Find the range of the data set: 10,18, 21, 28, 12, 20

Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).

Roots of an equation refer to the values that when put into the variable of the equation, satisfy the equation and give the required value as 0.

Given:

g(x) = 3x⁵ - 2x⁴ + 9x³ - x² + 12 = 0

To find: Function having same set of potential rational roots as g(x).

Finding:

=> Then, m = ±1, ±2, ±3, ±4, ±6

    2. Let 'n'  denote the rational roots of 3.

=> Then n = ±1, ±3

Hence, the rational roots [tex]\frac{m}{n}[/tex] will be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].

The rational roots will be taken of 12 and 3 in the same position as in g(x).

Hence, the rational roots of f(x) will also be given by:   ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].

Thus, Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).

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(COMPLETE QUESTION:

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x

C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3

D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48)

Using the equation of the parabola, the inequality represented is:

y ≥ -(x + 2)² + 8.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (-2,8), hence:

h = -2, k = 8.

y = a(x + 2)² + 8.

The y-intercept is of (0,4), when when x = 0, y = 4, which we use to find a as follows:

4 = 4a + 8

4a = -4

a = -1.

Hence the parabola is:

y = -(x + 2)² + 8.

The exterior of the parabola is shaded, that is, the part that is above the concave down parabola, hence the inequality is:

y ≥ -(x + 2)² + 8.

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Answer: I calculated the surface area of a cube whose edge is 4.2 m

Step-by-step explanation: hope this helps

Answer: 1

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2}lg\frac{25}{4} -2lg\frac{4}{5} +lg\frac{320}{125}=\\\\lg\sqrt{\frac{5^2}{2^2} } -lg(\frac{4}{5})^2+lg\frac{5*64}{5*25}=\\\\lg\sqrt{(\frac{5}{2})^2 } -lg\frac{4^2}{5^2} +lg\frac{64}{25}=\\\\[/tex]

[tex]lg\frac{5}{2} -lg\frac{16}{25}+lg\frac{64}{25} =\\\\ lg\frac{5}{2}+lg\frac{64}{25} -lg\frac{16}{25} =\\\\lg\frac{5*64}{2*25} -lg\frac{16}{25}=\\\\ lg\frac{5*2*32}{2*5*5}-lg\frac{16}{25}= \\\\lg\frac{32}{5}-lg\frac{16}{25}=\\\\lg\frac{32*25}{5*16}=\\\\lg\frac{16*2*5*5}{5*16} =\\\\lg(2*5)=\\\\lg10 =\\\\1[/tex]

Answer:

D. 24

Step-by-step explanation:

The area of a triangle is [tex]\frac{1}{2} (bh)[/tex].

The height is already given: 8

But we need to find the base and since the hypotenuse is given and it's a right triangle, we can use the pythagorean theorem. (Hypotenuse is longest, slanted side of a right triangle)

The pythagoren theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the sides, and c is the hypotenuse.

Plugging in the given values => [tex]8^2+b^2=10^2[/tex]

We have to solve for b. So, squaring 8 and 10 we get [tex]64+b^2=100[/tex].

Next, subtract 64 from both sides to get b by itself: [tex]b^2=36[/tex]

Square root both sides to get [tex]b=6[/tex].

Now that we have our base we can plug it in to the area of triangle formula: [tex]1/2(6*8)[/tex].

Multiply inside the parenthesis: 1/2(48) => 24

Solving a linear equation, we can see that each box has 15 jars.

We know that Neve has 12 full boxes of jars of slime, and 7 jars of slime, then if each box has N jars, the total number of jars that Neve has is given by the linear equation:

12*N + 7

Now we know that Neve has 187 jars in total, then we can write:

12*N + 7 = 187

We want to find the value of N, which is the number of jars in each box, so we need to solve the linear equation:

12*N + 7 = 187

12*N = 187 - 7

12*N = 180

N = 180/12 = 15

We conclude that there are 15 jars in each full box.

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Answer: less

Step-by-step explanation:

Answer:     The answer is less than  

because negative are always less than positives

Step-by-step explanation:

I hope this helps

The equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.

It follows from the task content that the time at which the snowfall in the towns in discuss will be equal be determined.

According to.the word phrases given;

A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour. Hence, we have;

4 + 3x.

Also, a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. Hence ,we have;

1 + 5x

Consequently, when the snowfalls are equal, we have;

4 + 3x = 1 + 5x

3 = 2x

x = 3/2.

x = 1 and a half hours.

