i) Given that ax2+ 6x + c is always negative, what conditions must apply to the constants a and c? ii) Give an example of values of a and c which satisfy the conditions found in part (i).​

Our assumption that two consecutive elements of the Fibonacci sequence can be divisible by 13 is false, and the proposition is proved.

We begin with the fact that the Fibonacci sequence is an increasing sequence; that is, each element is greater than the one before it.

The sequence is defined as follows:

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, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, and so on.

Now, let us prove the proposition by contradiction. Assume that there are two consecutive elements of the Fibonacci sequence that are divisible by 13. Then there must be some integer n such that:

F(n) = 13m, andF(n + 1) = 13p,

where m and p are integers.

Since the Fibonacci sequence is defined recursively by F(n) = F(n-1) + F(n-2), we can obtain an expression for F(n-2) in terms of F(n) and F(n-1):

F(n-2) = F(n) - F(n-1)Since F(n) and F(n-1) are both divisible by 13, their difference must also be divisible by 13.

Therefore, F(n-2) is divisible by 13 as well. However, this contradicts the well-ordering principle, which states that every non-empty set of positive integers has a least element.

Since the Fibonacci sequence is an increasing sequence, there must be some least element k such that F(k) is divisible by 13 but F(k-1) is not. But this means that F(k-2) cannot be divisible by 13, which contradicts our assumption that both F(n) and F(n-1) are divisible by 13.

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The volume and the surface area of the prism is 6 and 22 square inches²

First, lets find the volume of the prism

Volume:

[tex]\text{Volume}=\text{(Area of the base)}\times\text{height}[/tex]

[tex]\text{Volume}=(3\times2)\times1[/tex]

[tex]\text{Volume}=6 \ \text{square inches}^2[/tex]

Since the volume of the prism is 6, now to find the Surface area of the cubes.

[tex]\text{Surface area}= \text{Total area of the 2-dimensional surfaces to make 3-dimensional }[/tex]

[tex]\text{Surface area}=2\times3=6, \ 3\times1=3, \text{and} \ 1\times2=2[/tex].

[tex]\text{Surface area}=6(2)+3(2)+2(2)=22 \ \text{square inches}^2[/tex]

The surface area of the prism is 22.

Therefore, the volume and the surface area of the prism is 6 and 22 square inches²

From the information provided the measure of the angles are given as,

m ∠EFH = 71; and m ∠EFG = 142°.

Angles are measured in degrees, which is why they are called "degrees". A complete circle equals 360 degrees, so it is divided into 360 parts. Each part of the revolution is a degree. Any angle, whether acute, obtuse, reflected or right, can be measured with a protractor. Although based on right angles, we are able to distinguish acute, obtuse or reflex angles. But if we have two acute angles to measure, we cannot determine the greater angle between the two. Therefore, we need to use a protractor to measure angles accurately.

According to the Question:

It is to be noted that

m ∠GFH = m ∠EFH

⇒ m ∠EFH = 71°

⇒ m ∠EFG = m ∠GFH + m EFH

Hence,

m ∠EFG = 71 + 71

              = 142°

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The length of the secant AC, obtained using the tangent secant theorem is AC = 25 units

The tangent secant theorem indicates that when a secant ABC and a tangent, CD meets at an external point C  to a circle, the relationship between segments are; AC × BC = CD².

Segment addition postulate indicates that we get;

AC = AB + BC

Where;

AB = 3·x + 1

BC = 9

Therefore;

AC = (3·x + 1) + 9 = 3·x + 10

AC × BC = (3·x + 10) × 9 = 27·x + 90

AC × BC = 27·x + 90

CD = 15

CD² = 15² = 225

AC × BC = CD²

Therefore; 27·x + 90 = 225

27·x = 225 - 90 = 135

x = 135/27 = 5

x = 5

AC = 3·x + 10

Therefore; AC = 3 × 5 + 10 = 25

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Answer:

239 miles in 0.75 of an hour

Step-by-step explanation:

Answer: 22.3

Step-by-step explanation:

The dummy variable is used to capture the effect of the categorical variable and it has no effect on the quadratic or cubic relationship between the independent and dependent variable.

When x is a dummy variable, there will be no difference in OLS estimators between quadratic and cubic regression models. This statement is true.OLS stands for Ordinary Least Squares regression. It is a statistical method used to determine the relationship between one or more independent variables (predictors) and a dependent variable. The OLS regression method minimizes the sum of squared residuals (differences between actual and predicted values).Dummy variables are used in regression analysis to represent categorical variables.

These are represented by a variable with a binary value of 1 or 0, depending on whether the observation falls in that category or not. This variable is used to represent a categorical variable in regression analysis so that the model can capture the effect of that variable in the analysis.In regression analysis, the regression model is a function of the independent variable, also called the predictor variable, and the dependent variable. A quadratic regression model is a polynomial regression model of degree 2. It means that the relationship between the dependent and independent variable is a quadratic function.

