For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1. 8x2?

Therefore , the solution of the given problem of function comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and

Domain :[ -∞,0 ] U [ 0,∞].

According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.

Here,

Part A:

=> 4/6x² - 5x²/4x

=> 8 - 15x + 3x³/12x²

=>  3x³- 15x +8 / 12x²

=> x(3x²- 15 ) + 8 / 12x²

Part B:

Domain : x ∈ R : x≠ 0

Part c:

The function domain at x= 0 Domain :[ -∞,0 ] U [ 0,∞]

Therefore , the solution of the given problem of equation comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and Domain :[ -∞,0 ] U [ 0,∞].

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After simplification the correct matching is

1) 9i - A)[tex]\sqrt{-81}[/tex]

2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]

3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]

4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Here to convert radical to simplified form we need to simplify them then

A)=> [tex]\sqrt{-81}[/tex] = [tex](\sqrt{i*9*9} })[/tex] =  9i

B) =>  [tex]4\sqrt{54} = 4\sqrt{9*6}= 4\sqrt{3^2*6}= 4*3\sqrt{6} = 12\sqrt{6}[/tex]

C) => [tex]\sqrt{-50} = \sqrt{i^2*25*2}=\sqrt{i^2*5^2*2}=5i\sqrt{2}[/tex]

D) => [tex]\sqrt{-252} = \sqrt{i^2*36*7}=6i\sqrt{7}[/tex]

Hence the correct matching is

1) 9i - A)[tex]\sqrt{-81}[/tex]

2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]

3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]

4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]

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To simplify a square root, simply factor the number and extract the roots of any perfect squares found from the radical sign.

Simplify a radical expression that use the Product Property.

To convert radicals to simplified forms, we must first simplify them.

A) = [tex]\sqrt{-81}[/tex]

   = ([tex]\sqrt{i*9*9}[/tex] )

   =  9i

B) = 4[tex]\sqrt{54}[/tex]

    = 4[tex]\sqrt{9*6}[/tex]

    = 4[tex]\sqrt{3^{2}*6 }[/tex]

    = 4*3√6

    = 12√6

C) = [tex]\sqrt{-50}[/tex]

    = [tex]\sqrt{i^{2}*25*2 }[/tex]

    = [tex]\sqrt{i^{2}*5^{2}*2 }[/tex]

    = 5i√2

D) = [tex]\sqrt{-252}[/tex]

    = [tex]\sqrt{i^{2}*36*7 }[/tex]

    = 6i√7

As a result, the correct match is

1) 9i - A) [tex]\sqrt{-81}[/tex]

2) 5i - C) [tex]\sqrt{-50}[/tex]

3) 12 - B) 4[tex]\sqrt{54}[/tex]

4) 6i - D)[tex]\sqrt{-252}[/tex]

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It is impossible to solve a 3-sided triangle because triangles require 3 sides and 3 angles in order to be solved.

A triangle is a three-sided polygon, and the sum of its angles is always 180 degrees. In order to solve a triangle, you must know the length of all three sides and the measure of all three angles. If you know two sides and the angle between them (the angle opposite to one of the sides), you can use the Law of Sines to determine the other angle. If you know two angles and a side, you can use the Law of Cosines to determine the other two sides. With all three sides and angles known, you can use the Pythagorean Theorem to check your work. However, if you only have three sides, it is impossible to solve the triangle because you do not have enough information.

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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.

Like terms with the same variables are added together.

Let the equation be n + 2n + 9

simplifying the above equation, we get

3n + 9

Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.

Like terms with the same variables are added together.

Let the equation be n + 2n + 9

simplifying the above equation, we get

3n + 9

Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

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The constant of proportionality is 2

From the question, we have the following parameters that can be used in our computation:

1 scoop of ice cream = 1/2 cup of milk

5 scoops of ice cream = 2.5 cups of milk

The constant of proportionality (k) is then calculated as

k = Scoop of ice cream/Cup of milk

So, we have

k = 5/2.5

Evaluate

k = 2

In (a), we have:

k = 2

A proportional relationship is represented as

s = km

Where

s = scoop of ice cream

m = cup of milk

So, we have

s = 2m

In (b), we have

s = 2m

To graph the relationship, we start by generating a table of values and then plot the points

Recall that

s = 2m

So, we have

18 = 2m

Divide by 2

m = 9

Hence, the number of cups is 9

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The amount of cherries bought by the Harrison is 62.5 pounds.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

The amount of cherries bought by the Harrison should be more than the cherries bought by the Liam which is 5/8. Thus, The amount of cherries bought by the Harrison is more than the 5/8 or 62.5 pounds of cherries percent.

The cherries bought by the Liam is 5/8 pounds

The cherries bought by the Harrison is more than the Liam.

As in the problem the number of cherries bought Harrison (let) should be more than the cherries bought by the Liam (let ). Therefore,

H > L

As we know that the number of cherries bought by the Liam is 5/8 pounds. Keep the value of  in the above equation, we get,

H > 5/8

This equation can be rewritten in the percentile form as,

h > (5/8) * 100 %

h > (5/2) * 25 %

h > 62.5 %

Hence, The amount of cherries bought by the Harrison is more than 5/8 pounds or 62.5 pounds of cherries percent.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

perp. -2

y - 2 = -2(x + 5)

y - 2 = -2x - 10

y = -2x - 8

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]2y=6-2x\implies 2y=-2x+6\implies y=\cfrac{-2x+6}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -1 \implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1} \implies 1}}[/tex]

so we're really looking for the equation of a line whose slope is 1 and it passes through (6 , -7)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{6}) \implies y +7= 1 (x -6) \\\\\\ y+7=x-6\implies {\Large \begin{array}{llll} y=x-13 \end{array}}[/tex]

Answer:

All real numbers for both Range and Domain

R

or

(−∞,∞)

The number of times which the two computers back up at the same time in twenty four hours as required is; 144.

