How do you write a function from a table of values?

The two parts of the exponential notation can be named as the "Base" and the second part is number raised to base called as Exponent .

Consider the Exponential Expression : aⁿ ;

The above exponent notation is read as the number "a" to the power of "n" ,

it means that the number "a" is multiplied "n" number of times .

The two parts of this Exponential Notations are :

the number "a" is called the base and "n" is called as the power or exponent .

Therefore , the two parts of the exponential notation are the base and the power/exponent .

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The new function's mathematical formula f(x) is 7*.

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Answer: the answer is f(x)=2^(5x)

Step-by-step explanation:

step 1: do the math and divide numbers by more numbers.

Step 2: then add the exponent to another exponent which is a variable.

step 3: then combine the common denominators and you have your answer!

A dilation of a line is a transformation that changes the size of the line but preserves its shape.

It is a type of similarity transformation. A dilation can either be a reduction, in which the line is made smaller, or an enlargement, in which the line is made larger. In both cases, the line's shape is preserved, but the size is changed.

The center of dilation, also known as the scale factor, is a fixed point around which a dilation takes place. The scale factor is a value that represents the amount of change in size, it can be greater than 1 for an enlargement or less than 1 for a reduction.

In geometry, a dilation is represented by a multiplication of the coordinates of a point by a scale factor. For example, a dilation of a line with a scale factor of 2 will result in the line being twice as long as the original line.

In conclusion, a dilation of a line is a transformation that changes the size of the line but preserves its shape. The center of dilation or scale factor is a fixed point around which a dilation takes place and is represented by a multiplication of the coordinates of a point by a scale factor.

It can be either an enlargement or a reduction depending on the scale factor value.

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Classifying Triangle by Sides or Angles: Equilateral triangle, Isosceles triangles, Scalene triangle, Right triangle, Obtuse triangle, Acute triangle, Equiangular triangle.

A triangle is said to be equilateral or equiangular if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.

A triangle with two sides that have the same length is said to be isosceles. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

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On solving the provided question, we can say that the equation of the following will be y = x-$25

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation will be y = x-$25

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The value of K that will make the expressions equivalent is 10.

Considering the two expressions:

7 + (1/2)x - 3 + (3/4)x and 1 whole number (1/4)x + k - 6

we shall write the expression 7 + (1/2)x - 3 + (3/4)x in the form of the expression having k and then compare to know the value of k as follows;

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

(1/2)x + (3/4)x = 5x/4

7 - 3 = 10 - 3 - 3

7 - 3 = 10 - 6

so;

7 + (1/2)x - 3 + (3/4)x = 5x/4 + 10 - 6

by comparison;

5x/4 is equal to the mixed fraction 1 whole number (1/4)x

k = 10 as obviously -6 is equal to -6.

Therefore, 10 is the value of k that will make expressions equivalent.

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The end behavior of the graph is that it approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

This can be seen by examining the equation of the function. If the leading coefficient is negative, then the graph will be shifted down. As x approaches negative infinity, the term with the highest degree will grow exponentially and dominate the equation, causing the graph to approach negative infinity. Similarly, as x approaches positive infinity, the highest degree term will dominate the equation again, and the graph will approach positive infinity. For example, if the function is f(x) = -2x^4 + 0.5x + 8, the end behavior will be -∞ as x approaches -∞ and +∞ as x approaches +∞. This is because the highest degree term is -2x^4, which has a negative leading coefficient, so the end behavior of the graph will be shifted down. As x approaches negative infinity, the -2x^4 term will dominate the equation, causing the graph to approach negative infinity. Similarly, as x approaches positive infinity, the -2x^4 term will again dominate the equation, causing the graph to approach positive infinity.

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Yes, a dilation with a scale factor of 1 /3 a reduction.

What is a scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Here, w

We have to determine if dilation with a scale factor of 1 /3 a reduction.

We concluded that a dilation with a scale factor between 0 and 1 is a reduction because the image will decrease in size.

On the other hand, a dilation with a scale factor greater than 1 is an enlargement, where the image increases in size.

Hence, a dilation with a scale factor of 1 /3 a reduction.

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Therefore , the solution of the given problem of ratio comes out to be Jessie votes to Rachel votes is 6:5.

