Solve. Complete the table for the consecuIf the sum of a number and eight is tripled​, the result is four less than twice the number. Find the number.
tive integers.

The range of this relation include the following: D. {-2, 3, 5}.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.

Based on the information provided in this scenario, the domain and range of this relation in interval notation are as follows:

Domain = {3, 6, 8}

Range = {-2, 3, 5}.

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I think it might be:

Between 1754 and 1885 European imperialism was global. Nations like Britain, France, and Spain grew their Empires in the Americas, on the continent of Africa, and in parts of Asia. Their colonies created power and wealth for European businesses and governments. Eventually, many European countries held a meeting to decide how to divide up the world to avoid wars and conflict between themselves. This meeting was called the Conference.

Answer:11.4999...

Step-by-step explanation:

Any number when rounding that starts with 1, 2, 3 4 will be rounded down. All numbers above will be rounded up. Therefore, you find the largest number that will still round down.

The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.

Using the formula A = P(1 + r/n)^(nt), where:

A = the amount in the account after t years

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

a) If interest is compounded annually:

A = 2000(1 + 0.05/1)^(1*7) = $2,835.08

b) If interest is compounded quarterly:

A = 2000(1 + 0.05/4)^(4*7) = $2,888.95

c) If interest is compounded monthly:

A = 2000(1 + 0.05/12)^(12*7) = $2,905.03

d) If interest is compounded continuously:

A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36

Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.

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The trigonometric ratios for this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the triangle, we have that:

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Answer:

21,  22, 23   or

-23, -22 , -21

Step-by-step explanation:

The 3 consecutive integers are x, x + 1, and x + 2

Sum of the squares of the 3 consecutive integers:

x² + (x+1)² + (x+2)² = 1454     Expand this equation

x² + x² + 2x + 1 + x² + 4x + 4 = 1454   Combine like terms

3x² + 6x + 5 = 1454

3x² + 6x + 5 - 1454= 0

3x² + 6x - 1449 = 0

Use quadratic equation to solve for the roots of x:  (a = 3, b = 6,

c= -1449)

x = 21, -23

The consecutive numbers are: x, (x + 1), (x + 2)

21,  22, 23

-23, -22 , -21

the the coordinates of the resulting point are (18, -8). of the resulting point are (18, -8).

What is center of dilation?

The center of dilation is a fixed point in the plane.

Starting with point B(5, -2), if we move it 4 units to the right and 2 units down, we get:

B'(9, -4)

Next, we need to dilate the point by a factor of 2, using the origin as the center of dilation. This means we need to multiply both the x-coordinate and y-coordinate of B' by 2.

So, doubling the x-coordinate of B' gives:

2 × 9 = 18

And doubling the y-coordinate of B' gives:

2 × (-4) = -8

Therefore, the coordinates of the resulting point are (18, -8).

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The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.

The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.

Circle's standard equation is written as:

x²+y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is : x²+y²-2x-8=0

Get the centre of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This demonstrates circle's centre is on the x-axis.

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The circle has a radius of three units.

For the circle x²+y²=9, radius is expressed as:

r² = 9

r = 3 units

As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.

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Answer: 3/2 or 1 1/2 or 1.5

Step-by-step explanation:

9/8 times 2 is 2.25 or 9/4

9/4-6/8= 3/2 or 1 1/2 or 1.5

By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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Is the function above continuous: B. not continuous at x = 0.

In Mathematics and Geometry, a continuous function can be defined as a type of function in which there is no discontinuities or breaks between the intervals for the points plotted on a graph.

In Mathematics and Geometry, a discrete function can be defined as a type of function in which the ordered pair of values on the x-axis and y-axis are separate from each other and unconnected.

By critically observing the graph shown above, we can reasonably infer and logically conclude that it represents a discrete function because it is not continuous at x is equal to 0 i.e x = 0.

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Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

The function is f(x)=115.[tex](1.58)^x[/tex] and number of people after 6 months is 1789.

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here according to the table initial people f(0) = 115

Now using exponential formula

=> f(x) = f(0).[tex](1+r)^x[/tex]

If x = 1 then f(1)= 182 then,

=> 182 = 115.[tex](1+r)^1[/tex]

=> 1+r = 182/115

=> 1+r = 1.58

=> r = 1.58-1=0.58

Then the exponential function is

=> f(x)=115.[tex](1.58)^x[/tex]

Now x=6 then,

=> f(6) = 115.[tex]1.58^6[/tex] = 1789

Hence number of people after 6 month is 1789.

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Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.

Step-by-step explanation:

Therefore, the perimeter of the rectangle is 42 centimeters.

The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.

Here,

To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.

