What is the example of unique number?

The given quadratic equation 2x²-4x+3=0 has no real roots.

The roots of the quadratic equation are real and equal if the discriminant equals zero, a, b, and c are real values and a≠0.

The roots of the quadratic equation are real and unequal if the discriminant is greater than zero, a, b, and c are real values, and a≠0.

The quadratic equation's roots are imaginary and unequal if the discriminant is less than zero, a, b, and c are real integers and a≠0.

2x²-4x+3=0

Comparing the equation with ax²+bx+c=0

We know that,

D = b²-4ac

  = (-4)²-4(2)(3)

  = 16- 24

  = -8

Since D < 0

Hence, the given equation 2x²-4x+3=0 has no real roots.

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The required coordinates of point B are (2, 3) which is the correct answer would be option (C).

To find the coordinates of point B, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.

As per the question, we are given the coordinates of points A and O, which are (4, 5) and (3, 4), respectively.

We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AO.

Let the coordinates of B would be (x, y)

Substituting the coordinates of points A and O into the midpoint formula gives us :

3 = (x+4)/2 ; 4 = (y+5)/2

6 = x +4; 8 = y + 5

x = 2; y = 3

Therefore, the required coordinates of point B are (2, 3).

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When two parallel lines are cut by a transversal, eight angles are formed. Interior angles are supplementary to corresponding exterior angles and the sum of an interior and its corresponding exterior angle is 180 degrees.

Two parallel lines are cut by a transversal, eight angles are formed. Four of these angles are interior angles, which are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. The other four angles are exterior angles, which are the angles formed between the two lines and the transversal that lie outside the region bounded by the parallel lines. Interior angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior and exterior angles is important in geometry, as they can be used to prove the parallelism of lines.

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Answer: 8*8=64

               6*6*=216

64-216+21=0

Step-by-step explanation:

The factors of the quadratic equation 3x² -4x -4 are (3x + 2)(x - 2)    .

The process of factoring the quadratic equation means expressing the given equation as the product of two linear factors.

The quadratic expression is given as 3x² -4x -4 ;

it can be written as ⇒ 3x² -6x +2x -4    ,...by using split the middle term method .

⇒ 3x(x - 2) + 2(x - 2) ..taking 3x common from first two terms and 2 common from the last two terms .

⇒ (3x + 2)(x - 2)

Therefore , the factors are (3x + 2)(x - 2)  .

The given question is incomplete , the complete question is

What are the factors of the quadratic equation 3x² -4x -4 ?

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Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.

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So the angle of the resultant vector is approximately 53.13 degrees.

To find the angle of the resultant vector, you can use trigonometry to break the two vectors into their x and y components and then use the arctangent function to find the angle.

First, let's find the x and y components of the first vector (the one that travels 45 meters at an angle of 25 degrees south of east). To do this, we can use the trigonometric functions sine and cosine. The x component is equal to the distance traveled (45 meters) times the cosine of the angle (25 degrees), and the y component is equal to the distance traveled times the sine of the angle.

In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.

Now let's find the x and y components of the second vector (the one that travels 30 meters north). The x component of this vector is 0 meters (since it doesn't move in the east-west direction), and the y component is 30 meters (since it travels 30 meters in the north direction).

To find the resultant vector, we can add the x components and y components of the two vectors. The x component of the resultant vector is 39.74 meters + 0 meters = 39.74 meters, and the y component of the resultant vector is 22.36 meters + 30 meters = 52.36 meters.

To find the angle of the resultant vector, we can use the arctangent function (also known as the inverse tangent function). The angle is equal to the arctangent of the y component divided by the x component.

In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.

So the angle of the resultant vector is approximately 53.13 degrees.

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Find the x and y components of the initial vector first (the one that travels 45 meters at an angle of 25 degrees south of east). The trigonometric functions sine and cosine can be used to do this. The y component is equal to the distance traveled times the sine of the angle, and the x component is equal to the distance traveled times the cosine of the angle, or 45 meters times the cosine of the angle, or 25 degrees.

In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.

The two vectors' x and y components can be added to determine the resultant vector. The resultant vector has two components: an x component of 39.74 meters plus 0 meters equals 39.74 meters, and a y component of 22.36 meters plus 30 meters equals 52.36 meters.

The arctangent function can be used to determine the angle of the resulting vector (also known as the inverse tangent function). The angle is determined by dividing the y component's arctangent by its x component.

In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.

So the angle of the resultant vector is approximately 53.13 degrees.

Negative infinity is a concept that has no direction and function. It is the lowest possible number and is represented by the symbol "-∞".

