ƒ(x) = − x² – 14
-
Find f(6)

The distance between the two points (0,1) and (6,−7) is 10.

Distance can be defined as the length between two points.

To calculate the distance between the two points, we use the formula below.

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1

Hence, the distance between the two points is 10.

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If the given triangle has all three sides as congruent and the angles are same then the triangle is an equilateral triangle.

We will use the figure given below to prove the triangle as an equilateral triangle.

In the above figure,

Given, vertices of a triangle are A(X1, Y1), B(X2, Y2), and C(X3, Y3).

According to the properties of the equilateral triangle, the sides of an equilateral triangle should be equal in measure.

So, we use the distance formula:

d = √((x2 - x1)^2+(y2 - y1)^2 to verify if all three sides are congruent and equal to each other

If AB = BC = CA.

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

If the given triangle satisfies the above condition then the triangle is an equilateral triangle.

If the given triangle has all three sides as congruent then the triangles angles are also equal.

Hence, if the given triangle has all three sides as congruent and the angles are same then the triangle is an equilateral triangle.

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To find the vertical asymptote, look for the values of x where the denominator of a function equals 0. To find the removable discontinuity, look for the values of x where the numerator of a function equals 0.

Vertical asymptotes are x-values where the denominator of a fraction is equal to 0. To find the vertical asymptote, we need to set the denominator equal to 0 and solve for x. This will give us the x-values where the graph of the function has a vertical asymptote. Removable discontinuities are x-values where the numerator of a fraction is equal to 0. To find the removable discontinuity, we need to set the numerator equal to 0 and solve for x. This will give us the x-values where the graph of the function has a removable discontinuity. In both cases, once we have the x-values, we can plot the graph of the function and see where the vertical asymptote and removable discontinuity are located. We can also use these x-values to determine the behavior of the function in the vicinity of the vertical asymptote or removable discontinuity.

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Answer:

a- 30

b- 90

Step-by-step explanation:

150 learn math

120 learn english

150+120 is 270

270 - 240  = 30

so 30 students learn both.

120 - 30 = 90

so 90 learn english only

get it?

Answer:

The slope of the line described by the equation 15x – 10y = 10 is m = 15/10 = 1.5, and the y-intercept is b = 10/15 = 2/3.

Step-by-step explanation:

Answer:Slope is 1.5, and the y-intercept is -1

Step-by-step explanation:

So in order to get the slope and y-intercept, you have to put the equation in slope form, y=mx+b

Here’s the work for it

15x-10y=10

-15x -15x

-10y=-15x+10

Now divide -10 on both sides

y=1.5x-1

Now that it’s in the right form, you can easily see the slope is 1.5 and the y-intercept is -1

I hope this helps, please let me know if it was right!

The angle RST of the arc will be equal to 46°.

A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be drawn by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.

Given that the angle RUS is 46 and the angle URT is 36.

The angle RST has the same arc that is made by the angle RUS. From that theorem, we can conclude that the angle RUS will be equal to the angle RST.

∠RUS = ∠RST

∠RST = 46°

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AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. Hence proved

AAS (Angle-Angle-Side):

Suppose we have two triangles from figure ABC and DEF, where,

∠B = ∠E [Corresponding angles] ∠C = ∠F [Corresponding angles] And

AC = DF [Adjacent sides]

By angle sum property of triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equation 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in triangle ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by ASA congruency,

Δ ABC ≅ Δ DEF

So AAS (Angle-Angle-Side) congruence rule is hence proved.

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The hypotheses that would determine if the proportion of households that support starting school earlier has changed this year is C. H 0: p = 0.65, H alpha: p greater-than 0.65.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a given set of observations.

It is tested to see if there has been no change at the null hypothesis, which means that the proportion is still 0.65 = 65%.

It is tested whether there has been a change at the alternative hypotheses, that is, whether the proportion is no longer 0.65 = 65%.

Therefore, the correct option is C.

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Complete options

Group of answer choices

H 0: p not-equals 0.70, H alpha: p = 0.70

H 0: p = 0.70, H alpha: p not-equals 0.70

H 0: p = 0.65, H alpha: p greater-than 0.65

H 0: p = 0.65, H alpha: p not-equals 0.65

Bar line is a notation used in place of repeating numbers. It is also graphical representation used in graphs.

Bar line is a simple notation used to express a repeating number by placing a line over the number that repeats.  when numbers go on forever and when not to use bar notation.