A cubic regression model is a polynomial regression model of degree 3. It means that the relationship between the dependent and independent variable is a cubic function. When x is a dummy variable, there will be no difference in OLS estimators between quadratic and cubic regression models. The OLS estimators will be the same because the dummy variable will have no effect on the fit of the model. Hence, this statement is true.

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Answer:

Step-by-step explanation:So that is a right angle,which means the sum is 90 degrees.so you subtract 90 from 62 then you have your answer.

Answer:

x = 28°

Step-by-step explanation:

It is given that the full angle measurement is a right angle (90°), denoted by the blue(?) box.

Set the equation:

Total angle measurement (90) = x + 62

I~

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 62 from both sides of the equation:

90 (-62) = x + 62 (-62)

x = 90 - 62

x = 28

x = 28° is your answer.

~

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The vector space that has exactly one basis is the trivial vector space, which is the vector space containing only the zero vector.

A basis for a vector space is a set of linearly independent vectors that span the entire space. In a non-trivial vector space (a space that contains more than just the zero vector), there are infinitely many possible bases. This is because any set of linearly independent vectors that span the space can be used as a basis.

However, in the trivial vector space, there is only one vector (the zero vector), and it is linearly independent of itself. Therefore, the trivial vector space has exactly one basis, which is the set containing only the zero vector. Any other set of vectors in the trivial vector space is linearly dependent, and therefore cannot be used as a basis.

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Answer:

in image

Step-by-step explanation:

if it helped you please mark me a brainliest :))

The area of the rectangle is 136 square units.

What are quadrilateral graph ?

A quadrilateral graph is a graphical representation of a quadrilateral, which is a four-sided polygon. It is a coordinate system that uses a Cartesian plane, where the x and y axes are used to plot the four vertices of the quadrilateral. The four vertices of the quadrilateral are represented by four points on the graph, and the sides of the quadrilateral are represented by the line segments connecting the points. By examining the coordinates of the vertices and the lengths of the sides, we can determine the properties of the quadrilateral, such as whether it is a parallelogram, a rectangle, a square, a trapezoid, or a kite. Quadrilateral graphs are useful tools for visualizing and analyzing quadrilaterals in geometry.

To find the area of a rectangle, we need to know the length of two adjacent sides. Let's use the points Q and R to determine the length of the rectangle.

Length of QR = √((x₂- x₁)² + (y₂ - y₁)²)

= √((-4 - 6)²+ (-3 - 3)²)

= √((-10)²+ (-6)²)

= √(100 + 36)

= √(136)

Similarly, we can find the length of ST:

Length of ST = √((x₂ - x₁)²+ (y₂ - y₁)²)

= √((9 - (-1))² + (-2 - (-8))²)

= √((10)² + (6)²)

= √(100 + 36)

= √(136)

Since QR and ST are opposite sides of the rectangle and have equal length, we know that the rectangle is indeed a rectangle. Therefore, the area of the rectangle is simply the product of the length and width:

Area of rectangle = length * width

= √(136) * √(136)

= 136 square units

Hence, the area of the rectangle is 136 square units.

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Answer: X= 15

Step-by-step explanation:

Triangular prism formulas

volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length.

area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.

Answer:

56 feet

Step-by-step explanation:

P = 2(1 + w)

P = 2(20 + 8)

P = 2(28)

2x28 = 56 feet

so the answer is 56 feet.

Answer:

P = 2l + 2w (2 times the length plus 2 times the width)

P = 2(40) + 2(20)

P = 80 + 40

P = 120 ft

You can also add the four sides together. (20 + 20 + 40 + 40

Step-by-step explanation:Since fencing the garden is the measure of perimeter of the garden and length and width of the rectangle are given, we find the perimeter of rectangle which is 2*width +2*length=2*20+2*40=40+80=120 feet of fence are needed.

After answering the provided question, we can conclude that Therefore, the coordinates of M' are (11, -8).

In mathematics, a coordinate is a number or combination of integers that indicates the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a specific coordinate system, such as the Rectilinear or polar coordinate systems. In the Cartesian coordinate system, a point is located by its distance from the origin along the x-axis and its distance first from origin along the y-axis. These distances are represented by two digits, the x-coordinate and indeed the y-coordinate. The point's position in the plane is specified by the two coordinates.

(x', y') = (x, y) - (a, b)

a) To find the coordinates of K', we need to use the above formula with (a, b) = (-6, 2) and (x, y) = (3, 4) (the coordinates of K in the original figure)

(x', y') = (x, y) - (a, b)

= (3, 4) - (-6, 2)

= (3 + 6, 4 - 2)

= (9, 2)

Therefore, the coordinates of K' are (9, 2).