We can use the formula for the area of a rectangle:

Area of rectangle = length x width

Plugging in the values we have:

108cm² = length x 9cm

Solving for the length, we can divide both sides by 9cm:

length = 108cm² / 9cm

length = 12cm

So, the length of the rectangle is 12 centimeters.

To find the perimeter of the rectangle, we can use the formula:

Perimeter of rectangle = 2 x (length + width)

Plugging in the values we have:

Perimeter of rectangle = 2 x (12cm + 9cm)

Perimeter of rectangle = 2 x 21cm

Perimeter of rectangle = 42cm

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Answer:

To check whether 40, -40, 16, or -16 is the solution of the equation 28 = d - 12, we can substitute each value into the equation and see if it results in a true statement.

When we substitute 40 into the equation, we get:

28 = 40 - 12

Simplifying, we get:

28 = 28

This is a true statement, so 40 is a solution of the equation.

When we substitute -40 into the equation, we get:

28 = -40 - 12

Simplifying, we get:

28 = -52

This is not a true statement, so -40 is not a solution of the equation.

When we substitute 16 into the equation, we get:

28 = 16 - 12

Simplifying, we get:

28 = 4

This is not a true statement, so 16 is not a solution of the equation.

When we substitute -16 into the equation, we get:

28 = -16 - 12

Simplifying, we get:

28 = -28

This is not a true statement, so -16 is not a solution of the equation.

Therefore, the only solution of the equation 28 = d - 12 is d = 40.

Answer:

tanQ = 1

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ OPQ is an exterior angle of the triangle , then

∠ R + ∠ Q = 135°

90° + ∠ Q = 135° ( subtract 90° from both sides )

∠ Q = 45°

Then

tanQ = tan45° = 1

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{3} \end{cases}\implies 4\sqrt{3}=\cfrac{s\sqrt{3}}{2} \\\\\\ 8\sqrt{3}=s\sqrt{3}\implies \cfrac{8\sqrt{3}}{\sqrt{3}}=s\implies 8=s[/tex]

Answer:

To differentiate the given expression, we will need to use both the product rule and the quotient rule.

Let's first rewrite the expression using the reciprocal identity for x:

2y/5x = 2y * (5x)^(-1)

Now we can use the product rule and the quotient rule to find the derivative with respect to x:

d/dx [2y * (5x)^(-1)] = 2y * d/dx[(5x)^(-1)] + (5x)^(-1) * d/dx[2y]

Using the chain rule, we can find the derivative of (5x)^(-1) with respect to x:

d/dx[(5x)^(-1)] = -1/(5x)^2 * 5 * (dx/dx)

d/dx[(5x)^(-1)] = -1/(5x)^2

Using the chain rule again, we can find the derivative of 2y with respect to x:

d/dx[2y] = 2 * (dy/dx)

Substituting these expressions back into the original equation, we get:

d/dx [2y/5x] = 2y * (-1/(5x)^2) + (5x)^(-1) * 2 * (dy/dx)

Simplifying this expression, we get:

d/dx [2y/5x] = -2y/(5x)^2 + 2/(5x) * (dy/dx)

Therefore, the derivative of 2y/5x with respect to x is -2y/(5x)^2 + 2/(5x) * (dy/dx).

Answer:

1/6 of flowers were blue

The standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.

It is a type of curve with a curved line in the middle and two straight lines on the sides. Conic sections include circles, ellipses, parabolas, and hyperbolas.

The standard form of the equation of a conic is

Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.

In this case, the equation of the conic is x²  + y²  - 16x - 16y - 192 = 0.

To derive this equation, we'll use the distance formula to calculate the distance between the vertices and the foci. The distance between the vertices and the foci is given by

d = √((x_1 - x_2)²  + (y_1 - y_2)²)

where (x_1, y_1) is the coordinates of the first vertex and (x_2, y_2) is the coordinates of the first foci.

For the first vertex, (x_1, y_1) = (0, 8). For the first foci, (x_2, y_2) = (0, √48). Thus, the distance between the two points is

d = √((0 - 0)²  + (8 - √48)² )

= √(0 + (-8 - √48)² )

= √(-16 - 2√48 + 48)

= √(32 -2√48)

= 2√(16 - √48)

= 2√(16 - 6.9)

= 2√(9)

= 2(3)

= 6

So, the distance between the vertices and the foci is 6.

The equation of the conic can then be written as x² + y² - 16x - 16y - (-8)² = 0, which simplifies to x² + y² - 16x - 16y - 192 = 0.

Thus, the standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.

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yes is answer   for all option   .we can check it by rules of rounding off numbers .

what is rounding ?

Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.

In the given question,

Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.

To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).

If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.

If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.

Using these rules, we can see that:

350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.