It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.

On this note, the least common multiple of both backup times represents when the two computers back up at the same time.

Hence, since the LCM of 5 and 2 is; 10.

It follows that the two computers back up at the same time after every ten minutes.

Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;

= ( 24 × 60 ) / 10

= 24 × 6

= 144 times.

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The directions of XYZ in graph are left and right, top and bottom and outward from the screen respectively.

The term graph is known as a pictorial representation or a diagram that represents data or values in an organized manner.

Here we have to find the directions of XYZ on the graph.

Here we have know that X-Y-Z matrix is a three-dimensional structure whereby the x-axis and y-axis denote the first two dimensions and the z-axis is the third dimension.

And then in a graphic image, then the x denotes width, y denotes height and the z represents depth.

The directions of the x axis is in the plane of the screen and is positive toward the right and negative toward the left. Where as the directions of the y axis is in the plane of the screen and is positive toward the top and negative toward the bottom.

Finally the directions of the z axis is perpendicular to the screen or keyboard, and is positive extending outward from the screen.

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In linear equation, Ben is 9 years old currently.

What in mathematics is a linear equation?

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. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Ben's mom = 22 years

Ben is 9 years old currently.

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Binomial is the referred to the polynomial algebraic expression that has two terms.

An expression with two dissimilar terms joined by an addition or subtraction operator is called a binomial in algebra. Since there are two terms, for instance, 2xy + 7y is a binomial. According to the quantity of terms present, algebraic expressions can be divided into different types, such as monomial, binomial, trinomial, etc.

An expression in algebra with two terms is called a binomial. Alternatively stated, a binomial expression is an algebraic expression made up of two terms that are dissimilar and have constants and variables. Using mathematical operators like + (plus) and - (minus), these terms are joined. Depending on how many terms it contains, an algebraic expression is classified as a binomial, monomial, trinomial, quadrinomial, etc.

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Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.

A mathematical concept known as a square root is indeed a factor of a number that, when multiplied on its own, equal the original value. For instance, 3 and -3 are the cube roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.

Here,

In this case, The square root of 2 is "irrational" (cannot be expressed in a fraction) because, if It Could,

You Would Have the Nonsensical Situation That The Fraction Would Have Even Integer value

At Both The Top And Bottom And Could Therefore Always Be Simplified.

.

Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.

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The slope is $125 and the slope tells the annual due payment of $125.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take two points from the graph as (2, 400) and (4, 650)

Then, the slope of line is

slope, m = ( 650- 400) / ( 4- 2)

slope, m = 250 /2

slope , m = 125

Hence, the slope is 125.

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The number of different ways is 7560 ways

From the question, we have the following parameters that can be used in our computation:

Chiefs = 1

Supporting chiefs = 2

Members = 10

Inferior officers = 2

There are 10 members.

So, the number of ways to select a chief is 10

Now, there are 9 members left

The number of ways to select a supporting chief is then represented as

Supporting chief = ⁹C₂

Now, there are 7 members left

The number of ways to select an inferior officer is then represented as

Inferior officers = ⁷C₂

So, the total number of ways is

Ways = 10 * ⁹C₂ * ⁷C₂

Evaluate

Ways = 7560

Hence, the number of ways is 7560

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On solving the provided question, we can say that stabilizing selection type of selection does this demonstrate is shown by frequency distribution.

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9,

stabilizing selection type of selection does this demonstrate is shown by frequency distribution.

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Complete question: The frequency distribution of birthweights in human infants is bell shaped with most birthweights in the middle of the range of birthweights. What type of selection does this exemplify?

Answer: $3.06

Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.

Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .

Examples of negation are ,

Logical operations are performed to check the trueness of an expression.

These are generally Boolean expressions or algebraic functions.

A negation of a basic assertion is made by  inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.

Under negation, what was true becomes false and the vice - versa.

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The area of the scale drawing is 108 square inches.

I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108

Answer:

3x³ is a polynomial of degree

The degree of the polynomial 3x³ is 3

Answer:

17.85

Step-by-step explanation:

175% * 10.20 = 17.85

Answer:c/π=d

Step-by-step explanation: the d and π was multiply with the d and if we want separate with it, we need to use the opposite way to get it.

Answer:

Weight change per week = -0.875 or -7/8

Step-by-step explanation:

Sara recorded her dog's weight change as -3.5 pounds after 4 weeks of dieting. We know the weight loss is consistent each week, so we need to find out how much the dog loses in one week.

To find out the weight change per week, we can use the formula:

Weight change per week = Total weight change / Total number of weeks

Plugging in the known values:

Weight change per week = -3.5 / 4

Weight change per week = -0.875

The dog loses 0.875 pounds each week.

or -0.875 pounds is the weekly weight change of the dog during the dieting period.

Answer:

Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.

Angle 1: (right angle) 90 degrees

Angle 2: 45 degrees

Angle 3: 45 degrees

2 equations that could be used to solve for missing lengths are:

[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]

Now, According to the question:

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

Quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

ABCD ~ A'B'C'D'

So,

[tex]\frac{AB}{A'B'} = \frac{BC}{B'C'}\\ \\ \frac{CD}{C'D'} = \frac{AD}{A'D'}[/tex]

Hence,  2 equations that could be used to solve for missing lengths are:

[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]

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The ratios are not equivalent.

the x & y angles are alternate angles.

The alternate exterior angle theorem states that if two lines are parallel and are intersected by a transversal, then the alternate exterior angles are considered as congruent angles or angles of equal measure.

Here, we have,

from the given figure , we get,

the x & y angles are alternate angles.

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