(x', y') = (x, y) - (a, b)

= (5, -6) - (-6, 2)

= (5 + 6, -6 - 2)

= (11, -8)

Therefore, the coordinates of M' are (11, -8).

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The Jumble is an MP3 player owned by Greg. The Jumble chooses music for the user to hear at random. Greg's Jumble features nine rap tracks, seven rock songs, and six classical songs.  The probability of not selecting a rap song is 0.59.

The total number of songs on the Jumble is 6 + 7 + 9 = 22.

To find the probability of not selecting a rap song, we need to find the number of songs that are not rap songs, which is the sum of the number of classical and rock songs on the Jumble:

6 + 7 = 13

Therefore, the probability of not selecting a rap song is:

13/22

To round this to two decimal places, we can divide 13 by 22 using a calculator or long division to get:

0.59

Therefore, the probability of not selecting a rap song is 0.59 or 59%.

The complete question is:-

Greg has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Greg's Jumble has 6 classical songs, 7 rock songs, and 9 rap songs on it. What is P(not a rap song) If necessary, round your answer to 2 decimal places.

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Answer:

the area is 40

Step-by-step explanation:

Answer:a

Step-by-step explanation:

Answer:

  PEMDAS or BIDMAS

Step-by-step explanation:

You want to know how to remember the order of operations.

Commonly used acronyms for the Order of Operations are ...

  PEMDAS

  BIDMAS

The letters of these stand for ...

  P, B — parentheses or brackets

  E, I — exponents or indices

  M, D — multiplication and division

  A, S — addition and subtraction

Expressions enclosed in grouping symbols (parentheses or brackets) have the highest precedence. They are evaluated first, according to the order of operations.

Exponents (indices) are evaluated next. A sequence of exponent operations, such as a^b^c is evaluated right to left, as a^(b^c), unless parentheses modify the order.

Because exponents and indices have a higher precedence than other arithmetic operations, something like 2^3x is evaluated as (2^3)x, not 2^(3x), and √2p is (√2)p, not √(2p). It is fairly common to see a square root erroneously written as 3^1/2 = (3^1)/2 = 3/2 when 3^(1/2) = √3 is intended.

Multiplication and division have the same precedence. Even though M precedes D (or D precedes M, depending on which acronym you use), they are evaluated in order of appearance left to right. As with exponents, a common error is forgetting to put parentheses around numerators and denominators. For example, 3/2π is different from 3/(2π).

Similarly, addition and subtraction have the same precedence and are evaluated in order of appearance, left to right.

The composition (ring) operator (∘) is used to signify a sequence of functional or transformation operations. For example (f∘g)(x) is the composition of functions f and g. The functions or transformations in a composition are evaluated right to left:

  (f∘g)(x) = f(g(x))

Operations performed on functions can be written in confusing ways. For example, ...

  [tex]y = f^{-1}(x)\qquad\text{means }x=f(y),\text{ not }y=\dfrac{1}{f(x)}[/tex]

The notation using a positive exponent stands in contrast:

  [tex]\sin^4(x)\qquad\text{usually means }(\sin(x))^4,\text{ not }\sin(\sin(\sin(\sin(x))))[/tex]

On the other hand, an exponent applied to a function name can mean recursive application of the function, as in sin²( ) = sin(sin(...)). It can also mean an n-th derivative. Context is important in such situations.

The statement is valid in light of the fact that the stretch can oblige three head developments every moment.

The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.

At the point when this happens, we broadcast that there is plausible that the occasion will happen. In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.

By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.

As a result, the claim is true because the time allows for three head movements per minute.

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.

[tex]10.4[/tex] cookies were divided here between small tray as well as a large tray.

A cookie is indeed a piece of information from a webpage that is saved in a browser for subsequent retrieval by the website. Cookie are used to let a server know whether visitors have visited a specific website again.

You will have the greatest user experiences . for example if you provide enough, whereas denying cookies may make it harder for you to use the website. Consider purchasing online. When you browse further, cookies allow the website to maintain track of all the products you've added to your cart.

[tex]2s + 3l = 64[/tex] (equation 1)

[tex]6s + 4l = 122[/tex] (equation 2)

From equation [tex]1[/tex], we can solve for [tex]s[/tex] in terms of [tex]l[/tex]:

[tex]2s + 3l = 64[/tex]

[tex]2s = 64 - 3l[/tex]

[tex]s = (64 - 3l)/2[/tex]

We can then substitute this expression for [tex]s[/tex] into equation [tex]2[/tex]:

[tex]6s + 4l = 122[/tex]

[tex]6((64 - 3l)/2) + 4l = 122[/tex]

Simplifying:

[tex]192 - 9l + 4l = 244[/tex]

[tex]-5l = -52[/tex]

[tex]l = 10.4[/tex]

Now that we know that a large tray contains [tex]10.4[/tex] cookies, we can substitute this value back into equation [tex]1[/tex] to solve for [tex]s[/tex]:

[tex]2s + 3l = 64[/tex]

[tex]2s + 3(10.4) = 64[/tex]

[tex]2s = 20.8[/tex]

[tex]s = 10.4[/tex]

Therefore, a small tray contains [tex]10.4[/tex] cookies, and a large tray contains [tex]10.4[/tex] cookies.

