Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.



The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across [tex]x-[/tex] or [tex]y-[/tex] axis, and then change [tex]x-[/tex] or [tex]y-[/tex] coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change [tex]x-[/tex] or [tex]y-[/tex] coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  [tex]y-[/tex] axis

Horizontal translation is shifting the graph along  [tex]x-[/tex] axis.

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Measuring and recording the length of each side of a parallelogram means using a measuring tool, such as a ruler or a tape measure, to determine the length of each of the four sides of the parallelogram and then recording that measurement.

The measurement should be noted with the appropriate unit of measurement (inches, centimeters, etc.) and recorded in a way that is easy to understand and reference later.

To measure and record the length of each side of a parallelogram, the following steps can be taken:

It is important to note that a parallelogram has opposite sides of equal length and opposite angles of equal measure. Therefore, after measuring and recording the length of two sides, you can use this property to measure the other sides without measuring them again.

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The response will be;

''The vertical line test is used to determine if each input has exactly one output.''

A relation between a set of inputs having one output each is called a function.

Given that;

The sample answer is,

''The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.''

Now,

Since, The sample answer is,

''The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.''

Hence, The correct response for the sample answer is,

''The vertical line test is used to determine if each input has exactly one output.''

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The number of times that the heart beat in one year is 4.20 x 10^7.

Scientific notation is used to compress large numbers in smaller numbers. It is used to transform large numbers into smaller number.

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, the notation 7 x 10² is equivalent to 700

The number of heart beat in one year = average heart beat per day  number of days in a year

(1.15 x 10^5 x (3.65 x 10^2)

= (1.15 x 3.65) x (10^5 + 2)

= 4.20 x 10^7

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The extension or reduction of the line takes place when a line segment is dilated from a point on the line.

When a line segment is dilated from a point on the line, the line segment is extended or reduced in size, depending on the dilation factor.

This dilation can be done by either shrinking the line, making it longer or using a combination of both.

When the dilation is done, the original line and the resulting line will be the same length, but their position will be different. The line segment will be moved or rotated around the point of dilation, so the original line will be in a different position than the resulting line.

The point of dilation will be the same distance from both the original and the resulting line.

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We can manually convert a scatter plot to a four-quadrant graph. For this conversion we shall have to follow the steps noted below :

1) At first, we shall have to delete the trend line from our scatter diagram.

2) Then, we shall have to reformat our X-axis.

3) After that, we shall have to reformat our Y axis.

4) At last, once we have updated both the X and Y axis values, we should have an XY Scatter Diagram with Four Quadrants.

The goal of the XY Scatter chart with quadrants is to create a chart in Excel that plots data points on a percentage scale for X and Y and also shows quadrants with a different scale. Instead of the normal 0 to 100, the X and Y axis run from 100% to 0%.

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Answer:

Second, Third and fifth options

Step-by-step explanation:

Angle 1 not equal to Angle 2 (Add up to 180 degrees)

Angles 1 and 4 - Vertically opposite angles (Equal)

Angles 3 and 6 - Alternate angles (Equal)

Angle 3 not equal to Angle 5 (Add up to 180 degrees) - angles of a parallelogram

Angles 7 and 2 - Alternate angles and vertically opposite angles (Equal)

Angle 7 not equal to Angle 1 (Same reasoning as angles 3 and 5)

Persons who regularly interact with the system as part of their jobs are called operational stakeholders

A person who has an interest in the project, is connected to it, or is positively or negatively impacted by it is referred to as a stakeholder. Operation, on the other hand, refers to any ongoing process or action, such as hospital management or any manufacturing activity.

Operational stakeholders must be involved, their needs should be recorded in the stakeholder register, and the risk management plan should take into account any influence they may have, whether good or negative.

Some Instances of operational stakeholders (based on the business) are: Operators of manufacturing facilities, managers of production lines, instructors, help desk personnel, customer service representatives, salesperson, etc.

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The two true statements regarding the circle equation are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9"

"The center of the circle lies on the x-axis."

