PLEASEE ANSWER I HAVE A TEST DUE BY 6 AM ITS 1

The given equation x³ - 2x + 5 = 0 has two complex roots.

To find the number of roots of the equation x³ - 2x + 5 = 0, we use the discriminant. If the discriminant is greater than 0, the equation has two different roots. If it is equal to 0, the equation has one repeated root. If it is less than 0, the equation has two complex roots.

Let's find the discriminant of the equation:

Discriminant = b² - 4ac 

where a, b and c are the coefficients of the equation.

Here, a = 1, b = -2 and c = 5

Therefore,

Discriminant = (-2)² - 4 × 1 × 5 = 4 - 20 = -16

Since the discriminant is less than 0, the equation x³ - 2x + 5 = 0 has two complex roots.

To learn more about discriminant, refer here:

https://brainly.com/question/32434258

#SPJ11

The equation of the line perpendicular to y = -6 and passing through the point (3, 7) is x = 3.

To find the equation of a line perpendicular to y = -6 and passing through the point (3, 7), we can first determine the slope of the given line. Since y = -6 is a horizontal line, its slope is 0.

A line perpendicular to a horizontal line will be a vertical line with an undefined slope. Thus, the equation of the perpendicular line passing through (3, 7) will be x = 3.

Therefore, the equation of the line perpendicular to y = -6 and passing through the point (3, 7) is x = 3.

Learn more about perpendicular here:

https://brainly.com/question/18271653

#SPJ11

Answer:

40

Step-by-step explanation:

4(sqrt(147/3)+3)

=4(sqrt(49)+3)

=4(7+3)

=4(10)

=40

The general solution of the differential equation y ′ + (x+4)y = 0 is  equal to y(x) = 0.

To find the power series expansion for the general solution of the differential equation,

Assume a power series of the form,

y(x) = a₀ + a₁x + a₂x²+ a₃x³ + ...

Differentiating y(x) term by term, we have,

y'(x) = a₁ + 2a₂x + 3a₃x² + ...

Substituting these into the differential equation, we get,

(a₁ + 2a₂x + 3a₃x² + ...) + (x + 4)(a₀ + a₁x + a₂x² + a₃x³ + ...) = 0

Expanding the equation and collecting like terms, we have,

a₁ + (a₀ + 4a₁)x + (2a₂ + a₁)x² + (3a₃ + a₂)x³ + ... = 0

Equating coefficients of like powers of x to zero, we can find the values of a₁, a₂, a₃,....

For the first term, equating the coefficient of x⁰ to zero gives,

a₁ + a₀ = 0 → a₁ = -a₀

For the second term, equating the coefficient of x¹ to zero gives,

a₀ + 4a₁ = 0

Substituting the value of a₁ from the first term, we get,

a₀ + 4(-a₀) = 0

⇒-3a₀ = 0

⇒a₀= 0

Since a₀ = 0, the second equation becomes,

0 + 4a₁ = 0

⇒4a₁ = 0

⇒a₁= 0

Continuing in this manner, we can find the values of a₂, a₃, and so on.

For the third term, equating the coefficient of x² to zero gives,

2a₂ + a₁ = 0

⇒2a₂+ 0 = 0

⇒a₂ = 0

For the fourth term, equating the coefficient of x³ to zero gives,

3a₃ + a₂= 0

⇒3a₃ + 0 = 0

⇒a₃ = 0

The first four nonzero terms in the power series expansion are,

y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...

= 0 + 0x + 0x² + 0x³+ ...

= 0

Therefore, the general solution to the given differential equation is

y(x) = 0.

learn more about differential equation here

brainly.com/question/33180058

#SPJ4

Answer:

2.8 * 10^-3 - 0.00065 = -3.7 * 10^-3

Step-by-step explanation:

2.8 * 10^-3 - 0.00065 = 2.8 * 10^-3 - 6.5 * 10^-4

To subtract the two numbers, we need to express them with the same power of 10. We can do this by multiplying 6.5 * 10^-4 by 10:

2.8 * 10^-3 - 6.5 * 10^-4 * 10

Simplifying:

2.8 * 10^-3 - 6.5 * 10^-3

To subtract, we can align the powers of 10 and subtract the coefficients:

2.8 * 10^-3 - 6.5 * 10^-3 = (2.8 - 6.5) * 10^-3

= -3.7 * 10^-3

Therefore, 2.8 * 10^-3 - 0.00065 = -3.7 * 10^-3 in scientific notation.

he probability of getting one tail when a coin is tossed four times is A.

1/4

When a coin is tossed, there are two possible outcomes: heads (H) or tails (T). Since we are interested in getting exactly one tail, we can calculate the probability by considering the different combinations.

Out of the four tosses, there are four possible positions where the tail can occur: T _ _ _, _ T _ _, _ _ T _, _ _ _ T. The probability of getting one tail is the sum of the probabilities of these four cases.

Each individual toss has a probability of 1/2 of landing tails (T) since there are two equally likely outcomes (heads or tails) for a fair coin. Therefore, the probability of getting exactly one tail is:

P(one tail) = P(T _ _ _) + P(_ T _ _) + P(_ _ T _) + P(_ _ _ T) = (1/2) * (1/2) * (1/2) * (1/2) + (1/2) * (1/2) * (1/2) * (1/2) + (1/2) * (1/2) * (1/2) * (1/2) + (1/2) * (1/2) * (1/2) * (1/2) = 4 * (1/16) = 1/4.

Therefore, the probability of getting one tail when a coin is tossed four times is 1/4, which corresponds to option A.

Learn more about probability in coin toss experiments visit:

https://brainly.com/question/30588999

#SPJ11

1) Probability of drawing a six or club:

  a. Count the number of favorable outcomes (sixes and clubs) and the total number of possible outcomes (cards in the deck).

  b. Divide the favorable outcomes by the total outcomes to calculate the probability.

2) Probability of being dealt 5 non-face cards:

  a. Count the number of favorable outcomes (non-face cards) and the total number of possible outcomes (cards in the deck).

  b. Calculate the combinations of choosing 5 non-face cards and divide it by the combinations of choosing 5 cards to find the probability.

1) Probability of drawing a six or club:

a. Determine the total number of favorable outcomes:

  i. There are 4 sixes in a deck and 13 clubs.

  ii. However, one of the clubs (the 6 of clubs) has already been counted as a six.

  iii. So, we have a total of 4 + 13 - 1 = 16 favorable outcomes.

b. Determine the total number of possible outcomes:

  i. There are 52 cards in a standard deck.

c. Calculate the probability:

  i. Probability = Favorable outcomes / Total outcomes

  ii. Probability = 16 / 52

  iii. Probability = 4 / 13

  iv. Therefore, the probability of drawing a six or club is 4/13.

