Find the value of k and x2
x^2+ 13x + k = 0, x1=-9

Answer:

x = 107

Step-by-step explanation:

44+29+107=180

a triangle equals 180 with all the degrees added together :)

The series solution up to and including x⁴ is given by y(x) = 1 + 6x + (1/2)x² + (5/6)x³ + (1/4)x⁴ + ...

1.(a) A sequence is said to converge if its terms approach a specific value as the index of the terms increases without bound. In other words, as you go further along in the sequence, the terms get arbitrarily close to a particular limit value.

A sequence is said to diverge if its terms do not approach a specific value or if they move away from any possible limit as the index increases without bound. In other words, there is no single value that the terms of the sequence tend to as you go further along.

(b) Is there a sequence 01, 02, a3... with lan) <0.0001 for all n = 1,2,3,... that diverges No, there is no such sequence. If a sequence has a limit, then for any positive epsilon (ε), there exists a positive integer N such that for all n > N, |an - L| < ε, where L is the limit. In this case, if the limit exists, all terms beyond a certain index will be arbitrarily close to the limit, and it would violate the condition lan) < 0.0001 for all n = 1,2,3,... Therefore, if the condition holds, the sequence must converge.

(c) Is there a sequence 1000 01, 02, 03... with an < for all n = 1,2,3,... n 45 135 405 that diverges No, there is no such sequence. The sequence you provided starts with 1000, and each subsequent term increments by 1. Since the terms are increasing, the sequence does not approach any limit and therefore diverges.

2. (a)The nth term in the sequence an, assuming the sequence starts at a₀ we can observe that each term is obtained by multiplying the previous term by 4. So the expression for the nth term in the sequence can be given as

Aₙ = a₀ × 4ⁿ⁻¹

Given that a₀ = 15, the expression for the nth term in the sequence is:

aₙ = 15 × 4ⁿ⁻¹

(b) Does the series obtained by adding the terms of the sequence, Σan, converge or diverge

The series obtained by adding the terms of the sequence converges or diverges, we need to calculate the sum of the terms. Let's denote the sum of the series as S.

S = a₀ + a₁ + a₂ + ... + aₙ

Substituting the expression for an derived in part (a), we have:

S = 15 + 15 × 4⁰ + 15 × 4¹ + 15 × 4² + ... + 15 × 4ⁿ⁻¹

Using the formula for the sum of a geometric series, we can simplify this expression:

S = 15 × (1 + 4⁰ + 4¹ + 4² + ... + 4ⁿ⁻¹)

The sum of a geometric series with a common ratio greater than 1 is given by:

S = a × (1 - rⁿ) / (1 - r)

In this case, a = 15 and r = 4. Letting n approach infinity, we have:

S = 15 × (1 - 4ⁿ) / (1 - 4)

As n approaches infinity, the term 4ⁿ grows larger and larger. Since the common ratio (4) is greater than 1, the term 4ⁿ approaches infinity. Therefore, the sum of the series also approaches infinity.

Hence, the series obtained by adding the terms of the sequence diverges.

3) A series solution up to and including x⁴ for the initial value problem (IVP) y" - xy' + y² = 1 with the initial conditions y(0) = 1 and y'(0) = 6, we can use the power series method.

Let's assume that the solution y(x) can be expressed as a power series:

y(x) = a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴ + ...

Differentiating y(x) with respect to x, we get:

y'(x) = a₁ + 2a₂x + 3a₃x² + 4a₄x³ + ...

Similarly, differentiating y'(x) with respect to x, we obtain:

y''(x) = 2a₂ + 6a₃x + 12a₄x² + ...

Now, let's substitute these expressions into the given differential equation:

y''(x) - xy'(x) + y(x)² = 1

(2a₂ + 6a₃x + 12a₄x² + ...) - x(a₁ + 2a₂x + 3a₃x² + 4a₄x³ + ...) + (a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴ + ...)² = 1

Expanding and collecting the terms with the same power of x, we get:

(2a₂ - a₀) + (6a₃ - a₁ - 2a₂) x + (12a₄ - 2a₁ + 3a₃) x² + ...

To satisfy the equation, each coefficient of x must be equal to zero. Setting the coefficients to zero, we have:

2a₂ - a₀ = 0 (Coefficient of x⁰)

6a₃ - a₁ - 2a₂ = 0 (Coefficient of x¹)

12a₄ - 2a₁ + 3a₃ = 0 (Coefficient of x²)

Using the initial conditions y(0) = 1 and y'(0) = 6, we have:

a₀ = 1 (Initial condition)

a₁ = 6 (Initial condition)

Solving the equations above, we find

a₂ = a₀/2 = 1/2

a₃ = (a₁ + 2a₂)/6 = (6 + 2/2)/6 = 5/6

a₄ = (2a₁ - 3a₃)/12 = (2(6) - 3(5/6))/12 = 1/4

Therefore, the series solution up to and including x⁴ is given by:

y(x) = 1 + 6x + (1/2)x² + (5/6)x³ + (1/4)x⁴ + ...