Remember that the equation for a circle of center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + y^2 - 2x - 8  =0

First we need to complete squares on x, remember the perfect square trinomial:

(a - b)^2 = a^2 - 2ab + b^2

So we can rewrite:

x^2 + y^2 - 2x - 8  =0

(x^2 - 2x) + y^2 = 8

Now we can add and subtract 1:

(x^2 - 2x) + y^2 + 1 - 1 = 8

(x^2 - 2x + 1) + y^2 - 1 = 8

(x - 1)^2 + y^2 = 8 + 1

(x - 1)^2 + y^2 = 3^2

So, the center is (1, 0) and the radius is 3.

Then the true statements are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" it is also 3.

"The center of the circle lies on the x-axis." because the center is at (1, 0).

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Answer:

x = 64

Step-by-step explanation:

The given polygon is a quadrilateral — a closed figure with 4 sides. We know that the measures of the interior angles of a quadrilateral sum to 360º (e.g., the measures of a rectangle's four angles: 90º + 90º + 90º + 90º = 360º). Using this information, we can construct an equation with xº and the rest of the angle measures given in the diagram.

xº + 100º + 130º + 66º = 360º

To solve this equation, we can subtract (100 + 130 + 66)º from both sides.

xº = 360º - (100 + 130 + 66)º

xº = 360º - 296º

xº = 64º

x = 64

On solving the provided question, we can say that- in the triangle UB = UG so, <UBG = <UGB, x+ 10 + x+ 10 + 3x = 180 => x = 32

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

UB = UG

so, <UBG = <UGB

x+ 10 + x+ 10 + 3x = 180

5x + 20 = 180

5x = 160

x = 32

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Leala writes essay in 10 minutes contains roughly 83 words.We can find by unitary method.

The unitary method is a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.We can find multiplying by other values.

Multiplication is one of the basic mathematical operations. When two or more numbers are multiplied together the answer obtained is called the product. In the case of the multiplication of two numbers the first number in which the other is being multiplied is called the multiplicand.

Now

Number of word=500

Number of minutes=10

she writes in 60 minute= 500

she writes in 10 minute= 500/60 *10

                                       =500/6

                                        =83.33 words

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Answer:

4

Step-by-step explanation:

36 ÷ 9= 4

you just want to take the 36 glasses and put them into nine rows of four

The application of laws of exponents on the exponential functions gives;

1) ? = -2

2) ? = 4

Some of the laws of exponents are;

- When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

- When dividing two bases of the same value, keep the base the same, and then subtract the exponent values.

- Where a power is being raised by another power, multiply the exponents together and keep the base the same.

1) (2x^(?)y⁴)⁻³ = 1x⁶/8y¹²

Expanding this gives;

2⁻³x^(-3?)y⁻¹² = ¹/₈x⁶y⁻¹²

¹/₈x^(-3?)y⁻¹² = ¹/₈x⁶y⁻¹²

Equating like terms gives;

-3? = 6

? = 6/-3

? = -2

2) (a^3b^-2)^? = a^12 / b^8

Applying laws of exponents gives;

a^(3?)b^(-2?) = a^(12)b(-8)

Equating like terms gives;

3? = 12

? = 12/3

? = 4

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The least number of comparisons needed to sort (order) five elements is 8.

Insertion sort is a simple sorting algorithm that works similar to the way you sort playing cards in your hands. The array is virtually split into a sorted and an unsorted part. Values from the unsorted part are picked and placed at the correct position in the sorted part.

Characteristics of Insertion Sort:

This algorithm is one of the simplest algorithm with simple implementation

Basically, Insertion sort is efficient for small data values

Insertion sort is adaptive in nature, i.e. it is appropriate for data sets which are already partially sorted.

There are 5! = 120 possible outcomes.

Therefore a binary tree for the sorting procedure will have at least 7 levels.

Indeed, 2h ≥ 120 implies h ≥ 7.

But 7 comparisons is not enough.

The least number of comparisons needed to sort (order) five elements is 8.

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The volume of sum of the volume of the cylinder and rectangular prism will be 388.26 cubic cm.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

A bottle consists of a cuboid and a cylinder.

The volumes are given as,

V = πr²h + L × W × H

V = 3.14 × (3/2)² × 4 + 10 × 8 × 4.5

V = 28.26 + 360

V = 388.26 cubic cm

The volume of sum of the volume of the cylinder and rectangular prism will be 388.26 cubic cm.