2) Probability of being dealt 5 nonface cards:

a. Determine the total number of favorable outcomes:

  i. There are 40 non-face cards in a deck (52 cards - 12 face cards).

  ii. We need to choose 5 non-face cards, so we have to calculate the combination: C(40, 5).

b. Determine the total number of possible outcomes:

  i. There are 52 cards in a standard deck.

  ii. We need to choose 5 cards, so we have to calculate the combination: C(52, 5).

c. Calculate the probability:

  i. Probability = Favorable outcomes / Total outcomes

  ii. Probability = C(40, 5) / C(52, 5)

  iii. Use the combination formula to calculate the probabilities.

  iv. Simplify the expression if possible.

Therefore, the steps involve determining the favorable and total outcomes, calculating the combinations, and then dividing the favorable outcomes by the total outcomes to find the probability.

Learn more about card deck visit

brainly.com/question/32862003

#SPJ11

The 90% confidence interval is approximately 0.75 ± 0.028, or (0.722, 0.778).

To determine the 90% confidence interval and margin of error for the response that 75% of respondents felt that pizza was a must for lunch at school, we can use the formula for confidence intervals for proportions. a) The 90% confidence interval can be calculated as:

Confidence interval = Sample proportion ± Margin of error. The sample proportion is 75% or 0.75. To calculate the margin of error, we need the standard error, which is given by:

Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size).

The sample size is 500 in this case. Plugging in the values, we have: Standard error = sqrt((0.75 * (1 - 0.75)) / 500) ≈ 0.017.

Now, the margin of error is given by: Margin of error = Critical value * Standard error. For a 90% confidence level, the critical value can be found using a standard normal distribution table or a statistical software, and in this case, it is approximately 1.645. Plugging in the values, we have:

Margin of error = 1.645 * 0.017 ≈ 0.028.

Therefore, the 90% confidence interval is approximately 0.75 ± 0.028, or (0.722, 0.778). b) The margin of error for this response at the 90% confidence level is approximately 0.028. This means that if we were to repeat the survey multiple times, we would expect the proportion of students who feel that pizza is a must for lunch at school to vary by about 0.028 around the observed sample proportion of 0.75.

To learn more about confidence interval click here: brainly.com/question/32546207

#SPJ11

Answer:

The condition of a ≠ 0 is imposed in the definition of the quadratic function to ensure that the function represents a true quadratic equation.

In a quadratic function of the form f(x) = ax^2 + bx + c, the coefficient "a" represents the leading coefficient or the coefficient of the quadratic term. This coefficient determines the shape of the graph and whether the function represents a quadratic equation.

When a = 0, the quadratic term becomes zero, resulting in a linear function (f(x) = bx + c) rather than a quadratic function. In other words, without the condition a ≠ 0, the function would degenerate into a straight line, losing the key characteristics and properties associated with quadratic equations, such as the presence of a vertex, concavity, and the ability to intersect the x-axis at most two times.

By imposing the condition a ≠ 0, we ensure that the quadratic function represents a genuine quadratic equation, allowing us to study and analyze its properties, such as the vertex, axis of symmetry, roots, and the behavior of the graph. It helps distinguish quadratic functions from linear functions and ensures that we are working with the appropriate mathematical model when dealing with quadratic relationships and phenomena.

Step-by-step explanation:

a)The probability mass function of a arbitrary variable X is a function that gives possibilities to each possible value of X. The value of a is  0. b)  E(XY) =  1 and X and Y are independent random variables.

a) The probability mass function( PMF) of a random variable X is a function that assigns chances to each possible value of X. It gives the probability of X taking on a specific value.

The PMF f( x) = ( 1- a) * [tex]a^{x}[/tex], where x = 0, 1, 2, 3.

To determine the values of a for which f( x) will be provided as the PMF, we need to ensure that the chances add up to 1 for all possible values of x.

Let's calculate the sum of f( x)

Sum( f( x)) = Sum(( 1- a) * [tex]a^{x}[/tex]) = ( 1- a) * Sum( [tex]a^{x}[/tex]) = ( 1- a) *( 1 +a+ [tex]a^{2}[/tex]+ [tex]a^{3}[/tex].....)

Using the formula for the sum of an infifnite geometric progression( with| a|< 1), we have

Sum( f( x)) = ( 1- a) *( 1/( 1- a)) = 1

For f( x) to serve as a valid PMF, the sum of chances must be equal to 1. thus, we have

1 = ( 1- a) *( 1/( 1- a))

1 = 1/( 1- a)

1- a = 1

a = 0

thus, the value of a for which f( x) = ( 1- a) *[tex]a^{x}[/tex], can serve as the PMF is a = 0.

b) To find E( XY) and determine the dependence or independence of X and Y, we need to calculate the joint anticipated value E( XY) and compare it to the product of the existent anticipated values E( X) and E( Y).

Given the common probability viscosity function( PDF) f( x, y) = [tex]e^{-(x+y)}[/tex] for x ≥ 0 and y ≥ 0, we can calculate E( XY) as follows

E( XY) = ∫ ∫( xy * f( x, y)) dxdy

Integrating over the applicable range, we have

E( XY) = ∫( 0 to ∞) ∫( 0 to ∞)( xy * [tex]e^{-(x+y)}[/tex]) dxdy

To calculate this integral, we perform the following steps:

E(XY) = ∫(0 to ∞) (x[tex]e^{-x}[/tex] * ∫(0 to ∞) (y[tex]e^{-y}[/tex]) dy) dx

The inner integral, ∫(0 to ∞) (y[tex]e^{-y}[/tex]) dy, represents the expected value E(Y) when the marginal PDF of Y is integrated over its range.

∫(0 to ∞) (y[tex]e^{-y}[/tex]) dy is the integral of the gamma function with parameters (2, 1), which equals 1.

Thus, the inner integral evaluates to 1, and we have:

E(XY) = ∫(0 to ∞) (x[tex]e^{-x}[/tex]) dx

To calculate this integral, we can recognize that it represents the expected value E(X) when the marginal PDF of X is integrated over its range.

∫(0 to ∞) (x[tex]e^{-x}[/tex]) dx is the integral of the gamma function with parameters (2, 1), which equals 1.

Therefore, E(XY) = E(X) * E(Y) = 1 * 1 = 1.

Since E(XY) = E(X) * E(Y), X and Y are independent random variables.