Ultimately, the equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.

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The circumference of track 3 is 691.43 feet

The circumference of a circle is the distance round the circle. It is the perimeter of the circle. The radius of a circle is a straight line that goes from the center of the circle to its circumference.

The circumference of a circle = 2πr

Where:

2 x (22/7) x 110 = 691.43 feet

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The ball will fall 35d after 5t seconds.

Equation Of Motion is used to define the basic concept of motion of object at various interval of times.

There are three equation of motion

[tex](i) v=u+at\\ \\ (ii) s=ut+\frac{1}{2} at^{2} \\ \\ (iii)v^{2}=u^{2} +2as[/tex]  (where s=distance, v=final velocity, u=initial velocity ,t=time,          a=acceleration)

According to the given question

Given distance = d

time=t

Acceleration a=g( gravity)

Using second equation of motion

[tex]d=ut+\frac{1}{2} at^{2}[/tex]     ( given u=0 as the ball was at rest, a=g , s=d)

[tex]d=\frac{1}{2} gt^{2}[/tex]........(1)

Using first equation of motion

Speed after t sec

[tex]v=u+at\\ \\ v=0+gt\\ \\ v=gt[/tex]    ....... (2)

Using second equation of motion distance after 5t seconds

since ball is moving with velocity "v", t=5t.

[tex]s=ut+\frac{1}{2} at^{2}\\ \\ d=v(5t)+\frac{1}{2} g(5t)^{2}[/tex]

Substituting the value v=gt from equation (2)

[tex]d=(gt)(5t)+\frac{1}{2} g(5t)^{2}\\ \\ =5gt^{2} +\frac{1}{2} g(5t)^{2}[/tex]taking LCM as 2 and solving further we get

[tex]=35(\frac{1}{2}gt^{2} )[/tex]    

using equation (1) we get

=35d

Therefore , The ball will fall 35d after 5t seconds.

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By taking the difference between the total cost of the condo and the amount that he already paid, we conclude that Joe owes a total of $160,000 for the condo.

To find how much he owes on the condo, we need to find the difference between the total cost of the condo, which is $200,000, and the amount that he already paid, which is $40,000.

(Remember that difference means a subtraction)

It gives.

$200,000 - $40,000 = $160,000

In this way, we conclude that Joe owes a total of $160,000 for the condo.

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Answer:

14

Step-by-step explanation:

44.66 / (12.76 / 4) = 14

Answer:

i think it is 4

Step-by-step explanation:

Answer:

224 cm³

Step-by-step explanation:

Volume = Area of base x height

V = 32 x 7

V = 224 cm³

In this question, all the required information is given so we'll simply have to solve.

[tex]\large\boxed{\bold{V= \ base \ area× \ height}}[/tex]

Now, substitute the values according to the formula.

[tex]V= \ 32 × 7[/tex]

[tex]\large\boxed{\bold{ V= \ 224 \ {cm}^{3}}}[/tex]

The answer is a whole number so we won't have to round off.

Hence, the volume of the given rectangular prism is 224 cubic centimeters.

Perimeter of rectangular garden = 34 ft

Area of rectangular garden = 60 ft²

Perimeter = 2(length + width)

Area = (length)(width)

The rectangular garden has the following vertices:

Length of the rectangular garden = QR = |-5 - 7| = |-12| = 12 units

Width of the rectangular garden = RS = |3 -(-2)| = |3 + 2| = 5 units

Perimeter = 2(length + width) = 2(12 + 5) = 34 units = 34 ft

Area = (length)(width) = (12)(5) = 60 units = 60 ft²

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Answer:

shebolixashebshe is she she is she she he she and he are in love go to xvideos.com to see them rápīng each other

Step-by-step explanation:

426;/7/(/&/)m

The range in which the usage vary is from 682.77  kilowatt-hours to 2867.11  kilowatt-hours.

Given the charge of electricity charge is 6.434 cents  per​ kilowatt-hour.

