which graph shows solution?

The roots of h(x)=x³−2x²+9x−18 is 2, -3i and 3i.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

Given:

h(x)=x³−2x²+9x−18

so, (x-2) is the solution of h(x).

Now, the synthetic division

                                  (x-2) | x³−2x²+9x−18 | x² + 9

                                            x³ −2x²

                                      __________

                                                0   + 9x - 18

                                                         9x - 18

                                                     __________

                                                               0

now, again factorize x² + 9 = 0

 x = ±3i

Hence, the roots are 2, -3i and 3i.

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Answer:

Step-by-step explanation:

=0.25

The linear equation in slope-intercept form for the velocity of sound as a function of temperature is v = 0.068T + 293.2, where v is the velocity of sound and T is the temperature in degrees Celsius. Using this equation, the velocity of sound at 60°C is 339.6 m/s.

The velocity of sound in dry air increases as the temperature increases. At 40°C, sound travels at a rate of about 355 m/s, and at 49°C, it travels at a rate of about 360 m/s. To write a linear equation in slope-intercept form for the velocity of sound as a function of the temperature, first calculate the slope of the line by finding the difference in velocity divided by the difference in temperature: (360 - 355) / (49 - 40) = 0.068. This slope can be written as the coefficient of the T-term in the equation. To find the y-intercept, plug in the temperature at which the velocity was measured (40°C) and the corresponding velocity (355 m/s) into the equation of the form v = mT + b. Solving for b yields 293.2. Therefore, the linear equation in slope-intercept form is v = 0.068T + 293.2. To find the velocity of sound at 60°C, plug in 60 for T in the equation and solve for v, which yields 339.6 m/s.

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Mira's scale factor of 7 in would not be reasonable because it would make the dimensions of A' too small.

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The length and width of the wall of the barn are 12 feet and 6 feet respectively.

The formula for area of rectangle is -

Area of rectangle = length × width

Let the width of rectangle be x. So, the length of rectangle = x + 6. Keep the values in formula to find the length and width of the barn.

x × (x + 6) = 72

Performing multiplication

x²+ 6x - 72 = 0

x² + 12x - 6x - 72 = 0

x (x + 12) -6(x + 12) = 0

x = 6 and - 12

Thus, width of rectangle = 6 feet

Length of rectangle = x+ 6

Length of rectangle = 6 + 6

Length of rectangle = 12 feet

Thus, length and width are 12 and 6 feet.

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The complete question is -

The area of a rectangular wall of a barn is 72 square feet. Its length is 6 feet longer than the width. Find the length and width of the wall of the barn.

Answer:250(0.6)

Step-by-step explanation:

The value of the function is f ( x ) = 250 ( 0.6 )ˣ

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The values of x are in set x = { 0 , 1 , 2 , 3 , 4 , }

The values of y are in set y = { 250 , 150 , 90 , 54 , 32.4 }

Now , the equation will be y = 250 ( 0.6 )ˣ

when x = 0

y = 250 ( 0.6 )⁰

y = 250 ( 1 )

y = 250

when x = 1

y = 250 ( 0.6 )¹

y = 250 ( 0.6 )

y = 150

when x = 2

y = 250 ( 0.6 )²

y = 250 ( 0.36 )

y = 90

when x = 3

y = 250 ( 0.6 )³

y = 250 ( 0.216 )

y = 54

when x = 4

y = 250 ( 0.6 )⁴

y = 250 ( 0.1296 )

y = 32.4

Hence , the function is y = 250 ( 0.6 )ˣ

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Tickets are sold by airlines based on availability and demand. To increase their amount of earnings, they consider things like flight capacity, the time of year that people travel, the number of tickets available, and pricing.

Tickets are sold by airlines based on availability and demand. To choose the best course of action for their firm, they carefully analyse variables including aeroplane capacity, travel season, seat availability, and cost. Airlines assess the current market and forecast future trends using sophisticated mathematical models. This aids them in figuring out the ideal quantity of tickets to market and the finest selling price. To make sure that their tickets are reasonably priced, airlines also take into account the demand for their flights and the competition from other airlines. In order to make their tickets appealing to customers, airlines may consider promotional activities and unique offers. Airlines may increase their revenue by selling tickets at the proper price by studying the data and making wise judgements.