Bar line is also used in graphs. A bar line in the graph is a graphical representation based on the different parameters. They are drawn in cases when the items are compared based on the multiple parameters or observations.

There is another bar line called the vertical bar ( | ) also called the vertical line, vertical slash or upright slash is a symbol used in mathematics, computing and other areas to represent a specific type of logic or operation, depending on its context. Even within a single area such as computing, the vertical bar is applied in multiple ways.

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Consequently, the original number is 27 and the reversal is 72.

A number is a numerical unit of measurement and labeling in mathematics.

The natural numbers 1, 2, 3, 4, and so on are the first examples.

Number words are a linguistic way to express numbers.

So, let the ones and tens places' digits be y and x, respectively.

initial value = 10x+y

number in reverse = 10y plus x

In response to the query:

3(10x+y)-9 = 10y+x

30x+3y-9-10y-x= 0

29x-7y-9 = 0 ...(1)

Since the reversed number is greater:

10y+x-(10x+y)=45

10y-y-10x+x-45 = 0

9y-9x-45=0

y-x-5=0

y= x+5 ...(2)

Place equation (2) into equation (1) immediately:

29x-7(x+5)-9=0

29x-7x-35-9=0

22x=44

x = 2

Now enter x=2 into equation (2):

y= 2+5= 7

Therefore, consequently, the original number is 27 and the reversal is 72.

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Correct question:
On reversing the digits of a two-digit number obtained is 9 less than three times the original number. If the difference between these two numbers is 45 find the original number.

The statement that is false is: Correlation is used to define the variables of only non-linearly related data sets.

Correlation is a measure of the relationship between two variables of a data set and can be positive, negative, or 0. It is used to measure the degree to which the two variables of a data set resemble each other, regardless of whether the data set is linear or non-linear. The correlation between any two variables can be easily measured and compared, allowing for more detailed analysis of the data set.

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Answer:

Bias from using a convenience sample (C)

Step-by-step explanation:

This sampling method is an example of taking a convenience sample because the mobile phone service provider is only taking samples from the people that responded. The availability of certain people causes a bias in the data drawn from this sampling method.

Continuity of a function is when the function is continuous over the range of its domain. An example is a function f(x) = x^2, which is continuous over its domain of x∈R.

Continuity of a function is when the function is continuous over the range of its domain. A function is continuous if the graph of the function is a single, connected curve with no breaks or gaps. This means that for any point on the curve, the function is non-discontinuous. An example of a continuous function is f(x) = x^2, which is continuous over its domain of x∈R. This means that, no matter what value is put into the function, the output will always be a single value and the graph of the function will be a single, connected line. This is because the function is continuous over its entire domain, and therefore there are no breaks or discontinuities in the function. This is an example of continuity of a function.

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The value of x and y° are 29.1 and  76.6°.

What is rounding to tenth?

Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.

The length of sides of the triangle are x, 35, and 40.

Assume that AB = c = x, BC = a = 35, and AC = b = 40

m∠C = 45° and m∠B = y°.

Cosine law:

c² = a² + b² - 2ab cos C  ....(i)

b² = a² + c² - 2ac cos B  ....(ii)

a² = b² + c² - 2bc cos A  ....(iii)

Putting a = 35, b = 40, c = x, and C = 45° in law (i)

x² = 35² + 40² - 2×35×40 cos 45°

x² = 2825 - 2800 × (1/√2)

x = 29.07

x = 29.1  (nearest tenth)

Putting a = 35, b = 40, c = 29.1, and B = y° in law (ii)

40² = 35² + 29.1² - 2×35×29.1 cos y

1600 = 1225 + 846.81 - 2037 cos y

2037 cos y = 471.81

cos y = 471.81/2037

y = 76.60°

y = 76.6°

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During rigid transformations, the shape, size, and orientation of an object remain the same, while its position in space changes. This means that the distance between any two points on the object remains constant, as does the angle between any two lines. Additionally, the orientation of the object's axes (length, width, and height) remain the same.

Transformations are a general term for four different methods of changing the location and/or shape of a point, line, or geometric figure. The shape of the object is revealed in its pre-image, while its final form and position are revealed in the image following transformation.

A transformation is characterized by a significant alteration in appearance or form. Your life may change as a result of a significant event, such earning your driver's license, beginning college, or getting married. A significant, abrupt transformation is called a metamorphosis.