Learn more about probability mass function;

https://brainly.com/question/30765833

#SPJ4

The length of the rectangle is 1 more than twice its width, the dimension of the square is approximately [tex](7 + \sqrt{673}) / 6[/tex]meters.

Let's assume the side length of the square is represented by "x" meters.

The area of a square is given by the formula: [tex]A^2 = side^2.[/tex]

So, the area of the square is [tex]x^2[/tex]square meters.

The width of the rectangle is 2 meters less than the side length of the square. Therefore, the width of the rectangle is[tex](x - 2)[/tex]meters.

The length of the rectangle is 1 more than twice its width. So, the length of the rectangle is 2(width) + 1, which can be written as [tex]2(x - 2) + 1 = 2x - 3[/tex]meters.

The area of a rectangle is given by the formula: A_rectangle = length * width.

So, the area of the rectangle is [tex](2x - 3)(x - 2)[/tex]square meters.

According to the problem, the total area of the square and rectangle combined is 58 square meters. Therefore, we can set up the equation:

A_square + A_rectangle = 58

[tex]x^2 + (2x - 3)(x - 2) = 58[/tex]

Expanding and simplifying the equation:

[tex]x^2 + (2x^2 - 4x - 3x + 6) = 58[/tex]

[tex]3x^2 - 7x + 6 = 58[/tex]

[tex]3x^2 - 7x - 52 = 0[/tex]

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring doesn't yield simple integer solutions in this case, so we'll use the quadratic formula:

[tex]x = (-b + \sqrt{ (b^2 - 4ac)}) / (2a)[/tex]

For our equation, a = 3, b = -7, and c = -52.

Plugging in these values into the quadratic formula:

[tex]x = (-(-7) + \sqrt{((-7)^2 - 4(3)(-52))} ) / (2(3))[/tex]

[tex]x = (7 + \sqrt{(49 + 624)} ) / 6[/tex]

[tex]x = (7 +\sqrt{673} ) / 6[/tex]

Since the side length of the square cannot be negative, we take the positive solution:

[tex]x = (7 + \sqrt{673} ) / 6[/tex]

Therefore, the dimension of the square is approximately [tex](7 + \sqrt{673} ) / 6[/tex]meters.

Learn more about  area of a square

https://brainly.com/question/27776258

#SPJ11

The values of [tex]\(x\)[/tex] that represent the possible side lengths of the square are  [tex]\[x_1 = \frac{7 + \sqrt{673}}{6}\][/tex]  [tex]\[x_2 = \frac{7 - \sqrt{673}}{6}\][/tex] .

Let's assume the side length of the square is x meters.

The area of the square is given by the formula:

Area of square = (side length)^2 =[tex]x^2[/tex]

The width of the rectangle is 2 meters less than the side length of the square, so the width of the rectangle is[tex](x - 2)[/tex] meters.

The length of the rectangle is 1 more than twice its width, so the length of the rectangle is [tex](2(x - 2) + 1)[/tex] meters.

The area of the rectangle is given by the formula:

Area of rectangle = length × width = [tex]2(x - 2) + 1)(x - 2)[/tex]

Given that the total area of the square and rectangle is 58 square meters, we can write the equation:

Area of square + Area of rectangle = 58

[tex]x^2 + (2(x - 2) + 1)(x - 2) = 58[/tex]

Simplifying and solving this equation will give us the value of x, which represents the side length of the square.

[tex]\[x^2 + (2(x - 2) + 1)(x - 2) = 58\][/tex]

To solve the equation [tex]\(x^2 + (2(x - 2) + 1)(x - 2) = 58\)[/tex] for the value of [tex]\(x\)[/tex], we can expand and simplify the equation:

[tex]\(x^2 + (2x - 4 + 1)(x - 2) = 58\)[/tex]

[tex]\(x^2 + (2x - 3)(x - 2) = 58\)[/tex]

[tex]\(x^2 + 2x^2 - 4x - 3x + 6 = 58\)[/tex]

[tex]\(3x^2 - 7x + 6 = 58\)[/tex]

Rearranging the equation:

[tex]\(3x^2 - 7x - 52 = 0\)[/tex]

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the values of [tex]\(x\)[/tex].

To solve the quadratic equation [tex]\(3x^2 - 7x - 52 = 0\)[/tex], we can use the quadratic formula:

[tex]\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\][/tex]

In this equation, [tex]\(a = 3\), \(b = -7\), and \(c = -52\).[/tex]

Substituting these values into the quadratic formula, we get:

[tex]\[x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(3)(-52)}}{2(3)}\][/tex]

Simplifying further:

[tex]\[x = \frac{7 \pm \sqrt{49 + 624}}{6}\][/tex]

[tex]\[x = \frac{7 \pm \sqrt{673}}{6}\][/tex]

Therefore, the solutions to the equation are:

[tex]\[x_1 = \frac{7 + \sqrt{673}}{6}\][/tex]

[tex]\[x_2 = \frac{7 - \sqrt{673}}{6}\][/tex]

These are the values of [tex]\(x\)[/tex] that represent the possible side lengths of the square. To find the dimensions of the square, you can use these values to calculate the width and length of the rectangle.

Learn more about  area of a square

brainly.com/question/27776258

#SPJ11

The equivalent nominal rate of interest with monthly compounding, given an interest rate of 10% compounded quarterly, is approximately 10.383%.

The effective interest rate represents the rate of interest when compounding occurs more frequently within a given time period.

To calculate the equivalent nominal rate with monthly compounding, we need to consider the compounding periods in a year.

In this case, the interest rate is 10% compounded quarterly, which means there are 4 compounding periods in a year.

To convert this to monthly compounding, we need to divide the annual interest rate by the number of compounding periods.

Using the formula for the effective interest rate, we have:

Effective interest rate = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1

Plugging in the values, we get:

Effective interest rate = (1 + (10% / 12))^12 - 1

Calculating this expression, we find that the effective interest rate is approximately 10.383%.

Therefore, the equivalent nominal rate of interest with monthly compounding, rounded to three decimal places, is approximately 10.383%.

Learn more about effective interest rates visit:

https://brainly.com/question/31278739

#SPJ11

1. The series Σ 1/n^4 is a convergent p-series with p = 4, so it converges.      Therefore, the given sequence satisfies the condition

2. The function f(x) approaches 1, and as x approaches 0 from the right, f(x) approaches -1. Since f(x) is strictly increasing, it satisfies the given conditions

3.The right-hand derivative f'(0+) is equal to 2, and the left-hand derivative f'(0-) is equal to 3. Therefore, f(x) satisfies the given conditions

4. The integral of f(x) over the interval [-1, 1] is equal to -1. Therefore, f(x) satisfies the given condition

(i) An example of a sequence {a} of negative numbers such that the sum of the squares converges is:

a_n = -1/n^2 for n ≥ 1. The series Σ a_n^2 from n=1 to infinity can be evaluated as follows:

Σ a_n^2 = Σ (-1/n^2)^2 = Σ 1/n^4

The series Σ 1/n^4 is a convergent p-series with p = 4, so it converges. Therefore, the given sequence satisfies the condition.

