Radius: 3

Therefore, the correct option is D.

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Emma's model shows a weak negative correlation between the concentration of the water softening agent and time. True.

The correlation coefficient (r) provides a measure of the strength and direction of the relationship between two variables.

Emma's model of the curve of best fit has a correlation coefficient of r = -0.28.

Based on the value of the correlation coefficient, we can determine the following statement about Emma's model:

Since the correlation coefficient is negative (r = -0.28), it indicates a negative relationship between the concentration of the water softening agent and time.

The magnitude of the correlation coefficient being less than 1 suggests a weak correlation, meaning that the data points in Emma's model are somewhat scattered around the best-fit curve.

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Answer: 845 Billion

Step-by-step explanation:

HOW IS THIS COLLEGE LEVEL

844,758,200,030 is:

844 billion, 758 million, 200 thousand, 30.

7 rounds to 10, and 8 also rounds to 10, so:

845 billion

Sorry for the all caps but seriously XD

The sample size of 300  would most likely be closest to the actual parameter value of the population.

We have to find the a sample of which of the sizes which would

most likely be closest to the actual parameter value of a population.

In general, as the sample size increases, the estimate obtained from the sample is more likely to be closer to the actual parameter value of the population.

This is because a larger sample size provides more information and reduces the impact of sampling variability.

Therefore, among the given options, the estimate obtained from a sample size of 300  would most likely be closest to the actual parameter value of the population.

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Diego is making the mistake of not following the correct steps while solving a quadratic equation, which has led him to divide each side of the equation by 2 instead of square root(100). This mistake has occurred because he is trying to find a value instead of the actual answer to the problem.A)

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Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.

The values of a, b and c on the quadratic function are given as follows:

a. a = -2, b = 0, c = 0.

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The coefficients are given as follows:

a, b and c.

The function in this problem is given as follows:

y = -2x².

Hence the coefficients are given as follows:

a = -2, b = 0, c = 0.

Hence option a is the correct option in the context of this problem.

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The period is approximately 4 seconds, as it takes about 4 seconds for the particle to complete one full oscillation.

The period of the graph represents the time taken for one complete oscillation. The graph shows a periodic motion, which is a repeated motion that occurs at regular intervals.

In this context, the graph represents the motion of a particle undergoing simple harmonic motion, which is a type of periodic motion.The graph shows displacement on the y-axis and time on the x-axis.

The amplitude of the motion is represented by the maximum displacement of the particle, which is 4 cm in this case. The period of the motion is the time taken for one complete oscillation,

In this case, the frequency is approximately 0.25 Hz, which means that the particle undergoes one complete oscillation every 4 seconds

which is the time it takes for the particle to move from one extreme point to the other extreme point and back again. In this graph,

The frequency of the motion is the number of complete oscillations per unit time, which is the inverse of the period.

Overall, the period of the graph represents the time taken for one complete oscillation in a periodic motion, and in this context, it represents the time it takes for a particle undergoing simple harmonic motion to move from one extreme point to the other extreme point and back again.

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Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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