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Answer:

5

Step-by-step explanation:

there are five terms: 5xy, 9yz, 3zx, 5x, and 4y.

In mathematics, a term is a part of an expression that is separated by a plus or minus sign. In this expression, the terms are 5xy, 9yz, 3zx, 5x, and 4y. Note that the equation in the question is formatted a little awkwardly, so make sure to count how many terms you see yourself too!

Answer:

The distance between the points R(a+b,a-b) and S(a-b,a+b) is 2*sqrt(2)*sqrt(a^2+b^2).

Step-by-step explanation:

To find the distance between the two points, we can use the distance formula:

distance = sqrt((x2-x1)^2 + (y2-y1)^2)

Plugging in the coordinates of the two points, we get:

distance = sqrt((a-b-a-b)^2 + (a+b-a+b)^2)

Simplifying, we get:

distance = sqrt(2*(a^2 + b^2))

Multiplying both sides by sqrt(2) gives us:

distance = 2*sqrt(2)*sqrt(a^2+b^2)

Therefore, the distance between the points R(a+b,a-b) and S(a-b,a+b) is 2*sqrt(2)*sqrt(a^2+b^2).

Tess can make 9 throw pillows from the 6 yards of fabric.

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.

Given that Tess wants to make throw pillows for her couch. she has 6 yards of fabric. each pillow uses 2 over 3 yards of fabric.

The number of pillows will be calculated as,

Number of pillows = 6 ÷ ( 2 / 3 )

Number of pillows = ( 6 x 3 ) / 2

Number of pillows = 9

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The best example of discontinuity is a graph of a function with a "hole" or "jump" in it, where the value of the function suddenly changes without any gradual change.

Discontinuity occurs when a graph of a function has an abrupt change, either in the form of a "hole" or "jump" in it. In a graph of a continuous function, the values gradually change in a smooth manner. However, with a graph of a discontinuous function, the function suddenly changes without any gradual transition. This sudden change is often caused by a discontinuity in the domain or range of the function. For example, a discontinuity may occur where a function is undefined or has an undefined limit. Graphically, this is usually illustrated as a gap or jump in the graph of the function. This type of discontinuity is known as a removable discontinuity, since it can be removed by redefining the function at the point of discontinuity. Other types of discontinuity include infinite discontinuity, which occurs when the graph of a function approaches either positive or negative infinity, and jump discontinuity, which occurs when the graph of a function jumps from one value to another without any transition.

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The Frequency of graph is 3

The frequencies of each category are represented individually in a frequency graph; the frequencies of each category are shown cumulatively. By doing so, we are able to analyze the data's distribution in greater detail than we could have done by using a Frequency polygon and performing statistics.

A frequency polygon can also be used to display grouped data. This sort of line graph exists. The horizontal axis is a continuous scale, therefore the frequencies can be connected using straight line segments.

Looking at the graph we can see that the graph is oscillating between -3 and 3 and as frequency is a positive term taking modulus of this oscillation we get to know that the frequency is 3.

The Frequency of graph is 3

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Data integration combines data collected from various platforms to increase its value for your company. It enables your staff to collaborate more effectively and provide more for your clients.So IT is important to integrate information.

The combining of data from diverse sources with various conceptual, contextual, and typographic representations is known as information integration. It is utilised for data aggregation and mining from unstructured or partially organised sources. You may connect all of your data, people, and processes in a single solution by using an integrated solution. Today's top HSEQ management teams regard this strategy as best practise. The justification for this is straightforward: it improves reporting, efficiency, uniformity, speed, and ease of use. An integrated report's main goal is to describe to financial capital providers how a company builds, protects, or loses value over time. As a result, it includes pertinent information, both financial and otherwise.

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According to Proverbs 31, She should look for a man after God's heart a man who fears the Lord and has his life fixated on the principles of the Lord. A man with a godly wisdom. A man whose belief is in the Lord.

According to Proverbs 31, He should look for a lady of noble character, who nurtures and provides for her family, who brings pride to her man as she works graciously with her hands and knows the ways to provide for her family even during hard times, and mostly the women who fear the Lord. A woman of value and virtue in the Lord.

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She should seek for a man who has the heart of God, one who reveres the Lord and bases his actions on the rules of the Lord, according to Proverbs 31. a wise man who comes from God. a person who trusts in the Lord.