A ratio is the simple expression "a / b," where "b" must not be greater than zero, for an ordered pair of numbers "a" and "b." Two ratios are combined to form a ratio. The ratio might be represented as 1:3 if there was just one man and three girls. 3/4 are girls, while 1/4 are boys. A part is a statistic, a percentage of something's size, or a distinction between two or more objects.

Here,

Given: Rachel received 50 votes,

Mario got 40 votes, and Jessie got 60.

To calculate the proportion of Jessie votes to Rachal votes:

Thus,

=> 60 : 50

=>6:5

Therefore , the solution of the given problem of ratio comes out to be Jessie votes to Rachel votes is 6:5.

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3x+y=-1 is the equation for slope as -3 and point as (-1,2).

Algebraic expressions are used to express mathematical expressions, and algebraic expressions are used to express mathematical expressions. For example, 3x + 5 = 14 is an equation containing two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

slope=-3

point=(-1,2)

(y-y1)=m(x-x1)

y-2=-3(x+1)

y-2=-3x-3

3x+y=-1

The equation for slope as -3 and point as (-1,2) is 3x+y=-1.

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It is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm because the sum of two sides(2.5 cm and 4.5 cm) are smaller than three sides(8 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 2.5 and 4.5

2.5 + 4.5 < 8

7 < 8

Now we add 2.5 and 8

2.5 + 8 > 4.5

10.5 > 4.5

Now we add 4.5 and 8

4.5 + 8 > 2.5

12.5 > 2.5

It is possible to construct a triangle whose sides are 2.5 cm 4.5 cm and 8 cm because the sum of two sides(2.5 cm and 4.5 cm) are smaller than three sides(8 cm).

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Answer: -1/16

Step-by-step explanation:

3/8  --->  6/16

5/16 - 6/16 = (-1/16)

Answer:

    The x-intercept: The number of minutes it takes for the container to empty

The y-intercept: The number of gallons in the container before the drain is open

Hope this does helps!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

When doing the calculations it is seen that the ordered pair that would not be a solution would be number 2: (4,9) because if the X is 4 then the Y would be 13 and not 9.

The answers after calculations↓

(0,5)

(4,13)

(-2,1)

(2,9)

D) The example (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials.

The commutative property of addition for polynomials states that the order in which polynomials are added does not affect the result of the sum. In other words, it states that if we have two polynomials A and B, the result of adding A and B (A+B) will be the same as adding B and A (B+A).

For example, consider the polynomials (2x^2 + 5x) and (4x^2 - 4x). If we add these two polynomials in the order given, (2x^2 + 5x) + (4x^2 - 4x) = 6x^2 + x. Now, if we add these two polynomials in the reverse order, (4x^2 - 4x) + (2x^2 + 5x) = 6x^2 + x. We can see that the order of the polynomials does not affect the result of the sum, and thus it holds the commutative property of addition.

Option (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials, because it shows that the order of the polynomials does not matter and it gives the same answer.

It is important to note that the other options does not illustrate the commutative property.

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The given quadrilateral ABCD is a rectangle, and the value of x is -2.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. By connecting four non-collinear locations, it is created. Quadrilaterals always have a total internal angle of 360 degrees.

A quadrilateral with parallel sides that are equal to one another, and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Given that ABCD is a rectangle.

In rectangle all the angles are equal, hence equate the two angles as follows:

4x + 8 = 6x + 12

6x - 4x = 8 - 12

2x = -4

x = -2

Hence the value of x is -2.

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Construct a dilate, with scale factor 2, of a triangle using only a ruler and compasses.

The center of dilation—the location from where the picture is shrunk or expanded—is necessary to build a dilation. A scale factor, or the quantity that controls how big or tiny the new picture will be, is also necessary. If the scale factor is more than 1, the new picture will be bigger than the original image, creating an enlargement. We see a decrease if the scale factor is less than 1, as the new picture will be smaller than the original image.

Step-1

Let's dilate triangle PQR by a scale factor of 2 with a center of dilation at point C.

Step-2

First, we will use a straightedge to connect the center of dilation C to each vertex. We are going to extend those lines across the whole page.

Step-3

Next, we'll place the point of the compass on the center of dilation C and the pencil on vertex Q and measure that distance.