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Answer:

D

Step-by-step explanation:

Given the 2 equations

y = 3x - 5 → (1)

6x - 2y = 10 → (2)

Substitute y = 3x - 5 into (2)

6x - 2(3x - 5) = 10

6x - 6x + 10 = 10 ( subtract 10 from both sides )

6x - 6x = 0 , that is

0 = 0 ← True

This indicates the system has infinitely many solutions → D

Answer:

x = 30

since 3x = 90 degrees, then x = 90/3 = 30

Step-by-step explanation:

To determine whether the relationship between conscientiousness and performance is best described as linear or curvilinear, a statistical analysis can be conducted.

To begin the analysis, calculate the correlation coefficient between conscientiousness scores and job performance ratings. This will provide an initial indication of the relationship's direction and strength. A positive correlation suggests a linear or curvilinear relationship, while a weak or non-existent correlation may indicate no clear relationship.

Next, perform a regression analysis to model the relationship between conscientiousness and performance. Fit a linear regression model and assess the goodness of fit using metrics like R-squared.

If the linear model yields a high R-squared value and the residuals exhibit random patterns, it suggests a linear relationship between the variables. However, if the linear model produces a low R-squared and the residuals show a non-random pattern, it indicates a potential curvilinear relationship.

If the analysis indicates that the linear assumption is incorrect and a curvilinear relationship exists, it has implications for validity evidence and selection decision-making. Traditional selection methods that rely solely on linear relationships may not accurately predict job performance for individuals with extreme levels of conscientiousness.

Validity evidence may need to be re-evaluated, and selection procedures could be adjusted to consider the curvilinear nature of the relationship. Incorporating additional assessments or modifying selection criteria may be necessary to capture the nuances of the relationship and make more informed selection decisions.

In summary, to determine the nature of the relationship between conscientiousness and performance, conduct a statistical analysis involving correlation and regression. If a curvilinear relationship is found, it can impact the validity of selection decisions and require adjustments to selection procedures to accommodate the non-linear nature of the relationship.

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Answer:

$240

Step-by-step explanation:

60% = 0.6

400 divided by 0.6 = 240

1/2 + 1/5 = 5/10 + 2/10 = 7/10

Answer:

7/10

Step-by-step explanation:

1x5/2x5 + 1x2/5x2

=5/10+2/10

=7/10

Answer:

3c + 14d

Step-by-step explanation:

Hello There!

We can simplify this expression by combining like terms

Now what are like terms?

They are terms that have the same variable ex. 4a and 2a are like terms as they have the same variable (a)

Now lets look back at the expression and see if there are any like terms

which there are (4c and -c) and (6d and 8d)

so lets combine them

4c - c =3c

6d + 8d = 14d

so the simplified version would be 3c + 14d

Answer:

B) 3c+14d

Step-by-step explanation:

We use the addition property for the following question

First we rearrange the following problem and we get

4c-c+6d+8d

The easiest way is to just add and subtract or if you want have a better understanding, you can factor our the like terms which gives us

(4-1)c+(6+8)d

and then we can simplify to get

3c+14d

Answer:

x +12

Step-by-step explanation:

Answer:

x + 12

Step-by-step explanation:

[tex](x + 3) + 9[/tex]

[tex]x + 3 + 9[/tex]

[tex] = x + 12[/tex]

Answer:

EF = 8

Step-by-step explanation:

BC is half of AB, which means that DE will be half of EF. So if DE is 4, which is half of EF, then EF must be 8.

hope this helped! :)

Answer:

It would be 8% .

Good luck ^^

Answer:

x = 3

Step-by-step explanation:

8.4 ÷ 6 = 1.4

4.2 ÷ 1.4 = 3

The inverse Laplace transformation of the given Laplace transform `-2s² + 2L^-1 F(s)` is `(t³ - t)u(t)`.