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Answer:

$64.36 or 63.63

Step-by-step explanation:

[tex]22.9+27.6 = 50.5[/tex]

To find tax multiply by .08 and then add to the total

[tex]50.5*.08 = 4.04[/tex]

[tex]50.5 + 4.04 = 54.54[/tex]

I'm not sure of the tip is including the tax or not. However, with tax, multiply the total after tax by .18. Without tax multiply the total beforehand by .18. Then add to the total.

Tip after tax:

[tex]54.54*.18 = 9.82[/tex]

[tex]54.54+ 9.82 = 64.36[/tex]

Tip without tax:

[tex]50.5*.18 = 9.09[/tex]

[tex]54.54+9.09 = 63.63[/tex]

The solution to the linear function y = 1/4x + 5/4 is (1, 1.5)

A linear equation is an equation that can be written in the form ax + b = 0, where a and b are constants and x is a variable. It is a type of equation that describes a straight line when graphed.

The linear function given is y = 1/4x + 5/4

The solutions given are (1, 1.5) and (12, 4)

Let's test for the values.

For (1, 1.5)

y = 1/4(1) + 5/4

y = 1/4 + 5/4

y = (1 + 5)/4

y = 6/4

y = 1.5

This solution is true.

Let's test for (12, 4)

y = 1/4(12) + 5/4

y = 4.25

This solution is not true

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The expression that represents the net yardage for these plays is given as follows:

19.8x - 11.1y.

The net yardage is given by the sum of all yards gained for the sum of all yards lost.

For example, if Josh Allen passes for 350 yards but loses 20 yards on sacks, his net yardage is given as follows:

350 - 20 = 330 yards.

Then the expression that gives the total net yardage for this problem is given as follows:

25x + 0.9y - 12y - 5.2x.

The expression can be simplified combining the like terms, as follows:

25x - 5.2x + 0.9y - 12y.

(25 - 5.2)x + (0.9 - 12)y

19.8x - 11.1y.

(as combining the like terms means that all the terms with the same letter  and same exponent are added/subtracted).

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Answer:

Step-by-step explanation:

You want the sums of various geometric series.

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

 Sn = a1·(r^n -1)/(r -1)

When the series is infinite, the sum will converge if and only if |r| < 1.

The ratio can be found as the ratio of the first two terms:

  r = a2/a1

The ratio is ...

  r = 16/2 = 2

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 25/5 = 5

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 4/1 = 4

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 12/24 = 1/2

The sum of the first 8 terms is ...

  S8 = 24·((1/2)^8 -1)/(1/2 -1) = 24·(-255/256)/(-1/2) = 24(255/128)

  S8 = 47 13/16

The ratio is ...

  r = -6/3 = -2

The sum of the first 10 terms is ...

  S10 = 3·((-2)^10 -1)/(-2 -1) = 3(1023)/(-3)

  S10 = -1023

__

Additional comment

If you have a number of these, a spreadsheet or graphing calculator can do the math for you.

Answer:

3/s

Step-by-step explanation:

Answer:

3/s

Step-by-step explanation:

i had the same question our teacher went over it

The triangle given here, using distance formula, is found to be isosceles.

First, let's calculate the length of the sides of the triangle, by calculating the distance between the given points.

Use the following formula:

[tex]d = \sqrt{(x_{2} - x_{1}) ^2 + (y_{2} - y_{1}) ^2}[/tex] (the distance formula)

where (x1,y1) and (x2,y2) are the limits of a segment with length d.

Then, the distance between points X and Y is:

[tex]d_{XY} = \sqrt{(-5-2)^2 + (-4-(-1))^2} = \sqrt{49+9} = \sqrt{58}[/tex]

The distance between points Y and Z is:

[tex]d_{YZ} = \sqrt{(-2-(-5))^2 + (3-(-4))^2} = \sqrt{9+49} = \sqrt{58}[/tex]

and the distance between points Z and X is:

[tex]d_{ZX} = \sqrt{(2-(-2))^2 + (-1-3)^2} = \sqrt{16+16} = \sqrt{32}[/tex]

Then, you have two sides with the same length, which are sides XY and YZ and another side with a different length. When a triangle has two sides with the same length, such a triangle is isosceles.