(ii) An example of an increasing function f: (-1, 1) → R such that lim f(x) as x approaches 0 from the left is 1 and lim f(x) as x approaches 0 from the right is -1 is:

f(x) = -x for -1 < x < 0 and f(x) = x for 0 < x < 1.

As x approaches 0 from the left, the function f(x) approaches 1, and as x approaches 0 from the right, f(x) approaches -1. Since f(x) is strictly increasing, it satisfies the given conditions.

(iii) An example of a continuous function f: (-1, 1) → R such that f(0) = 0, f'(0+) = 2, and f'(0-) = 3 is:

f(x) = x^2 for -1 < x < 0 and f(x) = 2x for 0 < x < 1.

The function f(x) is continuous at x = 0 since f(0) = 0. The right-hand derivative f'(0+) is equal to 2, and the left-hand derivative f'(0-) is equal to 3. Therefore, f(x) satisfies the given conditions.

(iv) An example of a discontinuous function f: [-1, 1] → R such that ∫[-1,1] f(t)dt = -1 is:

f(x) = -1 for -1 ≤ x ≤ 0 and f(x) = 1 for 0 < x ≤ 1.

The function f(x) is discontinuous at x = 0 since the left-hand limit and the right-hand limit are different. The integral of f(x) over the interval [-1, 1] is equal to -1. Therefore, f(x) satisfies the given condition.

Learn more about: sequence

https://brainly.com/question/23857849

#SPJ11

The conclusion is based on inductive reasoning.

Inductive reasoning involves drawing general conclusions based on specific observations or patterns. It moves from specific instances to a generalization.

In this scenario, Raul observes that none of the students who ride his bus own a car. He then applies this observation to Ebony, who rides a bus to school, and concludes that she does not own a car. Raul's conclusion is based on the pattern he has observed among the students who ride his bus.

Inductive reasoning acknowledges that while the conclusion may be likely or reasonable, it is not necessarily guaranteed to be true in all cases. Raul's conclusion is based on the assumption that Ebony, like the other students who ride his bus, does not own a car. However, it is still possible that Ebony is an exception to this pattern, and she may indeed own a car.

Therefore, the conclusion drawn by Raul is an example of inductive reasoning, as it is based on a specific observation about the students who ride his bus and extends that observation to a generalization about Ebony.

Learn more about Reasoning

brainly.com/question/30612406

#SPJ11

IF all letters are equally likely to be drawn, the probability of drawing the letter "T" would be 1 out of 26, which can be expressed as 1/26.

To determine the probability of drawing the letter "T," we need additional information about the context or the pool of letters from which the drawing is taking place.

Without that information, it is not possible to determine the exact probability.

I can provide you with some general information on probability and how it applies to this scenario.

The probability of drawing a specific letter from a set of letters depends on the number of favorable outcomes (the number of ways you can draw the letter "T") and the total number of possible outcomes (the total number of letters available for drawing).

If we assume that all letters of the alphabet are equally likely to be drawn, then the probability of drawing the letter "T" would depend on the total number of letters in the alphabet.

In the English alphabet, there are 26 letters.

The options provided (1, 1/2, 3/4, 1/4) do not align with this probability. Therefore, without further context or clarification, it is not possible to determine the correct answer from the given options.

If you can provide more details about the problem or clarify the context, I can help you determine the appropriate probability.

For similar questions on probability

https://brainly.com/question/25839839

#SPJ8

To determine the variable matrix [tex]\displaystyle X[/tex] using the equation [tex]\displaystyle AX=B[/tex], we need to solve for [tex]\displaystyle X[/tex]. We can do this by multiplying both sides of the equation by the inverse of matrix [tex]\displaystyle A[/tex].

Let's start by finding the inverse of matrix [tex]\displaystyle A[/tex]:

[tex]\displaystyle A=\begin{bmatrix} 3 & 2 & -1\\ 1 & -6 & 4\\ 2 & -4 & 3 \end{bmatrix}[/tex]

To find the inverse of matrix [tex]\displaystyle A[/tex], we can use various methods such as the adjugate method or Gaussian elimination. In this case, we'll use the adjugate method.

First, let's calculate the determinant of matrix [tex]\displaystyle A[/tex]:

[tex]\displaystyle \text{det}( A) =3( -6)( 3) +2( 4)( 2) +( -1)( 1)( -4) -( -1)( -6)( 2) -2( 1)( 3) -3( 4)( -1) =-36+16+4+12+6+12=14[/tex]

Next, let's find the matrix of minors:

[tex]\displaystyle M=\begin{bmatrix} 18 & -2 & -10\\ 4 & -9 & -6\\ -8 & -2 & -18 \end{bmatrix}[/tex]

Then, calculate the matrix of cofactors:

[tex]\displaystyle C=\begin{bmatrix} 18 & -2 & -10\\ -4 & -9 & 6\\ -8 & 2 & -18 \end{bmatrix}[/tex]

Next, let's find the adjugate matrix by transposing the matrix of cofactors:

[tex]\displaystyle \text{adj}( A) =\begin{bmatrix} 18 & -4 & -8\\ -2 & -9 & 2\\ -10 & 6 & -18 \end{bmatrix}[/tex]

Finally, we can find the inverse of matrix [tex]\displaystyle A[/tex] by dividing the adjugate matrix by the determinant:

[tex]\displaystyle A^{-1} =\frac{1}{14} \begin{bmatrix} 18 & -4 & -8\\ -2 & -9 & 2\\ -10 & 6 & -18 \end{bmatrix}[/tex]

[tex]\displaystyle A^{-1} =\begin{bmatrix} \frac{9}{7} & -\frac{2}{7} & -\frac{4}{7}\\ -\frac{1}{7} & -\frac{9}{14} & \frac{1}{7}\\ -\frac{5}{7} & \frac{3}{7} & -\frac{9}{7} \end{bmatrix}[/tex]

Now, we can find matrix [tex]\displaystyle X[/tex] by multiplying both sides of the equation [tex]\displaystyle AX=B[/tex] by the inverse of matrix [tex]\displaystyle A[/tex]:

[tex]\displaystyle X=A^{-1} \cdot B[/tex]

Substituting the given values:

[tex]\displaystyle X=\begin{bmatrix} \frac{9}{7} & -\frac{2}{7} & -\frac{4}{7}\\ -\frac{1}{7} & -\frac{9}{14} & \frac{1}{7}\\ -\frac{5}{7} & \frac{3}{7} & -\frac{9}{7} \end{bmatrix} \cdot \begin{bmatrix} 33\\ -21\\ -6 \end{bmatrix}[/tex]

Calculating the multiplication, we get:

[tex]\displaystyle X=\begin{bmatrix} 3\\ 2\\ 1 \end{bmatrix}[/tex]

Therefore, the variable matrix [tex]\displaystyle X[/tex] is:

[tex]\displaystyle X=\begin{bmatrix} 3\\ 2\\ 1 \end{bmatrix}[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Main Answer:

False

Explanation:

The equation given, P(n) = 7.1 + 7.9 + 7.9^2 + 7.9^3 + ... + 7.9^(n-3) = (7(9^n-2 - 1))/8, implies that the sum of the terms in the sequence 7.9^k, where k ranges from 0 to n-3, is equal to the right-hand side of the equation. We need to determine if P(2) holds true.

To evaluate P(2), we substitute n = 2 into the equation:

P(2) = 7.1 + 7.9

The sum of these terms is not equivalent to (7(9^2 - 2 - 1))/8, which is (7(81 - 2 - 1))/8 = (7(79))/8. Therefore, P(2) does not satisfy the equation, making the statement false.

In the given equation, it seems that there might be a typographical error. The exponent of 7.9 in each term should increase by 1, starting from 0. However, the equation implies that the exponent starts from 1 (7.9^0 is missing), which causes the sum to be incorrect. Therefore, P(2) is not true according to the given equation.

Learn more about

To further understand the solution, it is important to clarify the pattern in the equation. Discrete math often involves the study of sequences and series. In this case, we are dealing with a geometric series where each term is obtained by multiplying the previous term by a constant ratio.

The equation P(n) = 7.1 + 7.9 + 7.9^2 + 7.9^3 + ... + 7.9^(n-3) represents the sum of terms in the geometric series with a common ratio of 7.9. However, since the exponent of 7.9 starts from 1 instead of 0, the equation does not accurately represent the sum.

By substituting n = 2 into the equation, we find that P(2) = 7.1 + 7.9, which is not equal to the right-hand side of the equation. Thus, P(2) does not hold true, and the answer is false.

#SPJ11

The given function, P(n) = 7.1 + 7.9 + 7.9² + 7.9³ + ... + 7.9ⁿ⁻³ = 7(9ⁿ⁻² - 1) / 8 would be true.

The given function, P(n) = 7.1 + 7.9 + 7.9² + 7.9³ + ... + 7.9ⁿ⁻³ = 7(9ⁿ⁻² - 1) / 8

Now, we need to determine whether P(2) is true or false.

For this, we need to replace n with 2 in the given function.

P(n) = 7.1 + 7.9 + 7.9² + 7.9³ + ... + 7.9ⁿ⁻³ = 7(9ⁿ⁻² - 1) / 8P(2) = 7.1 + 7.9 = 70.2

Now, we need to determine whether P(2) is true or false.

P(2) = 7(9² - 1) / 8= 7 × 80 / 8= 70

Therefore, P(2) is true.

Hence, the correct option is True.

Learn more about P(2)  at https://brainly.com/question/28737823

#SPJ11

a) To calculate the annual demand, you need to use the last digit of your student number. Let's say your student number is BBAW190102 and the last digit is 2. The formula to calculate the annual demand is 400 + 10 * the last digit. In this case, it would be 400 + 10 * 2 = 420.

b) To calculate the weekly demand forecast for 2021, you need to divide the annual demand by the number of weeks in a year (52). So, the weekly demand forecast would be 420 / 52 = 8.08 (rounded to two decimal places).

c) The economic order quantity (EOQ) can be calculated using the formula EOQ = sqrt((2 * D * S) / H), where D is the annual demand and S is the ordering cost. In this case, D is 420 and S is $1000. Plugging in these values, the calculation would be EOQ = sqrt((2 * 420 * 1000) / 500) = sqrt(1680000) = 1297.77 (rounded to two decimal places).

d) The reorder point is the level of inventory at which a new order should be placed. It can be calculated using the formula Reorder Point = D * LT, where D is the demand during lead time and LT is the lead time. In this case, D is 420 and LT is 4 weeks. So, the reorder point would be 420 * 4 = 1680. The safety stock is the buffer stock kept to mitigate uncertainties. It can be calculated by multiplying the standard deviation of weekly demand (10) by the square root of lead time (4). So, the safety stock would be 10 * sqrt(4) = 20.

e) The total annual cost of managing inventory can be calculated using the formula TC = (D/Q) * S + (H * (Q/2 + SS)), where D is the annual demand, Q is the order quantity, S is the ordering cost, H is the annual holding cost, and SS is the safety stock. Plugging in the values, the calculation would be TC = (420/1297.77) * 1000 + (500 * (1297.77/2 + 20)) = 323.95 + 674137.79 = 674461.74.

f) The pipeline inventory is the inventory that is in transit or being delivered. It includes the inventory that has been ordered but has not yet arrived. In this case, since the lead time is 4 weeks and the order quantity is EOQ (1297.77), the pipeline inventory would be 4 * 1297.77 = 5191.08 (rounded to two decimal places).

g) To achieve a 95% cycle service level, you need to calculate the new safety stock and reorder point. The new safety stock can be calculated by multiplying the standard deviation of weekly demand (10) by the appropriate Z value for a 95% service level, which is 1.65. So, the new safety stock would be 10 * 1.65 = 16.5 (rounded to one decimal place). The new reorder point would be the sum of the annual demand (420) and the new safety stock (16.5), which is 420 + 16.5 = 436.5 (rounded to one decimal place).

In summary:
a) The annual demand is 420.
b) The weekly demand forecast for 2021 is 8.08.
c) The economic order quantity (EOQ) is 1297.77.
d) The reorder point is 1680 and the safety stock is 20.
e) The total annual cost of managing inventory is 674461.74.
f) The pipeline inventory is 5191.08.
g) The new safety stock for a 95% cycle service level is 16.5 and the new reorder point is 436.5.

To know more about annual demand here

https://brainly.com/question/32511271

#SPJ11

the solutions to the equation are x = 100,000 and x = 0.0000001.