Explanation:

Laplace Transform: We are given the Laplace transform as:

`-2s² + 2L^-1 F(s)`

We can write the Laplace transform as a polynomial:

`-2s² + 2 / (s - 2)`

Inverse Laplace Transform:

Using partial fraction method, we can write:

`-2s² + 2 / (s - 2) = A / (s - 2) + Bs + C`

Multiplying by `s - 2`, we get:

`-2s² + 2 = A + Bs(s - 2) + C(s - 2)`

Substituting `s = 2`, we get:`

-6A = 2` or `A = -1/3`

Comparing coefficients of `s`, we get:

`B - 2C = 0` or `B = 2C`

Comparing constants, we get:`-2C - 2A = 0` or `C = 1/3`

Therefore, the partial fractions decomposition is:

`-2s² + 2 / (s - 2) = (-1/3) / (s - 2) + (2/3) s + (1/3)`

Taking inverse Laplace transform on both sides, we get:

`L^-1 {-2s² + 2 / (s - 2)} = L^-1 {(-1/3) / (s - 2) + (2/3) s + (1/3)}`

Using the linearity of inverse Laplace transform, we get:

`-2L^-1 {s²} + 2L^-1 {1 / (s - 2)} = (-1/3)L^-1 {1 / (s - 2)} + (2/3)L^-1 {s} + (1/3)L^-1 {1}`

We know that `L^-1 {1} = δ(t)` and `L^-1 {1 / (s - a)} = e^at u(t)`

where `a` is a constant. Substituting the values, we get:

`-2L^-1 {s²} + 2L^-1 {1 / (s - 2)} = (-1/3)e^{2t}u(t) + (2/3)L^-1 {s} + (1/3)δ(t)`

We know that `L^-1 {s^n} = t^n / n!`Therefore, `L^-1 {s} = 1`.

Substituting the values, we get:

`-2L^-1 {s²} + 2L^-1 {1 / (s - 2)} = (-1/3)e^{2t}u(t) + (2/3)t + (1/3)δ(t)`

Taking inverse Laplace transform of

`-2s² + 2L^-1 F(s)`, we get:

`L^-1 {-2s² + 2L^-1

F(s)} = L^-1 {(-1/3) / (s - 2) + (2/3) s + (1/3)}

= (t³ - t)u(t)`

Therefore, the option `(a) t³ - t` is the inverse Laplace transformation of `-2s² + 2L^-1 F(s)`.

Hence, the correct option is `(a) t³ - t`.

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Answer: 2.54(x)

Step-by-step explanation:

Since an inch is equal to about 2.54 centimeters, the expression which estimates the number of centimeters in X inches will be gotten by multiplying 2.54 by X. This will be:

= 2.54 × X

= 2.54(x)

For example, if there are 4 inches, the number of centimeters in it will be:

= 2.54(x)

= 2.54 × 4

= 10.16 inches

Answer:

39°

Step-by-step explanation:

The sum of AXE, AXC and CXF will be 180 because they together span a straight line (EF).

So: y + 90 + y - 12 = 180, which is an equation you can solve by simplifying it:

y + 90 + y - 12 = 180

2y + 78 = 180

y + 39 = 90

y = 90 - 39 = 51

So AXE = 51

AXC = 90

CXF = 51-12 = 39 (the answer)

Check: 51+90+39 = 180

Answer:

Step-by-step explanation:

To determine the number of possible pairs of people in a group of 23, you can use the concept of combinations. The formula to calculate combinations is given by:

C(n, r) = n! / (r!(n - r)!)

where C(n, r) represents the number of combinations of choosing r items from a set of n items, and the exclamation mark (!) denotes the factorial of a number.

In this case, you want to find the number of combinations of 2 people chosen from a group of 23. Using the formula, the calculation would be:

C(23, 2) = 23! / (2!(23 - 2)!)

        = 23! / (2! * 21!)

        = (23 * 22 * 21!) / (2 * 1 * 21!)

        = (23 * 22) / (2 * 1)

        = 23 * 11

        = 253

Therefore, there are 253 possible pairs of people that can be formed in a group of 23.

Step-by-step explanation:

Use ToA method (tan = opposite / adjacent)

For this question we have to use pythagoras' Theorem to find the adjacent side.

take a as the length of the adjacent side.

given b = 12

c = 13

By pythagoras' Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {a}^{2} = {c}^{2} - {b}^{2} \\ {a}^{2} = {13}^{2} - {12}^{2} \\ {a}^{2} = 169 - 144 \\ {a}^{2} = 25 \\ a = \sqrt{25} \\ = 5[/tex]

Now we can find tan(x)

tan(x) = Opposite / adjacent

[tex] = \frac{12}{5} [/tex]

Answer:

9 sec.

