which of the following statements is/are true

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.

The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7

x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

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If x∆y = 3x - y², then

5∆1 = 3×5 - 1² = 15 - 1 = 14

and

14∆6 = 3×14 - 6² = 42 - 36 = 6

So (5∆1)∆6 = 6.

The value of x equals quantity of (3 ± √23)/2.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given equation;

  x² - 3x = -8

    x² - 3x + 8 = 0

 x² - 2 X 3/2 x + 8 = 0

 x² - 2.3/2 x + (3/2)² - (3/2)² + 8 = 0

 (x - 3/2)² - 9/4 + 8 = 0

 (x - 3/2)² + 23/4 = 0

  (x - 1.5)² = -5.75

  x - 1.5 = ±√(-5.75)

 x = 1.5 ± i√(5.75)

  x = (3 ± i√21)/2

Thus, x equals quantity of 3 plus or minus I square root of 23 all over 2.

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A slope also known as the gradient of a line is a number. The correct option is A, C, and D.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

For the given question,

This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.

This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.

This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.

Hence, the correct option is A, C, and D.

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Answer:

ACD

Step-by-step explanation:

Answer:

please see photo for detailed analysis.

u=-54

you have -54 because

-54(-2)=108/9=12

Answer:

u =-54

Step-by-step explanation:

-2/9u=12

To solve for u multiply each side by -9/2 to isolate u

-9/2 * -2/9 u= 12 * -9/2

u =-54

Answer:

6x + 7y = 14

7x + 8y = 27

6 7. x = 14

7 8. y = 27

option B

Answer:

5x - 10

Step-by-step explanation:

→ Find the sum of the expression

3x - 4 + 2x - 6

→ Collect all the x terms

3x + 2x - 4 - 6

→ Simplify

5x - 10

A function assigns the values. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?

A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.

B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.

C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.

D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.

If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.

Hence, the correct option is D.

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Answer:

[tex]\fbox {all real numbers}[/tex]

Step-by-step explanation:

7x + 8 = 1/6 (42x + 48)

7x + 8 = 7x + 8

x = all real numbers

Answer:

The standard deviation is about 2.915

Step-by-step explanation:

Answer:

=  2.9154759474227

Step-by-step explanation:

The conclusion is a=c statement

A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:

If P, then Q.

P occurs.

Consequently, Q occurs.

The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.

Hence, By modus Ponens

a=b∧b=c ⇒ a=c

So, given a=b∧b=c Then

⇒a=c.

Hence the conclusion is a=c statement .

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Answer:

[tex]-6.5x+11[/tex]

Step-by-step explanation:

Expand The Brackets:

[tex]x-1+12-7.5x[/tex]

[tex]=x+(-1)+12+(-7.5x)[/tex]

Combine Like Terms:

[tex]=x+(-1)+12+(-7.5x)[/tex]

[tex]=(x+-7.5x)+(-1+12)[/tex]

Answer:

[tex]-6.5x+11[/tex]

I Hope This Helps  

The set of inequalities do not have a solution.

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal. But to compare the values, whether it is less than or greater than, different inequalities are used.

Given:

f(x)= x²-2

g(x) = -x²+5

To derive, y ≤ x² + 5 simply change the equality sign in the function g(x).

To derive  y > x² - 2 ,  following transformation on the function f(x)

The inequalities of the graphs become

y < x² - 2 and y ≤ x² - 5

From the graph of the above inequalities it can be seen that curves of the inequalities do not intersect.

Hence, the set of inequalities do not have a solution

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If the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Thus, you're a sphere.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

Mathematically, the volume of a sphere can be calculated by using this formula:

V = 4/3 × πr³

Similarly, the volume of a cylinder can be calculated by using this formula:

V = πr²h

In this context, we can infer and logically deduce that if the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Also, multiplying the volume of a cylinder by 1/3 would produce the volume of a sphere.

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Answer:

  (a)  5440.42 g

Step-by-step explanation:

The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...

  Q = Q₀(1/2)^(t/330) . . . . . where t is in days

__

The amount after 540 days is ...

  1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀

  Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g

The initial quantity was about 5440.42 grams.

Answer:

200 Bricks

Step-by-step explanation:

1/3 of the bricks were not used(which was 50 bricks), meaning that 3/3 is 150 bricks of the pile. Since 150 is 3/4 of the original pile, that means that there was 200 bricks at the beginning.

According to the function transformations, the value of h is -2

The complete question is in the attachment

The functions are given as:

[tex]f(x) = (2.5)^x[/tex]

[tex]g(x) = (2.5)^{x-h[/tex]

From the question, we understand that the function f(x) is translated to the left to get g(x)

From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).

This transformation is represented by:

(x, y) => (x + 2, y)

So, we have:

x - h = x + 2

Evaluate the like terms

h = -2

Hence, the value of h is -2

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Answer:H=-2

Step-by-step explanation:

Part 1

[tex](f\circ g)(x)=f(g(x))=\frac{\frac{1}{x}}{\frac{1}{x}-3}[/tex]

Multiplying the numerator and denominator by x,

[tex](f\circ g)(x)=\boxed{\frac{1}{1-3x}}[/tex]

Part 2

The domain for this function is all values of x except for when the denominator equals 0 (because then, it would be undefined).