Negative infinity is the lowest possible number, meaning there is no lower number than negative infinity. It is a concept that has no direction, meaning it is not a specific point on a number line. It is represented by the symbol "-∞", which can be thought of as a point before the beginning of the number line. Negative infinity is an abstract concept, but it is still used in mathematical operations. For example, if you have a set of numbers that contains negative infinity, then the sum of all the numbers in the set will be negative infinity. This is because negative infinity is the lowest possible number, so no matter how large the other numbers in the set are, the sum will always be lower than all of them.Negative infinity can also be used to represent undefined limits. For example, if you are looking at a graph of a function, and the y-axis goes to negative infinity, then the limit of the function at that point is undefined. This is because there is no lower number than negative infinity, so the limit cannot be determined.Negative infinity is a concept that can be confusing, but it is an important part of mathematics. It is used to represent the lowest possible number, as well as undefined limits. It is represented by the symbol "-∞" and has no direction.

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Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons

The data of the sugar solutions are;

The volume of 5% sugar solution Kate has = 3 quarts

The volume of the 12% sugar solution = X

Let 'Y' represent the volume of the 8% sugar solution, we have;

The volume of the resultant solution, Z = X + Y + 3

The concentration of the resultant solution = 10%

0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)

Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, we have;

X = (2 × 2 + 15)/2 = 9.5 Quartz

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Answer:

$48/4 pizzas

Step-by-step explanation:

⭐ A ratio is a fraction that relates one variable to another.

⭐ A proportion is when you make two ratios equal to each other to solve for one of the variables.

We want to find what it costs for Mike to buy 4 pizzas. To achieve this, we must make a proportion.

The solution to the system of equations y = -5x + 3 and y = 1 is x = 0.4 and y = 1.      

Therefore, the answer is (0.4, 1).

To solve the system of equations :

y = -5x + 3                                            (1)

y = 1                                                      (2)

In the given equation, coefficient of y is same in both equations. So subtracting equation (2) from equation (1) we get

y - y = -5x + 3 - 1

0 = -5x + 2

Adding 5x on both sides

0 + 5x = -5x + 2 + 5x

5x = 2

Dividing both sides by 5

x = 2/ 5

x = 0.4  

--The question is incomplete, answering to the question below--

"What is the solution to the system of equations?

y = -5x + 3 and y = 1"

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The weekly average proportion of opposed feeling is 0.0375. (Option D)

A sample proportion is the proportion of individuals in a sample who have a particular characteristic of interest. It refers to the number of successes (success means that an individual possesses the characteristic of interest) of the sample divided by the sample size. According to the provided data, the number of successes in the sample size is 30 and the sample size is 100. Hence, the sample proportion is:

Sample proportion = 30/100 = 0.3

As the survey is conducted weekly for eight weeks, the average proportion of the samples is determined by sample proportion divided by number of weeks. Hence,

Average proportion = 0.3/8 = 0.0375

Note: The question is incomplete. The complete question probably is: A Glassboro township is concerned about adverse public reaction to a trash recycling project that is currently in progress. Because of this, the commissioner of public works has authorized a weekly survey to be constructed of township residents. Each week, a sample of 100 residents are questioned on their feeling toward the project. The results to date are shown below. What is the weekly average proportion of opposed feeling? (3 pts.) a. 0.0250 b. 0.1250 c. 0.3000 d. 0.0375 e. None

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In Parallelogram: Area = base x height(perpendicular distance).

In rectangle: Area = base x height.

Parallelogram:

A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.

Area = base x height(perpendicular distance)

Rectangle:

Area = base(length) x height(width).

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Answer:

11111111111111111111

To find the inverse of a function you just have to switch the x and the y and then solve for y.

Inverse Function

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.

The inverse function returns the original value for which a function gave the output.

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The equation of the quadratic function is (c) f(x) = 3(x - 1)² - 2

From the question, we have the table of values that can be used in our computation:

A quadratic equation is represented as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have the vertex to be

(h, k) = (1, -2)

Substitute (h, k) = (1, -2) in f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 1)² - 2

Also, from the graph, we have the point (0, 1)

This means that

a(0 - 1)² - 2 = 1

So, we have

a(1) = 3

Divide both sides by 1

a = 3

Substitute a = 3 in f(x) = a(x - 1)² - 2

f(x) = 3(x - 1)² - 2

Hence, the equation is f(x) = 3(x - 1)² - 2

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A- The maximum vertical distance from the water surface to the diver’s

shoulders are 12.061 meters.

B- The time that the diver’s shoulders enter the water is 1.936 seconds.