To solve the equation [tex]x^{(3logx+5)}[/tex] = 105 + logx, we can use logarithmic properties and algebraic manipulations. Let's go through the steps:

Step 1: Rewrite the equation using logarithmic properties.

Using the property log([tex]a^b[/tex]) = b * log(a), we can rewrite the equation as:

log(x)^(3logx+5) = 105 + log(x)

Step 2: Simplify the equation.

Applying the power rule of logarithms, we can simplify the left side of the equation:

(3logx+5) * log(x) = 105 + log(x)

Step 3: Distribute the logarithm.

Distribute the log(x) to each term on the left side:

3log^2(x) + 5log(x) = 105 + log(x)

Step 4: Rearrange the equation.

Move all the terms to one side of the equation:

3log^2(x) + 5log(x) - log(x) - 105 = 0

Step 5: Combine like terms.

Simplify the equation further:

3log^2(x) + 4log(x) - 105 = 0

Step 6: Substitute u = log(x).

Let u = log(x), then the equation becomes:

3u^2 + 4u - 105 = 0

Step 7: Solve the quadratic equation.

Factor or use the quadratic formula to solve for u. The quadratic equation factors as:

(3u - 15)(u + 7) = 0

Setting each factor equal to zero, we have:

3u - 15 = 0   or   u + 7 = 0

Solving these equations gives:

u = 5   or   u = -7

Step 8: Substitute back for u.

Since u = log(x), we substitute back to solve for x:

For u = 5:

log(x) = 5

x = [tex]10^5[/tex]

x = 100,000

For u = -7:

log(x) = -7

x =[tex]10^{(-7)}[/tex]

x = 1/[tex]10^7[/tex]

x = 0.0000001

To know more about equation visit;

brainly.com/question/29538993

#SPJ11

a)The value of X = RM 15125.

b) The Gross Profit = RM 3000.

c) The Break-even price = RM 13333.33.

d) The Maximum markdown that could be given without incurring any loss = RM -1333.33.

The retailer buys a set of entertainment that is listed at RM X with trade discounts of 15% and 5%.He sells the set at RM 15000 with a net profit of 20% based on retail.

The operating expenses are 10% on cost.a) The value of X. The trade discount is 15% and 5% respectively.

Thus, the net price factor is, 100% - 15% = 85% = 0.85 and 100% - 5% = 95% = 0.95

The retailer's selling price is RM15000. The operating expense is 10% on cost.

Hence, 90% of the cost will be converted into the total expense. 90% = 0.9

The net profit is 20% of the retail price.20% = 0.20

Therefore, the cost of the set is,15000 × (100% - 20%) - 15000 × 80% = RM 12000

Let X be the retail price of the set of entertainment.

Therefore, we have,

X × 0.85 × 0.95 = 12000 ⇒ X = RM 15125

b) The Gross Profit

The gross profit is given by,Gross Profit = Selling price - Cost of goods sold

The cost of goods sold is RM 12000.

Therefore,Gross Profit = RM 15000 - RM 12000 = RM 3000

c) The Break-even price

The Break-even price is given by,Break-even price = Cost price / [1 - (operating expenses / 100%)]

The operating expense is 10% of the cost price. Therefore, 90% of the cost price will be converted into the total expense.

Break-even price = 12000 / [1 - (10/100)] = 12000 / 0.9 = RM 13333.33

d) The Maximum markdown that could be given without incurring any loss

The maximum markdown that could be given without incurring any loss is given by,

Maximum markdown = Cost price - Breakeven price = RM 12000 - RM 13333.33 = RM -1333.33

Therefore, the maximum markdown that could be given without incurring any loss is RM -1333.33. However, it is not possible to sell a product with a negative value.

Therefore, the retailer should not give any markdown.

Learn more about expenses at

https://brainly.com/question/14299648

#SPJ11

The solution is 97222 (mod 131) = 124.

the solution to the two problems:

(1) Find the missing digit x in the calculation below.

2x995619(523 + x)²

The first step is to expand the parentheses. This gives us:

2x995619(2709 + 10x)

Next, we can multiply out the terms in the parentheses. This gives us:

2x995619 * 2709 + 2x995619 * 10x

We can then simplify this expression to:

559243818 + 19928295x

The final step is to solve for x. We can do this by dividing both sides of the equation by 19928295. This gives us:

x = 559243818 / 19928295

This gives us a value of x = 2.

(2) Use the binary exponentiation algorithm to compute 9722? (mod 131).

The binary exponentiation algorithm works by repeatedly multiplying the base by itself, using the exponent as the number of times to multiply. In this case, the base is 9722 and the exponent is 2.

The first step is to convert the exponent to binary. The binary representation of 2 is 10.

Next, we can start multiplying the base by itself, using the binary representation of the exponent as the number of times to multiply.

9722 * 9722 = 945015884

945015884 * 9722 = 9225780990564

9225780990564 mod 131 = 124

Therefore, 97222 (mod 131) = 124.

Learn about mod in the given link,

https://brainly.com/question/31391032

#SPJ11

The show that all points the curve on the tangent surface of are parabolic is intersection of a plane containing the tangent line and a surface perpendicular to the binormal vector.

Let C be a curve defined by a vector function r(t) = , and let P be a point on C. The tangent line to C at P is the line through P with direction vector r'(t0), where t0 is the value of t corresponding to P. Consider the plane through P that is perpendicular to the tangent line. The intersection of this plane with the tangent surface of C at P is a curve, and we want to show that this curve is parabolic. We will use the fact that the cross section of the tangent surface at P by any plane through P perpendicular to the tangent line is the osculating plane to C at P.

In particular, the cross section by the plane defined above is the osculating plane to C at P. This plane contains the tangent line and the normal vector to the plane is the binormal vector B(t0) = T(t0) x N(t0), where T(t0) and N(t0) are the unit tangent and normal vectors to C at P, respectively. Thus, the cross section is parabolic because it is the intersection of a plane containing the tangent line and a surface perpendicular to the binormal vector.

Learn more about binormal vector at:

https://brainly.com/question/33109939

#SPJ11

Answer

Questions 9, answer is 4

Explanation

Question 9

Multiply each number by itself and add the results to get middle box digit

1 × 1 = 1.

3 × 3 = 9

5 × 5 = 25

7 × 7 = 49

Total = 1 + 9 + 25 + 49 = 84

formula is n² +m² + p² + r²; where n represent first number, m represent second, p represent third number and r is fourth number.

5 × 5 = 5

2 × 2 = 4

6 × 6 = 36

empty box = ......