The denominator is equal to 0 when x=1/3, so the domain is [tex]\boxed{x \neq \frac{1}{3}}[/tex]

Using proportions, it is found that the club needs to sell at least 832 tickets to make their desired profit.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The prize is of €58, with the event making a profit of €150, hence the amount of money they have to earn from tickets is given by:
A = 150 + 58 = €208.

The tickets are sold at €0.25, hence the number of tickets they have to sell is:

n = 208/0.25 = 208 x 4 = 832.

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Answer:

212520 different committees

Step-by-step explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps

Answer:

To whom it may concern the answer to this problem would be 212,520.

Step-by-step explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]

Remember that the 19! cancel each other out. Hope this helps!

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

We have given that,

A pool of possible candidates for a student council consists of 14 freshmen and 8 software.

We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible

[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]

The total number of the council is

[tex]_{10} C_5\times _9 C_7[/tex]

=252(36)

=9216

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

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Answer:

2nd option

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{4x+5+7x-6-8x+2}{3}[/tex]

         = [tex]\frac{3x+1}{3}[/tex]

         = [tex]\frac{3x}{3}[/tex] + [tex]\frac{1}{3}[/tex]

        = x + [tex]\frac{1}{3}[/tex]

Answer:

3.036, 3.36, 3.3661 , 3.5

Step-by-step explanation:

Look at the first 2 numbers

3.3661, 3.5, 3.36, 3.036

We can order them as 3.0 , 3.3 , 3.3 . 3.5

So 3.036 is first one

Now we have 2 of the 3.3's

One is 3.3661 and the other one is 3.3600

Because if you add a number to the end it will always be a zero and it wont change the answer

So  3.36 is second and 3.3661 is third one

3.5  is bigger than 3.3

So 3.5 is last

Answer:

[tex]y=\dfrac{5}{4}x^3+10[/tex]

Step-by-step explanation:

Given information:

Create two equations by substituting the given points into the given equation:

Equation 1:  point (0, 10)

[tex]\implies a(0)^3+d=10[/tex]

[tex]\implies 0+d=10[/tex]

[tex]\implies d=10[/tex]

Equation 2:  point (2, 20)

[tex]\implies a(2)^3+d=20[/tex]

[tex]\implies 8a+d=20[/tex]

Substitute Equation 1 into Equation 2 and solve for a:

[tex]\implies 8a+d=20[/tex]

[tex]\implies 8a+10=20[/tex]

[tex]\implies 8a+10-10=20-10[/tex]

[tex]\implies 8a=10[/tex]

[tex]\implies \dfrac{8a}{8}=\dfrac{10}{8}[/tex]

[tex]\implies a=\dfrac{10}{8}[/tex]

[tex]\implies a=\dfrac{5}{4}[/tex]

Finally, substitute the found values of a and d into the original formula:

[tex]\implies y=\dfrac{5}{4}x^3+10[/tex]

Check by substituting the x-values of the two given points into the found equation:

[tex]x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}[/tex]

[tex]x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}[/tex]

Put(0,10)

Now

Put again (2,20) this time

Answer:

2 cos (2x)

Step-by-step explanation:

[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]

If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We have to make a tree diagram to show all possible arrangements of the letters in the word MAT.

M     ⇒ A  ⇒ T    

       ⇒ T  ⇒ A

A  ⇒ M ⇒ T

    ⇒ T ⇒ A

T ⇒ M ⇒ A

  ⇒ A  ⇒ M

If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.

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The graph of all the inequalities are given below.

Inequality is defined as an equation that does not contain an equal sign.

This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.

y ≥ x, the region is left to the line.

y < -(3/7)x – 7, the region is left to the line.

y ≤ (5/3)x – 8, the region is right to the line.

y ≥ 14 – (11/12)x, the region is right to the line.

y = -(3/2)x + 5, this is the equation of line.

All the graphs are shown below.

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Answer:

[tex](g \cdot h)(x)=x^2-2x+23[/tex]

Step-by-step explanation:

For composite functions, it's important to understand what the functions mean:

[tex](g\cdot h)(x)[/tex]  which is read as "g of h, of x" means [tex]g ( \text{ }h(x) \text{ })[/tex] which is read as "g of, h of x" (with slight pauses at the comma).  This means that x goes into the h function, and the output of the h function goes into the g function.

Putting "x" into the h function

[tex]h(x)=-x+4[/tex]

Since it is just "x" going into the h function, the function as written is the output when x is the input.

Putting the h function output, into the g function

[tex]g(x)=x^2-6x+3[/tex]

[tex]g(h(x))=(h(x))^2-6(h(x))+3[/tex]

Substitute

[tex]g(h(x))=(-x+4)^2+-6(-x+4)+3[/tex]

Squaring means the something multiplied by itself

[tex]g(h(x))=(-x+4)*(-x+4)+-6(-x+4)+3[/tex]

Use distributive property; (some people know binomial distribution as "FOIL" -- First, Outer, Inner, Last):

[tex]g(h(x))=[(-x)(-x)+4(-x)+4(-x)+4*4)]+[6x+4]+3[/tex]

Simplify the binomial terms:

[tex]g(h(x))=[x^2-8x+16]+[6x+4]+3[/tex]

Group like terms:

[tex]g(h(x))=x^2-2x+23[/tex]

Remember that [tex](g\cdot h)(x)[/tex]  means [tex]g ( \text{ }h(x) \text{ })[/tex]

[tex](g \cdot h)(x)=x^2-2x+23[/tex]

So, [tex](g \cdot h)(x)=x^2-2x+23[/tex]