According to Proverbs 31, He should look for a woman of noble character, who nurtures and provides for her family, who offers honor to her spouse as she works chastely with her hands and knows the ways to care for her family even through hard times, and most of all the ladies who fear the Lord. a lady of worth and virtue before the Lord.

The three types of discontinuity are listed as follows:

Jump Discontinuity.

Infinite Discontinuity.

Removable Discontinuity.

The term discontinuity is referred as if a function is referred to as the point at which a Mathematical object is discontinuous.

The function will be discontinues if they meet the following conditions,

There are 3 type of discontinuity in math and they are listed as jump, infinite and removable.

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The term "population regulation" refers to biological mechanisms that balance off disruptive occurrences, such as weather changes, alterations in the environment, the occurrence of disease epidemics, etc.

A straightforward equation that depicts population growth is as follows: Expression of Population Changes as a Percentage: Change in Population Size = (Births + Immigration) - (Deaths + Emigration). Let's say we had a population of 100,000 people.

The relative size of two functions' values for big values of the independent variable is what is meant when a term like "function growth" is used.

The term "population regulation" refers to biological mechanisms that balance off disruptive occurrences, such as weather changes, alterations in the environment, the occurrence of disease epidemics, etc.

A straightforward equation that depicts population growth is as follows: Expression of Population Changes as a Percentage: Change in Population Size = (Births + Immigration) - (Deaths + Emigration). Let's say we had a population of 100,000 people.

The relative size of two functions' values for big values of the independent variable is what is meant when a term like "function growth" is used.

The term "population regulation" refers to biological mechanisms that balance off disruptive occurrences, such as weather changes, alterations in the environment, the occurrence of disease epidemics, etc.

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Answer:

yes.

Step-by-step explanation:

The definition of a function:  "A function is defined as a relation between a set of inputs having one output each."

This means each x can only have 1 y value. You can check if this is a function using the vertical line test. To do the vertical line test draw vertical lines through the graph of the expression. If you even hit 2 points with a vertical line it is NOT as function.

The graph is of an upward facing parabola so it will be a function. We can graph and check this with the VLT which it passes.

The answer for the given question is following:

If the degree of a polynomial is odd and the leading coefficient is negative, the end behavior of the graph of the polynomial will be as follows:

For example, consider the polynomial f(x) = -x^3 + 3x^2 - 5x + 2. This polynomial has a degree of 3 (which is odd) and a leading coefficient of -1 (which is negative). The graph of this polynomial will have 1 turning point (which is odd) and will approach negative infinity as x approaches negative infinity and positive infinity.

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If the degree of the polynomial is odd, the graph of the polynomial will have an odd number of turning points.

For example, consider the polynomial

f(x) = -x^3 + 3x^2 - 5x + 2.

This polynomial has a degree of 3 (which is odd) and a leading coefficient of -1 (which is negative).

The graph of this polynomial will have 1 turning point (which is odd) and will approach negative infinity as x approaches negative infinity and positive infinity.

The answer is:

3 and 4

Step-by-step explanation:

multiplying 7/10 miles by 3 will give you 21/10 which is 2.1 miles

multiplying 7/10 miles by 4 will give you 28/10 which is 2.8 miles

Answer:

i think is 3 times and 4 times because.....

Step-by-step explanation:

For Tristan to  jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.

Considering the options given

A. 2 * 7/10 = 1.4 miles (this is not within the range)

B. 3 * 7/10 = 2.1 miles (this is within the range)

C. 4 * 7/10 = 2.8 miles (this is within the range)

D. 5 * 7/10 = 3.5 miles (this is not within the range)

Answer:

[tex]y=4x+10[/tex]

Step-by-step explanation:

Using the points [tex](8,40)[/tex] and [tex](0,10)[/tex],

[tex]m=\frac{40-10}{8-0}=4.5 \\ \\ \therefore y=4.5x+10[/tex]

This matches most closely with the second option.

The equation represents a direct variation, and the constant of variation for 5x = -3y is k = -5 / 3.

Proportionality is an essential topic with several applications in everyday life. Proportionality can be used to compare different quantities. Volume, for example, is inversely related to density.

The equation is given in the question as:

5x = -3y

We can rearrange it as y = -5x / 3

Hence, we see that y ∝ x, and the equation is of the form y = kx, where k is the proportionality constant. This denotes that y varies directly with x.

Here k = -5 / 3.

Hence, the constant of variation is k = -5 / 3.

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