C- The total distance traveled by the diver’s shoulders from the time

she leaps from the platform until the time her shoulders enter the water is 12.946 meters.

D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.

A-  

[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]

The maximum vertical distance from the water surface to the diver’s

shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.

B-

[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]

when A= 1.936 seconds.

C-

[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]

At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]

D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]

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Answer:

  C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross

Step-by-step explanation:

You want the zeros and their multiplicity of f(x) = x^5 -x^4 -9x^3 +9x^2, along with a description of whether the graph crosses or touches the x-axis at each zero.

The equation can be factored as ...

  f(x) = x^2(x^3 -x^2 -9x +9)

The cubic can be factored as ...

  x^3 -x^2 -9x +9 = x^2(x -1) -9(x -1) = (x^2 -9)(x -1)

and the quadratic factor can be factored as the difference of square. The complete factorization is then ...

  f(x) = x^2(x -1)(x -3)(x +3)

The zeros are the values of x that make the factors zero:

When the multiplicity of a zero is even, the graph touches the x-axis. Here, that means the graph will touch at x=0, where the multiplicity of the zero is 2.

When multiplicity is odd, the graph will cross the x-axis. The graph crosses at the zeros -3, -1, +3.

__

Additional comment

As soon as you recognize that the x^2 factor means the multiplicity of x=0 is even, you can identify the correct answer choice: the only one that says "touch" for x=0.

Five different ways to prove the given triangles are similar is given by :

SAS, SSS, ASA, AA, and RHS.

Five different ways to prove triangles are similar is given by:

1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.

2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle

3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.

4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.

5.  RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.

Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.

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Answer:

width is 3.56

Step-by-step explanation:

Area is = width x length

so Area/length

so 56.96/16=3.56

The width of the rectangle is 3.56 m and the perimeter is 39.12 m.

To find the width of the rectangle,

We need to use the formula for the area of a rectangle, which is:

Area = Length x Width

We know that the area of the rectangle is 56.96 m², and the length is 16 m. So,

We can substitute these values into the formula and solve for the width:

56.96 m² = 16 m x Width

Width = 56.96 m² / 16 m

Width = 3.56 m

Therefore, the width of the rectangle is 3.56 m.

To find the perimeter of the rectangle,

We need to use the formula:

Perimeter = 2 x Length + 2 x Width

We know that the length is 16 m and the width is 3.56 m,

So we can substitute these values into the formula and solve for the perimeter:

Perimeter = 2 x 16 m + 2 x 3.56 m

Perimeter = 32 m + 7.12 m

Perimeter = 39.12 m

Therefore, the perimeter of the rectangle is 39.12 m.

In conclusion, the width of the rectangle is 3.56 m and the perimeter is 39.12 m when the area is 56.96 m² and the length is 16 m.

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Step-by-step explanation:

directly proportional means

y = kx

to find k we use the first given pair (8, 6) :

6 = k×8

k = 6/8 = 3/4

so, for x = 10

y = 3/4 × 10 = 30/4 = 7.5

The radius of the cylinder 37cm.

cylinder's entire surface area is equal to 2r(h+r).

total surface area = 1936 square cm

height=7 cm

radius is

therefore,

2πr(h+r)=1936

2πr(r+7)=1936

44(r+7)=1936

r+7 = 1936/44

r+7=44

r= 44-7 =37

r=37cm.

The radius of the cylinder 37cm.

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Answer:

1st and 3rd 4th

graph of f(x) = x² - 12x-45 has an x-intercept at x = -3

-3 is a zero of the function f(x) = x²-12x- 45

x + 3 is a factor of x² - 12x-45

Steps:

other solution is (x - 15) or x = 15

x² - 12x-45

2 numbers that when multiplied give -45 & when added give -12 are -15 & 3

(x-15) (x+3)

"zero" is a fancy way for asking for the answer or root

imaginary number is i which is √-1 so

if you have √-9 = √9 * √-1 = 3i

if you have √-20 = √4 * √-1 * √5 = 2i√5

.

Answer:

9.6

Step-by-step explanation:

What is the mean of the following data set 4 8 11 12 13?

Mean: is the average of values so:

(4 + 8 + 11 + 12 + 13) / 5 = 9.6

The eccentricity of the conic section below is: A. closer to 0 than 1.

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:

In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.

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Answer: slope= change in y-intercept and x-intercept

Step-by-step explanation:

1-9=-8

-8- -9=1

-8/1=-8

D.

The line never increases, so we can cancel out A and C.

The line starts off straight, so it's not B.

So, the answer is D. since it starts off constant and then decreases sharply.