Total = 5 + 4 + 36 + empty box = 81

65 + empty box= 81

empty box= 81-64 = 16

since each number multiply itself

empty box= 16 = 4 × 4

therefore, it 4

1. Yes, F(z) = az is a linear transformation on C, the set of complex numbers, when considered as a real vector space. It satisfies both additivity and scalar multiplication properties.

2. L(z) = ž, where ž represents the conjugate of z, is a linear transformation on C when considering it as a real vector space. It preserves both additivity and scalar multiplication.

3. However, L(z) = ž is not a linear transformation on C when considering it as a complex vector space since the conjugation operation is not compatible with scalar multiplication in complex numbers.

1. Yes, F is a linear transformation.

2. No, L is not a linear transformation.

3. Yes, L is a linear transformation when considering C as a complex vector space.

1. To determine whether F is a linear transformation, we need to check two properties: additive preservation and scalar multiplication preservation. Let's take two vectors, z1 and z2, in C and a scalar c in R. Then, F(z1 + z2) = a(z1 + z2) = az1 + az2 = F(z1) + F(z2), which satisfies the additive preservation property. Also, F(cz) = a(cz) = (ac)z = c(az) = cF(z), which satisfies the scalar multiplication preservation property. Therefore, F is a linear transformation.

2. For L to be a linear transformation, it must also satisfy the additive preservation and scalar multiplication preservation properties. However, L(z1 + z2) = ž1 + ž2 ≠ L(z1) + L(z2), which means it fails the additive preservation property. Hence, L is not a linear transformation.

3. When considering C as a complex vector space, the definition of L(z) = ž still holds. In this case, L(z1 + z2) = ž1 + ž2 = L(z1) + L(z2) and L(cz) = cž = cL(z), satisfying both the additive preservation and scalar multiplication preservation properties. Therefore, L is a linear transformation when C is considered as a complex vector space.

Linear transformations are mathematical mappings that preserve vector addition and scalar multiplication. In the given problem, F is a linear transformation because it satisfies both the additive preservation and scalar multiplication preservation properties. On the other hand, L is not a linear transformation when C is considered as a real vector space because it fails to preserve vector addition. However, when C is treated as a complex vector space, L becomes a linear transformation as it satisfies both properties. The distinction arises due to the fact that complex vector spaces have different rules for addition and scalar multiplication compared to real vector spaces.

Learn more about transformation

brainly.com/question/11709244

#SPJ11

Using either indirect proof or conditional proof, it is derived the conclusion is (x)Ax ≡ (∃x)Cx.

To derive the conclusion of the given symbolized argument using either indirect proof or conditional proof, consider both approaches:

Indirect Proof:

Assume the negation of the desired conclusion: ¬((x)Ax ≡ (∃x)Cx)

Conditional Proof:

Assume the premise: (x)(Cx ⊃ Bx)

Now, proceed with the proof:

(x)Ax ≡ (∃x)(Bx • Cx) [Premise]

(x)(Cx ⊃ Bx) [Premise]

¬((x)Ax ≡ (∃x)Cx) [Assumption for Indirect Proof]

To derive a contradiction, assume the negation of (∃x)Cx, which is ∀x¬Cx:

∀x¬Cx [Assumption for Indirect Proof]

¬∃x Cx [Universal Instantiation from 4]

¬(Cx for some x) [Quantifier negation]

Cx ⊃ Bx [Universal Instantiation from 2]

¬Cx ∨ Bx [Material Implication from 7]

¬Cx [Disjunction Elimination from 8]

Now, derive a contradiction by combining the premises:

(x)Ax ≡ (∃x)(Bx • Cx) [Premise]

Ax ≡ (∃x)(Bx • Cx) [Universal Instantiation from 10]

Ax ⊃ (∃x)(Bx • Cx) [Material Equivalence from 11]

¬Ax ∨ (∃x)(Bx • Cx) [Material Implication from 12]

From premises 9 and 13, both ¬Cx and ¬Ax ∨ (∃x)(Bx • Cx). Applying disjunction introduction:

¬Ax ∨ ¬Cx [Disjunction Introduction from 9 and 13]

However, this contradicts the assumption ¬((x)Ax ≡ (∃x)Cx). Therefore, our initial assumption of ¬((x)Ax ≡ (∃x)Cx) must be false, and the conclusion holds:

(x)Ax ≡ (∃x)Cx

Therefore, using either indirect proof or conditional proof, we have derived the conclusion.

Find out more on indirect proof here: https://brainly.com/question/31474742

#SPJ4

The proof uses a conditional proof, which assumes the truth of (x)Ax and proves that (∃x)Cx is true, which means that (x)Ax ≡ (∃x)Cx is true.

Indirect proof is a proof technique that involves assuming the negation of the argument's conclusion and attempting to demonstrate that the negation is a contradiction.

Conditional proof, on the other hand, is a proof technique that involves establishing a conditional statement and then proving the antecedent or the consequent of the conditional.

We can use conditional proof to derive the conclusion of the argument.

The given premises are: 1. (x)Ax ≡ (∃x)(Bx • Cx)

2. (x)(Cx ⊃ Bx) / (x)Ax ≡ (∃x)Cx

We want to prove that (x)Ax ≡ (∃x)Cx. We can do so using a conditional proof by assuming (x)Ax and proving (∃x)Cx as follows:

3. Assume (x)Ax.

4. From (x)Ax ≡ (∃x)(Bx • Cx), we can infer (∃x)(Bx • Cx).

5. From (∃x)(Bx • Cx), we can infer (Ba • Ca) for some a.

6. From (x)(Cx ⊃ Bx), we can infer Ca ⊃ Ba.

7. From Ca ⊃ Ba and Ba • Ca, we can infer Ca.

8. From Ca, we can infer (∃x)Cx.

9. From (x)Ax, we can infer (x)Ax ≡ (∃x)Cx by conditional proof using steps 3-8.The conclusion is (x)Ax ≡ (∃x)Cx.

The proof uses a conditional proof, which assumes the truth of (x)Ax and proves that (∃x)Cx is true, which means that (x)Ax ≡ (∃x)Cx is true.

To learn more about conditional proof follow the given link

https://brainly.com/question/33165821

#SPJ11

The simplified form of 3√2 + 4³√2 is 11√2.

To simplify 3√2+4³√2 we will use the formula for combining like radicals, which is a√m + b√m = (a+b)√m.

So, 3√2 + 4³√2 = 3√2 + 4√8

Now, we will try to simplify the √8.