Step-4

Now, without changing the size of the compass, we  will move the point of the compass to vertex Q, and make a mark on the line that is extended through Q.

Step-5

Notice that since we measured the distance from C to Q and then used that same distance to mark the line, we have now created a new point that is twice the distance from C that Q was.

We now repeat the process for each of the other vertices of the triangle.

Step-6

These marks represent the vertices of our dilated image. We often use the same letters with an apostrophe to show that it is the corresponding vertex.

Step-7

Finally, we use the straightedge to connect all of the new vertices.

Now,See how triangle P ′ Q ′ R ′  is tw ce the size of the original triangle.

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The balance of the account with the given data is given as follows:

$1,212.62.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

P = 900, r = 0.05, n = 4, t = 6.

Meaning that the balance is given as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 900\left(1 + \frac{0.05}{4}\right)^{4 \times 6}[/tex]

A(6) = $1,212.62.

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Joe's hourly rate before his raise is represented by the expression 10.25 - r, where r is the amount of the raise.

Joe's hourly rate before his raise is represented by the expression 10.25 - r, where r is the amount of the raise. The expression 10.25 - r represents the amount of Joe's hourly rate before his raise. This is because when we subtract r from 10.25, we are essentially taking away the raise that Joe received, which leaves us with the amount of his hourly rate before he received the raise. In other words, Joe's hourly rate before his raise is 10.25 minus the amount of the raise. This expression is used to calculate the amount of Joe's hourly rate before his raise.

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Constant functions have graph that are horizontal lines in the plane and are linear functions. Graph 3 is the correct answer.

One of the simplest forms of real-valued functions is a constant function, which is used to express a quantity that remains constant across time. Constant functions have graphs that are horizontal lines in the plane and are linear functions. The x-value serves as the function's domain, which is depicted on the x-axis, and the y-axis serves as its range, which is indicated by the symbol f(x).

We know that the constant functions remain constant, that is they do not change their value. Constant functions have graphs that are horizontal lines in the plane and are linear functions.

Hence, graph 3 is the correct answer.

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Answer:

C

Step-by-step explanation:

use 0 and 3 for example:

replace x with 0 give you 2*0=0

add 0 with 3 and you get 3

The probabilities for this problem are given as follows:

a) The first free throw that he makes is the fourth shot: 0.0430 = 4.30%.

b) The first is the second or the third: 0.3459 = 34.59%.

c) He misses the first three: 0.0741 = 7.41%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The probability of missing the first three is P(X = 0) when n = 3, hence:

0.42³ = 0.0741 = 7.41%.

For item a, the probability is the above probability multiplied by 0.58 (making the fourth), hence:

0.58 x 0.0741 = 0.0430 = 4.30%.

For the first being the second or the third, the probabilities are given as follows:

Hence:

0.2436 + 0.1023 = 0.3459 = 34.59%.

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Answer:

2

Step-by-step explanation:

The x coordinate of one of the endpoints of the dilated segment is; x = 8

In the case when a coordinate point (x, y) should be dilated by a scale factor k, it means that the coordinate would be (kx, ky).

Now, since the coordinate point of dilation is given as (4 ,1), it means that if the coordinate is dilated by a factor of 2, then the new coordinate points should be at (2(4), 2(1))

= (8, 2)

Therefore we can conclude that that will be a coordinate of one of the endpoints of the dilated segment and the x-coordinate here is 8

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Yes, 8, 15, 17 is a Pythagorean Triple and sides of a right triangle.

What is meant by Pythagorean?

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Yes, 8, 15, and 17 are triples of Pythagoras, and the sides are right triangles.

The Pythagorean theorem, also known as the Pythagorean theorem, is the fundamental relationship between the three sides of a right triangle in Euclidean geometry.

According to this rule, the area of ​​a square with two other sides is the area of ​​the square whose side is the opposite side of the hypotenuse, or right angle.

The name of this phrase evokes the Greek philosopher Pythagoras, who lived around 570 BC. was born. This theorem has probably been proven most frequently of all mathematical theorems using various techniques.

There are numerous proofs, some dating back thousands of years, involving both geometric and algebraic proofs.

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We estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n, because it allows us to make better predictions about the population mean than the standard normal curve.

True, True, True, False, True, True.