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Answer: 1 1/3

Step-by-step explanation: To find this answer, we simply divide the people by the oranges. So, 4 / 3 is 1.3333333333333...... We round this to about 1.3. So, that as a fraction is 1 1/3. So, each person gets 1 1/3. To check, we multiply 1 1/3 by 3 (people) and we get 4. I hope this helped!

The length of the sides of the rhombus JKLM is 12 units.

A rhombus is one of parallelograms. The opposite sides of a rhombus are parallel, and the opposite angles are equal. Furthermore, all of the sides of a rhombus are the same length, and the diagonals intersect at right angles.

In the problem, the sides of rhombus JKLM are:

JK = 2x + 4

JM = 3x

Since the length all of the sides of a rhombus are the same, then:

JM = JK

3x = 2x + 4

Substract both sides by 2x:

3x - 2x = 2x + 4 - 2x

x = 4

To find the length of a side, substitute x = 4 into:

JM = 3x

JM = 3(4) = 12

Hence, the length of the sides of the given rhombus is 12.

The picture in your question is missing. Most likely it was like on the attached picture.

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Answer:

12

Step-by-step explanation:

JK = JM

2x + 4 = 3x

x = 4

JK = JM = 3 x 4 = 12

Haven't answered an inequality question in a while so this
might be complete bullhonkey.

Answer:

154 minutes of talktime.

Step-by-step explanation:

To find out how many minutes of talktime John can have per month, we need to set up an equation using the information given.

Let x be the number of minutes of talktime John can have per month.

The equation for John's monthly phone bill is:

26.50 + 0.35x = 80

To find the value of x, we can solve for x by subtracting 26.50 from both sides:

0.35x = 53.50

To find the number of minutes, we can divide both sides by 0.35:

x = 153.57

To the nearest whole number, John can have 154 minutes of talktime per month.

Answer:

x = 3

Step-by-step explanation:

2x + 5 = 3x + 2

-5 -5

2x = 3x + 2 - 5

-3x -3x

2x - 3x = 2 - 5

-x = -3

x = 3

Answer:

a) (0,1)

b) k = 6.5

Step-by-step explanation:

When a line crosses the y-axis at a point, the point's x-coordinate must be 0. Let's substitute the value of x into the equation of the line to find its y-coordinate.

y - 4x = 1

Rearrange terms to isolate y.

y = 4x + 1

Substitute x = 0 into the equation.

When x = 0, y = 4(0) + 1

y = 0 + 1

y = 1

Thus, the coordinates of the point is (0, 1).

---

The second question uses the general equation of a straight line which is y = mx + c where m is the gradient of the line and c is the y-intercept of the line. As you can see from the graph drawn, the line cuts the y-intercept at (0, -3) so c = -3. You are given the y-coordinate of the point (which is 10) so you can find the x-coordinate (k) by substituting the value of y into the equation of the line once again.

y = 2x + c

You know the value of c from the y-intercept. c = -3

y = 2x - 3

Substitute y = 10 into the equation.

When y = 10, 10 = 2x - 3

10 + 3 = 2x

2x = 13

x = 6.5 when y = 10

Thus, the value of k is 6.5.

As per the concept of reasoning, the conditional statement is false.

The term reasoning in math is called as students who genuinely make sense of mathematical ideas can apply them in problem solving and unfamiliar situations and can use them as a foundation for future learning.

Here we have the conditional statement "if a human being has 7 heads, then they have 11 arms".

And here we need to find out whether this statement is true or false.

While we looking into the given statement we have identified that this is false because this statement is missing the necessary or sufficient words.

Simply said that it is not possible situation.

Therefore the statement is false.

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No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.

It is a branch of mathematics that deals with the occurrence of a random event.

A representative sample has to be in proportion, and the diagram shows that the greater part is not represented in proportion. Because it is not represented in proportion, it is not a representative sample.