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It is not mathematically accurate to say that 2+2=4+4=8.

In arithmetic, 2+2 equals 4 and 4+4 equals 8, so each equation is evaluated separately. The sum of 2+2 and 4+4 is indeed 8, but they are not equal to each other.

Perhaps you meant it as a playful or creative statement, but from a mathematical standpoint, it is not accurate.

What is an arithmetic equation?

An arithmetic equation is a mathematical statement that uses arithmetic operations to relate two or more quantities. It typically involves addition, subtraction, multiplication, and division of numbers.

Arithmetic equations can take many forms, but they generally follow the pattern of a mathematical expression or formula that uses variables or numerical constants to represent quantities. The goal of solving an arithmetic equation is to determine the value of the variable that makes the equation true.

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Complete question is: It is not mathematically accurate to say that 2+2=4+4=8.

the answer is

=3x+yx3+zx

=3x + 3y+3z

If below assumptions are not met, then the validity of the confidence interval may be compromised, and alternative methods may need to be used to estimate the mean increase in blood pressure.

In statistics, sampling is the process of selecting a subset of individuals or objects from a larger population for the purpose of studying or estimating certain characteristics of the population. The subset of individuals or objects is known as a sample.

Sampling is often used when it is impractical or impossible to collect data on the entire population. By studying a representative sample, statisticians can make inferences about the population as a whole with a certain level of confidence.

In order for a 95% confidence interval for the mean increase in blood pressure to be valid, the following assumptions must be made:

If these assumptions are not met, then the validity of the confidence interval may be compromised, and alternative methods may need to be used to estimate the mean increase in blood pressure.

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Por lo tanto, se pueden plantar 224 árboles en el terreno rectangular de 32m x 28m, considerando que cada árbol necesita 4m² para descollarse.

Para calcular el número de árboles que pueden plantarse en el terreno, primero necesitamos determinar el área total del terreno y luego dividirlo por el espacio requerido por cada árbol.
1. Calcula el área total del terreno rectangular:
Área = largo x ancho
Área = 32 m x 28 m
Área = 896 m²
2. Divide el área total entre el espacio requerido por cada árbol:
Número de árboles = Área total / Espacio por árbol
Número de árboles = 896 m² / 4 m²
Número de árboles = 224

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Answer:

.50 chance that she gets a chocolate chip cookie or 50 percent.

Step-by-step explanation:

half of all the cookies in the jar are chocolate chip cookies. 12/24 meaning that there is a 50/50 chance that she'll get a chocolate chip cookie

.50

The equation for the function is f(x) = 3 * cos (16x + [tex]\frac{16\pi }{3}[/tex] ) + 5.

What is an equation?

A assertion that two expressions with variables and/or numbers are equal is referred to as an equation. The fundamental driving forces behind the evolution of mathematics have been attempts to logically solve equations, which are really questions.

We know that f(x) = a cos (bx + c) + d.

We are given

a = 3 which is the amplitude

Period = 8π

b = 16

Phase shift = [tex]\frac{c}{b}[/tex]

⇒[tex]\frac{\pi }{3}[/tex] = [tex]\frac{c}{16}[/tex]

⇒ c = [tex]\frac{16\pi }{3}[/tex]

d = 5 as there is upward translation

So, from this we get the equation as

⇒f(x) = 3 * cos (16x + [tex]\frac{16\pi }{3}[/tex] ) + 5

Hence, the equation for the function is f(x) = 3 * cos (16x + [tex]\frac{16\pi }{3}[/tex] ) + 5.

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Question: Write an equation for a function with the given characteristics. A cosine curve with a period of 8π, an amplitude of 3, a right phase shift of π/3, and a vertical translation up 5 units.

f(x) = ______________

The transformation rule is to: rotate triangle ABC by 90 degrees around the origin

As we are given the coordinates of Triangle ABC as:

Coordinate of point A = (1, 1)

Coordinate of point B = (3, 1)

Coordinate of point C = (1, 4)

The coordinates of the transformed image A'B'C' are:

A' (-1, 1) ,

B'(-1, 3)

C' (-4, 1)

The transformation rule would be to rotate triangle ABC by 90 degrees around the origin

The rule for this transformation is:  (x,y) => (-y ,x)

A(1,1) => A' (-1,1) ,

B(3,1) => B'(-1 , 3)

C(1,4)  => C' (-4,1)

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