Step-by-step explanation:

I think you wrote the equations incorrectly.  It probably is

[tex]h = -16t^{2} + 144t + 100[/tex]

If that is true, then [tex]100 = -16t^{2} + 144t + 100[/tex]

                                    0 = -16[tex]t^{2}[/tex] + 144t

                                       -16t(t - 9) = 0

                                            t = 0 or t = 9

Answer:

B

Step-by-step explanation:

total area minus white area give you shaded area

Answer:

30

Step-by-step explanation: Because each batch has 18 total m&ms and there are 8 in each batch minus and then multiply.

The number of packages of plain M&M's on the shelf could be any multiples of 5.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of the number of packages of peanut M&M's to the total number of packages on the shelf = 8 : 18

That is, if there are total of 18 packages, 8 are peanut M&M's.

Number of plain M&M's out of 18 total packages = 18 - 8 = 10.

So,

Ratio of peanut M&M's to plain M&M's = 8 : 10

                                                                = 4 : 5

This indicates that, for a constant x,

Number of peanut M&M's = 4x

Number of plain M&M's = 5x

So the number of packages of plain M&M's on the shelf could only be the multiples of 5.

So it could be 5, 10, 15, 20, 25, 30, .......

Hence the number of plain M&M's on the shelf could be 5, 10, 15, 20, 25, 30, ......

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Answer:

320 odd three.

Step-by-step explanation:

9 but we cannot place the digits that are used in the two other digits and we can place only 7 digits. However, the result is not correct, because there are 320 odd three-digits numbers with different digits.

Answer:

Answer:

To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.

Answer:

answer A shows a rotation

A because B is a mirror, c is a translation

Answer:

A reflection over the y-axis.

Answer:

5.63cm

Step-by-step explanation:

to find length of side AB

12[tex]cos[/tex][62°]

=5.63cm

The slope (m) of the regression line can be estimated as approximately 0.6, while the y-intercept (b) can be estimated as around 2.5.

Upon analyzing the graph, we can make a rough estimate for the slope (m) and y-intercept (b) of the regression line. The slope represents the rate of change between the independent variable (x) and the dependent variable (y), while the y-intercept indicates the value of y when x is zero.

From the graph, we observe that the regression line appears to have a positive slope, suggesting a positive correlation between the variables. By estimating the change in y divided by the change in x for two points on the line, we can approximate the slope. In this case, considering the rise and run between two points, the slope (m) is approximately 0.6.

The y-intercept (b) can be determined by identifying the point where the regression line intersects the y-axis. In this graph, the intersection seems to occur around the y-value of 2.5, providing us with an estimated y-intercept.

To gain a more precise understanding of the regression line's characteristics and verify these estimates, it is recommended to utilize statistical techniques such as linear regression analysis. These techniques can provide accurate slope and intercept values, along with additional statistical measures like the coefficient of determination (R-squared) to assess the line's goodness of fit.

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Answer:

F(3) = -4.5

Step-by-step explanation:

Replacing x with 3 in F(x) = 0.5x - 6 results in F(3) = 0.5(3) - 6, or -4.5

F(3) = -4.5

1. The range of the graph is 28.

2. The equation of the midline is y = -0.45, the amplitude of the sinusoidal graph is 4.7.

1. To determine the range of a sinusoidal graph with a maximum point at (-22, 9) and a midline of y = -5, we need to find the minimum point of the graph.

Since the midline is y = -5, the average of the maximum and minimum values of the graph will be -5. In other words, the midpoint between the maximum point and the minimum point will lie on the midline.

Let's assume the minimum point is (x, y). Since the maximum point is (-22, 9), the midpoint between the maximum and minimum points can be calculated as:

Midpoint = (x + (-22))/2, (y + 9)/2

Setting the midpoint equal to the midline value, we have:

-5 = (x - 22)/2, (y + 9)/2

Simplifying the equations:

x - 22 = -10

y + 9 = -10

Solving for x and y, we get:

x = 12

y = -19

Therefore, the minimum point is (12, -19).

The range of the graph can be calculated as the difference between the maximum and minimum y-values:

Range = 9 - (-19)

     = 28

Therefore, the range of the graph is 28.

2. If the range of a sinusoidal function is -5.6 ≤ y ≤ 3.8, we can determine the equation of the midline and the amplitude of the graph.

The midline of the graph is the horizontal line that divides the range equally. In this case, the midline will be the average of the maximum and minimum values:

Midline = (3.8 + (-5.6))/2

       = -0.9/2

       = -0.45

Therefore, the equation of the midline is y = -0.45.

The amplitude of a sinusoidal function is half the range of the graph. In this case, the amplitude can be calculated as:

Amplitude = (3.8 - (-5.6))/2

         = 9.4/2

         = 4.7

Therefore, the amplitude of the graph is 4.7.

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Answer:

75%

Step-by-step explanation:

54/72 = 0.75