No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.

Hence, No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.

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The statement that is not true is the fourth one.

"Other points that are on line f are also solutions of the system".

We know that the graphs of lines f and g intercept at the point (4, 5). So trivially, the point (4, 5) belongs to both graphs.

That also means that (4, 5) is the solution of the system of equations:

y = f(x)

y = g(x).

And because these two are lines, these will intercept only once, then (4, 5) is the only solution of the system.

That means that the correct option (the false statement) is the fourth one.

"Other points that are on line f are also solutions of the system".

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[tex]\dfrac{2}{9} = 2\div 9 = 0.2222222222222...[/tex]

x is 2.

At the instant when dp/dt=41 and c = 15, the value of dc/dt is -0.273333.

The derivative of p with respect to time t is given by:

dp/dt = 2p dp/dc * dc/dt

Since dp/dt = 41, we have:

41 = 2p dp/dc * dc/dt

To find dp/dc, we can use the relationship between p and c:

p^2 = (20-c)^3

Taking the derivative of both sides with respect to c, we get:

2p dp/dc = -3(20-c)^2

Substituting this expression into the equation for dp/dt, we get:

41 = 2p * (-3(20-c)^2) * dc/dt

Plugging in the value of c = 15, we find:

41 = 2 * p * (-3(5)^2) * dc/dt

Using the relationship p^2 = (20-c)^3, we can find p:

p = sqrt((20-c)^3) = sqrt((20-15)^3) = sqrt(5^3) = 5

Substituting the value of p into the equation for dp/dt, we get:

41 = 2 * 5 * (-3(5)^2) * dc/dt

Solving for dc/dt, we find:

dc/dt = 41 / (2 * 5 * (-3(5)^2)) = 41 / (2 * 5 * (-3 * 5^2)) = 41 / (-150) = -41/150 = -0.273333...

So the value of dc/dt at the instant when dp/dt = 41 and c = 15 is approximately -0.273333.

Correct Question :

the positive variables p and c change with respect to time t. the relationship between p and c is given by the equation p2= (20−c)3. at the instant when dp/dt=41 and c = 15 what is the value of dc/dt?

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Answer:

[tex]-\frac{82\sqrt{5} }{15}[/tex]

Step-by-step explanation:

[tex]p^{2} =(20-c)^{3}[/tex]

[tex]2p(\frac{dp}{dt}) =3(20-c)^{2}(-\frac{dc}{dt} )[/tex]

Took the derivative of both sides ^

It gives you [tex]\frac{dp}{dt} =41[/tex] and [tex]c=15[/tex], so you just need [tex]p[/tex]

[tex]p=\sqrt{(20-15)^{3} } =5\sqrt{5}[/tex]

Now plug in

[tex]2(5\sqrt{5} )(41)=3(20-15)^{2} (-\frac{dc}{dt} )[/tex]

[tex]-\frac{410\sqrt{5} }{75} =\frac{dc}{dt}[/tex]

[tex]-\frac{82\sqrt{5} }{15} =\frac{dc}{dt}[/tex]

Terms = 3x² , 6x , 7

Coefficients = 3,6

Neither One  = x²

A quantity or number that is combined with a variable is known as a coefficient.

Adding a variable to a number produces a coefficient.

The variable next to it is often multiplied by an integer.

Three terms make up the trinomial: 3x² + 6x + 7

3x²

6x

7

Enter the first column as a result.

The coefficients at and are respectively 3 and 6.

The second column should have these two integers.

x² is not a term (because 3x² is a term) and is not a coefficient, because coefficients are numbers.

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Answer:

Similar by SAS

Step-by-step explanation:

:)

Answer:

r= 45 s=5

5(r-s)= 45-5= 40

Step-by-step explanation:

5(9-1) <--- You substitute the values

(5*9-5*1)<--- Multiply

45-5<--- Subtract

40 <-- Answer

r= 45

s=5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5(r - s)}\\\mathsf{= 5(9 - 1)}\\\mathsf{= 5(9) + 5(-1)}\\\mathsf{= 45 - 5}\\\mathsf{= 40}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{40}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The error is when h is some value, the error will be when h/2.