So, we will divide 8 by its largest perfect square factor. The largest perfect square factor of 8 is 4, as 4*2=8.√8 = √(4*2) = √4 * √2 = 2√2

We substitute this in 3√2 + 4√8 = 3√2 + 4*2√2 = 3√2 + 8√2 = (3+8)√2 = 11√2

Therefore, the simplified form of 3√2 + 4³√2 is 11√2.

Know more about perfect square here,

https://brainly.com/question/385286

#SPJ11

The numerical solutions of the given differential equation using different methods, along with their corresponding %errors compared to the analytical solution, are summarized in the table below:

| Method           | Numerical Solution   | %Error |

|------------------|----------------------|--------|

| Euler            |                      |        |

| Euler-Cauchy     |                      |        |

| Runge-Kutta      |                      |        |

To apply the Euler method to the given differential equation, we start with the initial condition (x = 0, y = 1) and take small steps of size h = 0.2 until x = 1.0. We can use the formula:

[tex]\[y_{i+1} = y_i + h \cdot f(x_i, y_i)\][/tex]

where [tex]\(f(x, y)\)[/tex] is the derivative of [tex]\(y\)[/tex]with respect to[tex]\(x\).[/tex] In this case,[tex]\(f(x, y) = \frac{1}{2y} - \frac{1}{2}x\).[/tex]

Calculating the values using the Euler method, we get:

|x  | y (Euler)    |

|---|--------------|

|0.0| 1.000000     |

|0.2| 0.875000     |

|0.4| 0.748438     |

|0.6| 0.621928     |

|0.8| 0.496267     |

|1.0| 0.372212     |

Learn more about numerical solutions

brainly.com/question/30991181

#SPJ11

The bearing of the line between points A and C is N 135.

To determine the bearing of the line between points A and C, we need to consider the given information. We start at point A, take a backsight on point B'', where the line A-B has a backsight bearing of N 45. Then, we measure 90 degrees right from that line to point C.

Since the backsight bearing from A to B'' is N 45, we add 90 degrees to this angle to find the bearing from A to C. N 45 + 90 equals N 135. Therefore, the bearing of the line between points A and C is N 135.

Learn more about: Bearing between lines

brainly.com/question/33195838

#SPJ11

The solution to the given simultaneous equations using Cramer's Rule is:

x = 4/17

y = 0

z = 20/17

To solve the simultaneous equations using Cramer's Rule, we need to set up the matrix equation and calculate determinants. Let's denote the variables as x, y, and z.

The given system of equations can be represented in matrix form as:

| 1  5  2 |   | x |   | x |

|          | * |   | = |   |

| 2  4 20 |   | y |   | x |

|          |     |   | = |   |

| 4  2 10 |   | z |   | x |

To solve for the variables x, y, and z, we will use Cramer's Rule, which states that the solution is obtained by dividing the determinant of the coefficient matrix with the determinant of the main matrix.

Step 1: Calculate the determinant of the coefficient matrix (D):

D = | 1  5  2 |

| 2  4 20 |

| 4  2 10 |

D = (1*(410 - 220)) - (5*(210 - 44)) + (2*(22 - 44))

D = (-16) - (40) + (-12)

D = -68

Step 2: Calculate the determinant of the matrix replacing the x-column with the constant terms (Dx):

Dx = | x  5  2 |

| x  4 20 |

| x  2 10 |

Dx = (x*(410 - 220)) - (5*(x10 - 220)) + (2*(x2 - 410))

Dx = (-28x) + (100x) - (76x)

Dx = -4x

Step 3: Calculate the determinant of the matrix replacing the y-column with the constant terms (Dy):

Dy = | 1  x  2 |

| 2  x 20 |

| 4  x 10 |

Dy = (1*(x10 - 220)) - (x*(210 - 44)) + (4*(2x - 410))

Dy = (-40x) + (56x) - (16x)

Dy = 0

Step 4: Calculate the determinant of the matrix replacing the z-column with the constant terms (Dz):

Dz = | 1  5  x |

| 2  4  x |

| 4  2  x |

Dz = (1*(4x - 2x)) - (5*(2x - 4x)) + (x*(22 - 44))

Dz = (2x) - (10x) - (12x)

Dz = -20x

Step 5: Solve for the variables:

x = Dx / D = (-4x) / (-68) = 4/17

y = Dy / D = 0 / (-68) = 0

z = Dz / D = (-20x) / (-68) = 20/17

Therefore, the solution to the given simultaneous equations using Cramer's Rule is:

x = 4/17

y = 0

z = 20/17

Learn more about equation  from

https://brainly.com/question/29174899

#SPJ11

To find the vertex form of the equation modeling function g, we start with the given equation for function f in standard form: [tex]\displaystyle\sf f(x) = x^2 - 4x - 32[/tex].

To obtain the vertex form, we need to complete the square. Let's go through the steps:

1. Divide the coefficient of the x-term by 2, square the result, and add it to both sides of the equation:

[tex]\displaystyle\sf f(x) + 32 = x^2 - 4x + (4/2)^2[/tex]

[tex]\displaystyle\sf f(x) + 32 = x^2 - 4x + 4[/tex]

2. Simplify the right side of the equation:

[tex]\displaystyle\sf f(x) + 32 = (x - 2)^2[/tex]

3. To model function g, we need to shift the vertex 2 units below and 3 units to the left. Therefore, we subtract 2 from the y-coordinate and subtract 3 from the x-coordinate:

[tex]\displaystyle\sf g(x) + 32 = (x - 2 - 3)^2[/tex]

[tex]\displaystyle\sf g(x) + 32 = (x - 5)^2[/tex]

4. Finally, subtract 32 from both sides to isolate g(x) and obtain the vertex form of the equation for function g:

[tex]\displaystyle\sf g(x) = (x - 5)^2 - 32[/tex]

Therefore, the vertex form of the equation modeling function g is [tex]\displaystyle\sf g(x) = (x - 5)^2 - 32[/tex].

The vertex form of g(x), which has the same a value as given function f(x)=X² - 4x - 32 and its vertex 2 units below and 3 units to the left of the vertex of f, would be g(x) = (x+1)² - 38.

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola. The given function f(x) = X² - 4x - 32 has a vertex (h,k). To find out where it is, we complete the square on function f to convert it into vertex form.

By completing the square, we find the vertex of f is (2, -36). But the vertex of g is 2 units below and 3 units to the left of the vertex of f, so the vertex of g is (-1, -38). Therefore, the vertex form of function g, keeping the same 'a' value (which in this case is 1), is g(x) = (x+1)² - 38 because h=-1 and k=-38.

https://brainly.com/question/28588982

#SPJ2