792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.

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Answer:

18 5-dollar bills

10 20-dollar bills

Total percentage of adults who preferred soccer or baseball: is 25%

what is percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100, or 50/100 as a fraction.

In the given question,

The circle graph shows the percentage of adults who preferred each sport. To find the percentage of adults who preferred soccer or baseball, we need to add the percentages for soccer and baseball.

Soccer: 11%

Baseball: 14%

Total percentage of adults who preferred soccer or baseball: 11% + 14% = 25%

Therefore, 25% of adults preferred soccer or baseball.

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the dimensions of the table runner are  [tex]20[/tex] inches in length and [tex]4[/tex] inches in width.

Let's denote the width of the table runner as "w" inches. Since the length is 5 times greater than the width, the length would be 5w inches.

The area of a rectangle is calculated by multiplying its length by its width. Given that the area of the table runner is 80 square inches, we can set up the following equation:

Length × Width = Area

[tex](5w) \imes w = 80[/tex]

Simplifying further:

[tex]5w^2 = 80[/tex]

Dividing both sides by 5:

[tex]w^2 = 16[/tex]

Taking the square root of both sides:

w = ±4

Since the width cannot be negative in this context, we discard the negative value. Therefore, the width (w) of the table runner is [tex]4[/tex] inches.

Substituting this value back into the equation for length:

Length   [tex]= 5w = 5 \times 4 = 20[/tex] inches

So, the dimensions of the table runner are  [tex]20[/tex] inches in length and 4 inches in width.

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Using the half angle formula, cos(-π/12) =  ±√[2 + √3]/4]

The half angle formula for cosine is cosФ/2 = ±√[(1 + cosФ)/2]

Since we want to find the value of cos(-pi/12) using the half angle formula, we have that cosФ/2 = cos(-π/12)

⇒ Ф/2 = -π/12

⇒  Ф = -π/12 × 2

⇒ Ф = -π/6

So, substituting this into the equation, we have

cosФ/2 = ±√[(1 + cosФ)/2]

cos(-π/6)/2 = ±√[(1 + cos(-π/6))/2]

= ±√[(1 + cos(π/6))/2]

Now, we know that cos(π/6) = √3/2

So, substituting this into the equation, we have that

cos(-π/6)/2 = ±√[(1 + cos(π/6))/2]

cos(-π/12 = ±√[(1 + cos(π/6))/2]

= ±√[(1 + √3/2)/2]

= ±√[[2 + √3]/2)/2]

= ±√[[2 + √3]/2 × 2]

= ±√[2 + √3]/4]

So,  cos(-π/12) =  ±√[2 + √3]/4]

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This is an image of a histogram representing the number of hours a group of students spent studying for a test. The horizontal axis shows the number of hours studied, and the vertical axis shows the frequency or number of students who studied that number of hours.

A histogram is a graphical representation of data that displays the frequency distribution of a set of continuous or discrete data. It consists of a series of adjacent rectangular bars, where the area of each bar represents the frequency of occurrences of a particular range of values.

Based on the histogram, it appears that the majority of students studied for 5-7 hours, with a frequency of 14 students. Additionally, it appears that 8 students studied for 2-4 hours, and 10 students studied for 8-10 hours. Finally, it appears that only 1 student studied for more than 10 hours.

Histograms are a useful way to display and analyze data because they allow us to quickly see the distribution and frequency of the data. In this case, we can see that the data is roughly symmetric around the 5-7 hour range, with fewer students studying for fewer or more hours.

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By answering the presented question, we may conclude that As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.

A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.

An isosceles triangle has two sides of equal length, but a right triangle has one angle that measures 90 degrees. As a result, an isosceles right triangle is one with two equal-length sides and one 90-degree angle.

The Pythagorean theorem states that in any right triangle, the two legs (the sides next to the right angle) are always of equal length. Hence, if we know that a triangle has one 90-degree angle and two equal-length sides, we already know that it is a right triangle and that the two legs are equal. As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.

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In this expression, the GCF is 5. Therefore, we can factor out a 5 to get 5(x² - y²).

The difference of squares formula states that the difference of two squares can be factored into the product of two terms, one of which is the sum of the terms and the other is the difference of the terms.

When factoring polynomials, it is important to factor out the greatest common factor (GCF).

In this expression, the GCF is 5.

Therefore, we can factor out a 5 to get 5(x² - y²).

Now, we can expand the parentheses and factor out the remaining terms. Since both terms are perfect squares, we can factor them using the difference of squares formula:

5(x² - y²) = 5(x + y)(x - y)

In this case, the terms are x and y, resulting in the factorization of  5(x² - y²) into 5(x + y)(x - y).

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