The formula for the t-distribution is given by:

t = (x-μ)/(s/√n)

Where x is the mean of the sample, μ is the mean of the population, s is the sample standard deviation, and n is the sample size.

The t-distribution approaches the standard normal distribution as n increases because the denominator, s/√n, gets smaller, making the t-distribution smaller. As n increases, the tails in the t-distribution become "fatter" because the denominator in the formula gets smaller and the resulting t-distribution has a wider range of values.

The shape of the t-distribution depends on its degrees of freedom, which is the number of values in the sample minus one. The more degrees of freedom, the more the t-distribution resembles the standard normal curve.

We use the Student's t-distribution when we estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n, because it allows us to make better predictions about the population mean than the standard normal curve.

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Answer:

Jon Marc knows the radius of one flower bed is 6.5 feet and the diameter of the other is 30 feet. a. Find the area of each flower bed. Use 3.14 for π.

Step-by-step explanation:

The total area of the patio will be 20 * 40 = 800 square feet.

The proportionate relationship between a linear dimension of a feature on a model, map, or drawing of an object and the same feature on the genuine thing. A scale model is a physical representation of an object that is geometrically equivalent (known as the prototype).

Since the scale drawing is 3 inches : 10 feet, this means that every 3 inches on the drawing represents 10 feet in real life. Hence, 1 inch on the drawing represents 10/3 = 3.33 feet in real life.

So the patio measures 6 inches by 12 inches on the drawing, which corresponds to 6 * 3.33 feet by 12 * 3.33 feet in real life, or 20 feet by 40 feet.

Therefore, the total area of the patio will be 20 * 40 = 800 square feet.

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The perimeter of the egg comprising of arcs AB, AC, BD, and CD is π·(6-√2)/2 centimeters

The perimeter of a figure is the length of the boundary line of a plane occupied by the figure.

The perimeter of the egg can be found by finding the sum of the lengths of the arcs that together form a composite figure of the perimeter of the egg

The length of arc AC centered at point B is found as follows;

The angle at the center B is the base angle of the isosceles right triangle

The acute angle of an isosceles right triangle is 45°, therefore, the angle at B = 45°

The radius of the arc AC, AB = AO + OB = BC

AO and OB are the radii of the circle with center O

AO = OB = 1 cm

AB = 1 + 1 = 2 = BC

The length of AC = (45/360)× 2×π×2 = π/2

AC = π/2

The radii and angle at the center of arc BD are also 2 cm and 45°

The length of arc BD is therefore, (45/360) × 2 × π × 2 = π/2

BD = π/2

The angle at the center of arc CD = ∠CED

∠CED ≅ ∠AEB (Vertical angle postulate)

∠AEB = ∠AEO + ∠BEO = 45° + 45° = 90°

∠CED = ∠AEB (Definition of congruency)

∠CED = ∠AEB = 90°

The radius of the arc CD, CE = ED = BC - EB

EB = √(1² + 1²) = √2

CE = 2 - √2

Length of arc CD = (90°/360°) × 2 × π × (2 - √2)) = π × (2 - √2))/2

CD = π·(2 - √2)/2

The radius of the arc AB = 1 cm

Angle at the center of arc AB = 180°

Length of arc AB = π × 1 = π

AB = π

The perimeter of the egg = AC + CD + BC + AB

Therefore;

The perimeter of the egg = π/2 + π × (2 - √2))/2 + π/2 + π = π·(6 - √2)/2

The perimeter of the egg is π·(6 - √2)/2 cm

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According to the information of the table, the value of B in the table is 20, So the option is C .

To calculate the value of B in the table we need to analyze the information that is available in the table to understand how to find this value. Once we understand the information we can perform the following mathematical operation calculating the constant of proportionality:

Constant of proportionality = Whole / Part

Constant of proportionality = 40 / 28

Constant of proportionality = 1.4285714

On the other hand, to find the value of B, we must perform the following operation:

Whole = Part × Constant

Whole = 14 × 1.4285714

B = 20

According to the above, the correct answer is the value of B equals 20, so the correct option is C.

Note: This question has the information disorganized and incorrect and is not understood. Below is the information organized for a better understanding:

A three-column table is given.

Part: A C D

Part: 14 28 63

Whole: B 40 90

What is the value of B in the table?

50

36

20

12

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