The error of a third-order accurate numerical differentiation method scales with the fourth power of the step size, i.e. if the step size is halved, the error will decrease by a factor of 2⁴=16. So if the error is when h is some value, the error will be when h/2.

The error in numerical differentiation methods can be approximated using Taylor series expansions. For a third-order accurate method, the error term in the Taylor series would be proportional to h⁴. Hence, reducing the step size by a factor of two would reduce the error by a factor of 2⁴ = 16. This relationship between step size and error holds for small step sizes. For larger step sizes, the error may not decrease in such a simple manner and other factors such as the smoothness of the function being differentiated and the presence of singularities or discontinuities may come into play.

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The sketches after 8 hours is 32

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

Bob is an artist and creates 3 sketches in 45 minutes

This means that

3 sketches = 45 minutes

Convert minutes to hour

3 sketches = 3/4 hour

Multipy both sides by 8

So, we have

8 * 3 sketches = 3/4 * 8 hours

Multipy both sides by 4/4

So, we have

32 sketches = 8 hours

Hence, the sketches is 32

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Answer:

32

Step-by-step explanation:

The area of a parallelogram is bh where b = base, h = height

This is one of the questions where plotting the points and seeing the parallelogram is vital

See the attached figure

height h = |difference between x-coordinates of A and C| =

= |6 - 2| = 4.

This will be the same as |difference between x-coordinates of B and D

base b = |difference between y-coordinates of A and B| =  |1-(-7)| = 8.

This will be same as |difference between y-coordinates of C and D|

Area = bh = 8 x 4 = 32

The relationship between ACT scores and gender varies depending on the data and analysis performed.

ACT scores are an important aspect in the college admissions process. They measure a student's knowledge and skills in English, mathematics, reading, and science.

In the first scenario, it states that the largest percentage of both genders' ACT scores are above 25. It also mentions that more male students have scores under 20 than female students.

In the second scenario, it mentions that the largest percentage of both genders' ACT scores are in the 20 to 25 range and that more female students have scores under 20 than male students.

In the third scenario, it states that the largest percentage of both genders' ACT scores are under 20 and that more male students have scores above 25 than female students.

In the fourth scenario, it mentions that the largest percentage of both genders' ACT scores are in the 20 to 25 range and that more male students have scores under 20 than female students.

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The amount of gallium-67  remain after 6.5 days = 2.5 grams

We know that the half-life of the radioactive isotope is nothing but the time needed for the isotope to be half of its initial value of mass.

This means, with each half-life, the isotope will be halved of its initial value.

The formula for the numbers of half-lives:

numbers of half-lives = total time passed / the half-life of the isotope

Here, total time passed  = 6.5 days

                                        = 156 hours

the half-life of the isotope = 98 hours

Let n represents the number of half lives.

Using above formula,

numbers of half-lives n =  156 / 98

numbers of half-lives n = 1.59

numbers of half-lives n ≈ 2

So, the remaining mass would be,

remainig mass m = initial mass / [tex]2^n[/tex]

m = 10 / 2²

m = 2.5 g

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The derivative of y with respect to x exist for all values of y, that is it does not exist for no value of y.

Therefore the answer is d. for no values of y

The curve y^2 = x is a parabolic function and its derivative is continuous for all x in its domain, which is x >= 0. The derivative of this function, which is y' = (dy/dx) = 1/2 * √x, is well-defined for all x >= 0 and therefore, the derivative exists for all values of y, including y = 0 and y = -1.

In general, a function is said to be differentiable at a point if its derivative exists at that point, and the derivative provides information about the rate of change of the function at that point.

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Answer:x=-4

Step-by-step explanation

1. Set y as 0. Doing so will help you solve for x

3x +20(0)=-12 aka 3x=-12

2. Divide each sides by 3

3x(divided by three) = -12 (divided by three)

x=-4

(your answer would be negative because a negative divided by a postitive is negative.)