Fixed customer charge = ​$7.81

Bill range = $51.74 to ​$​192.28

Since every value is in $ , we will first convert cents to dollar

per​ kilowatt-hour charge will be $6.434/100    ( as $1 = 100 cents )

per​ kilowatt-hour charge = $ 0.06434    …(1)

Lets us first find the lower range of usage

Last year's lowest bill was $51.74 (including the customer charge)

So last year lowest bill = $51.74-$7.81  = $43.93   …(2)

We know that (per KWh charge)x(no. of KWh used)=Total bill. …(3)

Substituting the values from (1) & (2) we get

(0.06434)x(no. of KWh used)=$43.93

no. of KWh used=[tex]\frac{43.93}{0.06434} = 682.77 KWh[/tex]

Similarly we will solve for maximum KWh used

Lets us find the maximum range of usage

Last year's highest bill was $192.28 (including the customer charge)

So last year highest bill = $192.28-$7.81  = $184.47   …(4)

Substituting the value of (1) & (4) in (3) we get

(0.06434)x(no. of KWh used)=$184.47

no. of KWh used=[tex]\frac{184.47}{0.06434} =2867.11 KWh[/tex]

Therefore ,  the The range in which the usage vary is from 682.77 kilowatt-hours to 2867.11  kilowatt-hours.

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Answer:
True for all x/infinite solutions.

Step-by-step explanation:

[tex]4x+6=2\left(2x+3\right) < - Base Equation[/tex][tex]4x+6=4x+6 < - Expand-The-Equation-and-Simplify![/tex]
[tex]4x+6-6=4x+6-6 < - Subtract-Six-From-Both-Sides![/tex]
[tex]4x=4x[/tex]
[tex]4x-4x=4x-4x < - Subtract -4x- from- both -sides![/tex]
[tex]0=0[/tex]
________________________________________________________
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The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 31.89

Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).

The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).

Linear regression determines the actual linear relationship between two variables based on a line of best fit. As a result, the slope of a straight line was used to depict linear regression indicating how altering one variable impacts modifying another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.

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Answer: 43.6 cm

Step-by-step explanation:

18.6+3.2= 21.8

21.8*2= 43.6

A research study variable that is believed to be related to the study's variable of interest is accurately described by each of the following terms except dependent.

Any variable employed in research that has a cause and effect relationship is referred to as a research variable (also known as a study variable) informally. An array of variables, including independent factors, dependent variables, and intervening variables, can be employed in a study, including research/study variables.

Independent and dependent variables are crucial in research since they provide the framework for a study to be carried out. Confounding factors, controlled variables, superfluous variables, and moderator variables are some other sorts of variables that could be used in a research.

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Answer:

3.9

Step-by-step explanation:

8.2-4.3=3.9

3.9+4.3=8.2

The equation is 7x+11y+14z=33.

So,

The family of planes equation passing through the intersection of the planes x+2y+3z4=0 and 2x+yz+5=0 is:

It is assumed that the required plane's x-intercept is twice its z-intercept.

Substitute k = 4/5 in equation (1) as follows:

As a result, the required plane's equation is 7x+11y+14z=15.

Also,

7x+11y+14z=15 is the equation of the plane passing through the point (2,3,1) and parallel to the plane.

Therefore, the equation is 7x+11y+14z=33.

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the complete question is given below;
Find the equation of the plane which contains the line of intersection of the planes x+2y+3z−4=0 and 2x+y−z+5=0 and whose x−intercept is twice its z−intercept. Hence, write the equation of the plane passing through the point (2,3,−1) and parallel to the plane obtained above.

Answer:

30

Step-by-step explanation:

30*30 is 900

Answer:

30

Step-by-step explanation:

let x =width

900=(×)(30)

900=30×

900/30=30×/30

30=×

= 30 width

Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let y be the total amount and x be the number of miles.

Samir can rent a moving truck from Company A for $35 plus $0.50 per mile. Then the equation will be

y = 0.5x + 35   ....1

Company B for $25 plus $0.70 per mile. then the equation will be

y = 0.7x + 25     ....2

For the same rent, the number of miles will be

0.7x + 25 = 0.5x + 35

0.2x = 10

x = 50 miles

Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.

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Samir can rent a moving truck from Company A for $35 plus $0.50 per mile or from

Which statement is true?

Company B for $25 plus $0.70 per mile .

A. Renting from Company A will always be cheaper.

B. Renting from Company B will always be cheaper.

C. Renting from both companies will cost the same if Samir drives the truck 50 miles.

D. Renting from Company B will be cheaper if Samir drives the truck 100 miles.

3. The x-coordinate of the image is equal to the negative of that of the pre-image. The y-coordinate remains the same.

4. The transformation is best represented  algebraically by (-x, y).

5. The location of the image of T is (4, -8).

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