Thus, the triangle given here, using distance formula, is found to be isosceles.

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Answer:

Step-by-step explanation:

x² = 8² + 1²

x² = 64 + 1

x² = 65

x = √65

or

x = 8.06

The required equation of the line in slope-intercept form is: y = (1/2)x + (3/2)

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The graph is given in the question, as shown

As per the given graph, we take two points (-3, -4) and (5, 0).

The slope formula is:

[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of two points on the line.

Plugging in the coordinates of the given points:

m = (0 - (-4)) / (5 - (-3)) = 4/8 = 1/2

The point-slope form of a line is:

y - y₁ = m(x - x1)

Plugging in the coordinates of the first point and the slope:

y - (-4) = (1/2)(x - (-3))

Simplifying:

y + 4 = (1/2)x + (3/2)

This is the required equation of the line.

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Use the chain rule to get the derivative (the slope), then use the given point to write the equation.

y = sin(sinx)

dy/dx = cos(sinx) cos(x)

x = 3π

sin(3π) = 0

cos(sin(3π)) = cos(0) = 1

cos(3π) = -1

m = dy/dx|x=3π = -1

y = -x + b

0 = -3π + b

b = 3π

y = -x + 3π

The value of a is 1 and c is 16. The equation is x^2+8x+16=0. The solution is obtained using discriminant.

What is discriminant?

In mathematics, a polynomial's discriminant is a function of the polynomial's coefficients. It is useful for figuring out a polynomial equation's sort of solutions without actually finding them. In other words, it distinguishes between the equation's solutions (as equal and unequal; real and nonreal), giving rise to the term "discriminant." . Any real number may represent the discriminant's value (i.e., either positive, negative, or 0).

We know that ax² + 8x + c = 0 has one real solution,

Therefore, D=0

So, b^2-4ac=0

⇒ 64-4ac=0

⇒ ac=16

So, when a=1, c=16.

Hence, the value of a is 1 and c is 16. The equation is x^2+8x+16=0.

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Since, there are multiple questions so the question I answered is attached below.

The first step in creating parallel lines is to use a straightedge to draw a line that intersects the first line.

How do parallel lines work?

In a plane, two lines are said to be parallel if they do not cross, even when extended in both directions indefinitely.

To create a parallel line with a ruler and compass, follow these steps:

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Evaluation of the expression gives  1/ 9. Option A

Index form is the power or exponent raised to a number or variable.

In mathematics, an index (or indexes) is the power or exponent that is added to a number or variable. For instance, the index of 2 in the number 24 is 4. Indexes is the plural form of the word. Constants and variables are concepts found in algebra. A constant is a number that cannot be altered. As opposed to a fixed quantity, a variable quantity's value can be altered or assigned any number. In algebra, indices are discussed in terms of numerical values.

From the information given, we have the expression to be.

= (3^(-4) )^(1/2)

Expand the bracket

= (3)^(-4*1/2)

= (3)^(-4*1/2)

= (3)^(-4/2)

= (3)^(-2)

Take the inverse of the square of 3

=1/3^2

=1/9

The expression is simplified to 1/ 9

Thus, evaluation of the expression gives  1/ 9. Option A

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The expression is simplified to 1/ 9

Now, According to the question:

Let's Know:

What is index form?

Index form is the power or exponent raised to a number or variable.

From the information given, we have the expression to be.

[tex]= (3^-^4 )^(^1^/^2^)[/tex]

Multiply the powers:

= [tex](3)^-^4^/^2[/tex]

= [tex](3)^-^2[/tex]

Take the inverse of the square of 3

[tex]=1/3^2[/tex]

=1/9

The expression is simplified to 1/ 9.

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[tex]9w+6=33[/tex]

Subtract 6 from both sides:

[tex]9w+6-6=33-6[/tex]

[tex]9w=27[/tex]

Divide both sides by 9:

[tex]\dfrac{9w}{9} =\dfrac{27}{9}[/tex]

[tex]\fbox{w = 3}[/tex]

Check:

[tex]9(3)+6=33\\27+6=33[/tex]

[tex]\checkmark[/tex]